Spectroscopy With Coherent Radiation

The following sections are included:

• CONTENTS

• PREFACE

• Autobiographical Notes
  • Early Life (1915–1935)
  • Cambridge University (1935–1937)
  • Columbia Graduate School and Early Research (1937–1940)
  • World War II
  • Columbia and Brookhaven
  • Harvard University (1947–1997)

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The history of this experiment is given in Part 3(a) of "Autobiographical Notes."

This paper covers part of the original development of the magnetic resonance method. The first successful magnetic resonance experiment was that of Rabi, Zacharias, Millman and Kusch [Phys. Rev. 53, 318 (1938) and 55, 526 (1939)] with LiCl, and it produced a simple symmetric resonance, as expected. Paper 1.1 reports on the second successful experiment and extends the resonance technique. Initially we expected the experiments would also produce a single simple resonance. Instead, we were at first deeply disappointed to find a jagged, broad and asymmetric resonance, worse even than the one in Fig. 7. I was originally assigned the study of this peculiar shape for my thesis project, but when I reduced the amplitude of the oscillatory field I discovered that the broad resonance became a very interesting six-line radiofrequency spectrum, as in Figs. 6 and 8. This was the first time a multiple line spectrum had been seen in magnetic resonance experiments. These experiments became models for many subsequent radio and microwave resonance spectroscopy experiments. So that we could all participate in the discoveries, my thesis topic was shifted to rotational magnetic moment transitions (Paper 2.2).

Although this paper is included in Section 1 because it pioneered new resonance techniques, it could also have been included in Sections 2 and 5. It included new theoretical methods for analyzing radiofrequency spectra of molecules and provided the most accurate values of the proton and deuteron magnetic moment as well as values for the nuclear spin–spin and the spin-rotational magnetic interaction constants in the molecule H₂. Papers 1.1, 2.1 and 2.2 form coherent and complementary reports on molecular H₂, D₂ and HD.

During the first decade of radiofrequency spectroscopy, little explicit use was made of the coherency of the radiation. Here I suggest the use of two successive coherent pulses and show that the central resonance is almost twice as narrow as the resonance with a single oscillating field and that the resonance frequency depends only on the average energy between the two oscillatory field regions. Consequently, if the magnetic field is nonuniform, the frequency is shifted, but not broadened. Furthermore, if the two oscillatory fields are coherently in phase, the first order Doppler shift is eliminated. One of the greatest advantages of the separated oscillatory fields method is that it can be extended to much higher frequencies, since the wavelength of the radiation need only be longer than the short lengths of the oscillatory field regions, not the distance between them. The separated oscillatory fields method is also applicable to fields that are separated in time rather than space and is sometimes then called the method of successive oscillatory fields. Although the method was originally developed for magnetic resonance experiments, it is equally applicable to electric resonance.

After our first experiments, the method was used in many laboratories, initially at radio and microwave frequencies, and is often called "the Ramsey method." It is used in cesium atomic clocks, the basis for the definition of the second. The method has also been applied by S. Chu and others [Phys. Rev. Lett. 63, 612–613 (1989)] to laser-cooled atomic fountains. Paper 1.17 discusses how the method of successive oscillatory fields has been extended to lasers.

Soon after this first paper on the use of successive coherent pulses in magnetic resonance, Erwin Hahn [E. L. Hahn, Phys. Rev. 77, 297 (1950), and 80, 580–594 (1950)] described his ingenious NMR spin echo technique. He used a radiofrequency pulse to flip nuclear spins 90°, allowed the signal to disappear by field inhomogeneities or T₂ relaxation, and then t sec after the first pulse he applied a 180° pulse so that the signal reappeared t sec later as a nuclear induction "spin echo." The spin echo technique was extensively used to measure nuclear magnetic resonance phenomena, particularly relaxation times. Subsequently, a variety of pulse shapes and phases have been used in NMR, in Fourier transform spectroscopy and in magnetic resonance imaging (MRI) by E. Hahn, C. Slichter, R. Ernst, W. Anderson, A. Pines, J. Waugh, W. Warren, P. Lauterbuhr and many others.

This paper is an extension of Paper 1.2 with the relative phases of the two successive oscillatory field pulses being changed. For zero phase difference the ordinary resonance shape is obtained. For a shift of π radians the transition probability is at a minimum at resonance and for a phase shift of π/2 the resonance is more like a dispersion curve. Under some circumstances the measurement accuracy can be increased by deliberately using a known phase shift.

The theoretical curves in this paper demonstrate the importance of accurately knowing the phase shift between the two fields. With a π/2 phase shift the principal resonance peak, for example, is far from the resonance frequency and an error would result if the observed peak were thought to be a zero phase shift resonance.

The results of this paper have been used to determine, experimentally, the phase shift from the resonance shape.

This paper and two others evolved from work over a single weekend by Bob Pound, Ed Purcell and myself. Bob Pound had obtained a very pure crystal of LiF for which he was studying the fluorine NMR resonance with puzzling results. If he placed the LiF sample in the magnetic field for less than a minute, he obtained little or no NMR signal. If he left the crystal in the magnetic field for 20 min or more, he obtained a strong NMR signal. If he removed the crystal from the high magnetic field for several minutes and then returned it to the high field, he found, as expected, no signal and had to wait an additional 20 min to recover the full signal. On the other hand, to his surprise, he found a large NMR signal immediately if he kept the sample in the zero field region for less than 20 sec. Bob consulted Purcell and myself as to why there was this spectacular difference. The three of us spent a weekend doing various experiments to determine what could be the property that the LiF crystal retained to produce this difference. By reorienting the crystal in various ways during the few seconds it was in zero field, we determined that the property was a scalar and not a vector or tensor. We then remembered that Dutch physicists had discussed the concept of spin temperature. By leaving the sample out of the high field for varying lengths of time, we could observe a smooth cooling curve that fit well the interpretation that the relevant property was the spin temperature.

To further test this concept, we removed the sample from the strong magnetic field, placed it in another high field region where the field direction was rapidly reversed, and returned the sample to the NMR magnet with a high field and observed that the sign of the NMR signal was reversed. After this reversal had been obtained we observed the cooling curve as the sample was stored for different times in the zero field region. We obtained a beautifully smooth cooling curve as the spin temperature cooled from negative room temperature to negative infinite temperature (equivalent to positive infinite temperature, as can be seen from the form of the Boltzmann factor e^-W/kT) and finally to positive room temperature. When the system was in a negative temperature state it was an amplifier since stimulated emission exceeded absorption, and in this respect the apparatus was the first man-made maser. However, the power was so low that it was exceeded by the circuit losses.

I suggested doing a low field magnetic resonance experiment on the crystal after it was removed from the high polarizing field, but before a final high field NMR measurement of its retained polarization. This procedure permits the observation of resonances at much lower fields than usual, as described in Paper 1.4. The method has been used subsequently in many NMR experiments by C. Slichter, A. Pines and others.

Different and independent early papers and lectures by the three authors and by F. Bloch indirectly implied the use of a rotating coordinate system in discussing spin systems, but it became apparent that the method was so convenient and powerful that we should write a review making explicit use of the rotating coordinate technique and showing the extent of its applications. One of the valuable characteristics of this technique is that it is equally applicable to classical and quantum-mechanical calculations. The rotating coordinates method anticipated Schwinger's extensive use of the interaction gauge in other quantum calculations.

This theoretical paper initially arose from my worry that irregularities of the static magnetic field between the two separated oscillatory field regions might shift the resonance frequency. I realized I could calculate a special case of the effect by noting that the passage of the molecule over the irregularities would be similar to the effect of an oscillatory field in the intermediate region. In other words the molecule would be subject to two oscillatory fields at different frequencies: one in the two end fields inducing the transitions and one in the intermediate region that might pull the resonance frequency. I show in the paper that such pulling does occur and that it does so not only with separated oscillatory fields but also with Rabi's single oscillatory field method. I also note that there are many ways in which there can be additional oscillatory fields, including their deliberate application or their use in another resonance experiment at the same time. After solving the general problem of an additional rotating field, I realized that F. Bloch and A. Siegert had earlier solved a special case.

An experimental confirmation of the frequency pulling by another oscillatory magnetic field is reported by H. R. Lewis, A. Pery, W. Quinn and N. F. Ramsey in Phys. Rev. 107, 446–449 (1957).

This paper is an extension of Paper 1.2 and notes that a sharp resonance can be obtained if several successive pulses are applied even at random times provided the pulses are all coherently driven by the same oscillator. This demonstration has made possible resonance experiments with the atoms spending most of their time in a large storage box and only occasionally and randomly passing into the oscillatory field region. One such experiment is described in Paper 1.12.

This paper extends Paper 1.2 to give general formulae and calculation procedures for determining the transition probabilities for a system with three different and possibly varying energy levels subject to several oscillatory fields of nonuniform amplitudes and phases. Because of the generality of the formulation, specific calculations have to be carried out with a computer. As examples, results are plotted for increasing numbers of oscillatory pulses and for different shapes of oscillatory fields.

Since the accuracies of my research measurements and of atomic clocks depend on precise spectral measurements, I studied theoretically line distortions that can lead to erroneous resonance results. When I was asked to write an article in a special publication honoring Otto Stem, I decided to publish my results there, because of my great admiration for Stern and all he had contributed to molecular beams. However, it may have been a mistake to do so, since many scientists in the field of precision measurements later complained that the article was valuable, but not available in most libraries. In this article, I discuss the effects of asymmetries in the oscillatory field amplitudes, of variations in the static field magnitudes, of neighboring resonances, of additional oscillatory fields and of phase shifts.

The history of the atomic hydrogen maser and the steps that led to its invention by Dan Kleppner and me are given in "Autobiographical Notes," 6(1). Our object was to get greater accuracy by trapping the atoms in a bottle with suitably coated walls for several seconds, which was much longer than the time the atoms could be in the intermediate region of a separated oscillatory field molecular beam apparatus. After several preliminary experiments, we realized that hydrogen atoms were particularly suitable since their very low electric polarizability suggested they would not stick to a surface such as Teflon, whose atoms also had low electric polarizability, so the Van der Waals forces would be very low. However, there was a serious problem since hydrogen was then very difficult to detect in an atomic beam apparatus. Consequently, we calculated the possibility of detecting the atomic hyperfine transition by the electromagnetic signal and found the signal should be sufficiently strong that a bottle of state-selected hydrogen atoms could radiate as a maser. Paper 1.10 reports the initial success of this method. The storage times were about 0.3 sec, in contrast to the 10^-4 sec required for an atom to cross the bottle once. As a result, the resonance was correspondingly narrow and the maser signal was extremely stable. Stabilities better than 10^-15 were achieved, making the hydrogen maser, for many years, the world's most stable atomic clock.

Although there had been previous resonance experiments with atoms in bottles at relatively high pressure or with inert buffer gases to make the mean free paths short compared to the bottle sizes, ours was the first experiment trapping atoms without a buffer gas and it experimentally demonstrated the advantages of trapping. Subsequently, there have been many experiments with trapped atoms and ions, usually with electromagnetic traps.

With various graduate students and collaborators, Dan Kleppner and I used the atomic hydrogen maser to measure accurately many properties of atomic H, D and T, including their hyperfine separations, the dependence of the hyperfine separations on applied magnetic and electric fields, the ratio of the magnetic moment of the free proton to that of the electron, and the values of the free proton magnetic moment in Bohr and nuclear magnetons.

The experimental value of the atomic hydrogen hyperfine separation at one time provided the original stimulus for the development of relativistic quantum electrodynamics (QED). Later these measurements and QED theory were used to determine the fine structure constant α, and now that α is determined from other experiments, the hyperfine measurements provide information about the distribution of magnetism within the proton.

Since the H maser is more stable over a day than the atomic cesium beam clock and provides a stable oscillation at a useful power level, it has been extensively used in long baseline radioastronomy, deep space navigation, and as a flywheel oscillator for other atomic clocks.

Our development of the theory of the atomic hydrogen maser is partially based on C. Townes and A. Schalow's theory of the molecular NH₃ maser, but differs in many respects. Although the theory we developed was primarily for the atomic hydrogen maser, it is applicable to other atomic masers. Subsequently, we developed additional design principles with H. C. Berg, S. B. Crampton, R. F. C. Vessot, H. E. Peters and J. Vanier, which we described in "Hydrogen Maser Principles and Techniques" [Phys. Rev. 138, A972 (1965)]. In our effort to avoid unnecessary approximations, our derivations in these papers became formal and hard to follow. As a result, for the benefit of friends and graduate students, I later prepared a paper called "Approximate Theory of the Hydrogen Maser," giving approximately the same results with much simplified derivations. Eventually I received so many requests for copies of this handwritten paper that I wished I had published it.

Since wall shifts are one of the principal limits to the stability of a hydrogen maser, the wall shifts of FEP Teflon have been studied carefully with different coatings and at different temperatures [P. W. Zitzewitz, E. E. Uzgiris and N. F. Ramsey, Rev. Sci. Instrum. 41, 81–86 (1970) and P. W. Zitzewitz and N. F. Ramsey, Phys. Rev. A3, 51–61 (1971)].

Since the principal disadvantage of the hydrogen maser is the small frequency shift introduced by collisions with the walls of the storage bottle, I realized that this shift could be reduced by a factor of ten by making the storage vessel ten times larger in diameter. Superficially, this appears to be impossible since the 21 cm wavelength of the radiation would be smaller than the 150 cm diameter of such a bottle and the phases inside the container would be mixed if the radiation were present throughout the chamber. However, in Paper 1.7, I had shown that a sharp resonance could be obtained even if the oscillatory field region were confined to a small part of the container provided the atoms could randomly move between the two regions. My graduate student E. E. Uzgiris and I then successfully built such a maser. This was the first experimental demonstration of the randomly successive coherent oscillatory field method described in Paper 1.7. We gave a more detailed description of the apparatus and the results in Phys. Rev. A1, 429–446 (1970).

After accurately measuring the hyperfine separation of atomic hydrogen (Paper 2.9), we wanted to do the same thing with atomic deuterium. Since the wavelength of the deuterium resonance radiation is 4.3 times longer than that of atomic deuterium, a much larger apparatus is required. For this reason, our first deuterium experiment was with an atomic hydrogen maser partially filled with with both hydrogen and deuterium as described in Paper 2.13. Although the measurement was successful, it was indirect and less accurate than would be expected for a deuterium maser.

After the large storage bottle experiment of Paper 1.12 was completed, Wineland and I used its large magnetic shield to construct a directly oscillating deuterium maser. This deuterium maser gave a more accurate value of the deuterium hyperfine separation than any previous experiment, including the one described in Paper 2.13.

Both the separated oscillatory fields method and the atomic hydrogen maser were invented to obtain greater accuracy in measuring molecular and atomic spectra, but their accuracy and stability made them particularly suitable for atomic clocks and frequency standards. Well-engineered cesium atomic beam devices with separated oscillatory fields are generally considered the most accurate over long periods of time and are now used to define the fundamental unit of time, the second. For many purposes, such as very long baseline interferometry (VLBI) in radioastronomy, the important requirement is high stability for several hours and for this purpose the atomic hydrogen maser with stability better than 10^-15 is superior. Many university industrial and government laboratories have contributed to the engineering and development of accurate and stable clocks. I have maintained a strong interest, resulting in contributions to improve accuracies (Paper 1.9), and have written review articles about atomic clocks (Paper 1.14), their history [J. Res. NBS 88, 301 (1983)], and their applications to diverse fields, including precision measurements, radioastronomy, navigation and tests of relativity [W. M. Itano and N. F. Ramsey, Scientific American 269 (1), 56 (1993)].

Since this review was written there have been spectacular advances in the sciences related to atomic clocks. W. Phillips experimentally discovered that atoms could be laser-cooled to much lower temperatures than had previously been thought theoretically possible and C. Cohen-Tannoudji explained this as Sisyphus cooling. Atoms have been cooled below a nanokelvin and Bose–Einstein condensation has been observed with weakly interacting atoms. Spectacular confirmations of the Einstein general relativity theory have been obtained by J. Taylor, R. Hulse and T. Damour by accurately measuring the changes in the received pulse rates from a binary pulsar.

Winners of the Nobel Prize are requested to lecture and provide a manuscript on the work for which the Prize was awarded. My lecture reviews the principles of the separated oscillatory fields method and of the atomic hydrogen maser, describes their uses in precision spectroscopy and atomic clocks, and discusses the applications of atomic clocks to precision measurements, definitions of units, radioastronomy, pulsar studies, navigation and tests of relativity.

After the invention of the methods of separated and successive oscillatory fields, their uses were initially limited to radio and microwave frequencies, because electromagnetic radiations at higher frequencies were too incoherent. This barrier was eliminated with the development of lasers. But, even with suitable lasers, it was not obvious that sharp separated oscillatory fields resonances would be obtainable, since atoms move several optical wavelengths between successive pulses, thus destroying the coherency. In Paper 1.16, I review different ways in which this problem can be overcome.

One way is to eliminate the effect of velocity by using coherent two-photon Doppler-free excitations in each of the two pulses. Another is to use three or four successive coherent pulses with the phase difference between the first two pulses being of opposite sign to that between the last two, in which case the motion-induced phase shift of the first pulse is opposite that of the second. Yet another is to use extremely short pulses and such short intervals of time between the first and the final pulse that the atoms move transversely less than a wavelength. As short femtosecond laser pulses have become available, this method has become increasingly popular. Examples of these different applications are given in Paper 1.16.

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The unexpected observation of six separate spectral lines for H₂ instead of the expected single line was only the first surprise with the new magnetic resonance method (Paper 1.1). The next occurred in what started out as my thesis project to understand the peculiar resonance shapes of H₂ and D₂. With D₂ there was a single dominant resonance, but I also showed (Fig. 1 of Paper 2.1) that there were six much weaker spectral lines and these were separated further apart than the six lines for H₂. This was very surprising since we were beginning to interpret the H₂ results in terms of the interactions of the nuclear magnetic moments with each other and with the magnetic field produced by the rotation of the molecule. But in D₂ the nuclear magnetic moments and the lowest rotational angular velocities are much smaller so the magnetic interactions should be very much smaller (dashed lines in Fig. 1). These observations showed that there must be an additional interaction, probably a deuteron quadrupole moment. The four of us agreed that such a discovery was too important to be the thesis project for just one participant. As we studied these resonances further with the improved apparatus, we obtained the sharper spectrum shown in Fig. 3 of Paper 2.1 and in the letter announcing the discovery of the deuteron quadrupole moment [Phys. Rev. 55, 318–319 (1939)]. The discovery was confirmed by our observations in HD and in transitions involving reorientations of the rotational magnetic moments (Paper 2.2).

We developed the theory of the magnetic and quadrupole interactions, including perturbations up to the third order, which accounted for the observed asymmetries. The observed separations of these resonances, and their dependence on the strength of the externally applied magnetic field, agreed fully with the theory, thus confirming the existence of the deuteron quadrupole moment. It showed that the deuteron was not spherical, as previously assumed, but was ellipsoidal, in the shape of an American football. As later pointed out by W. Rarita and J. Schwinger [Phys. Rev. 59, 436 (1941)], this shape implied the existence of a previously unanticipated tensor force between the proton and the deuteron.

While studying the nuclear moment resonances of H₂ and D₂, I discovered a different group of resonances that were associated with the reorientation of the molecular rotational magnetic moments. After deciding that the nuclear resonance studies, including the deuteron quadrupole moment, should be a joint project, we agreed that my Ph.D. thesis should be on the resonances associated with the molecular rotational magnetic moments of the molecular hydrogens. I found 6 resonances for H₂, 6 for D₂ and 12 for HD. From the rotational magnetic moments and G. C. Wick's theory, I obtained values for the high frequency (or second order paramagnetic) term in the magnetic susceptibility of the molecule.

When I adapted our successful theory of the nuclear resonances to the rotational moment resonances, the agreement between theory and experiment was almost but not quite perfect. I then realized that the orientation of the molecule was changed in the molecular rotational experiments so differences in the molecular diamagnetic susceptibility would shift the resonance frequencies. When I introduced into the theory such a diamagnetic susceptibility term with only one free parameter, the rotational resonances agreed perfectly with theory and I obtained an empirical value for the orientation dependence of the magnetic susceptibility. I later [Phys. Rev. 78, 221–222 (1950)] developed the theory of the orientation dependence of the magnetic susceptibility and derived from our measurement the quadrupole moment of the electron distribution in the H₂ molecule. Several years later (Paper 5.3), I showed that this result, combined with values for the magnetic susceptibility, gave the principal second moments of the electron distribution of the H₂ molecule.

The Columbia Molecular Beam Laboratory, so highly successful before World War II, was mostly disassembled during the war, so Rabi and I devoted our initial postwar effort to restarting the lab, and Paper 2.3 was the first publication. Later, W. A. Nierenberg and I [Phys. Rev. 72, 1075–1089 (1947)] extended this work to other sodium halides and further developed the theories of the internal molecular interactions.

In subsequent years, similar methods were used to study other diatomic molecules.

Arriving at Harvard in 1947, I decided to build a molecular beam resonance apparatus of much higher resolution than any previous apparatus. Three graduate student and I designed and built one with a uniform magnetic field region 150 cm long, ten times longer than previously, which should have given spectral lines ten times narrower than the best previously obtained because the molecules would be in the resonance region ten times longer. However, for this narrowing to occur the magnetic field had to be highly uniform along its length (otherwise the transitions would occur at different frequencies in the different fields). I thought we could obtain this uniformity with laminated soft iron pole tips, but we did not succeed. It then occurred to me that if we induced the transitions with two short coherent oscillatory fields only at the beginning and end of the uniform region the resonances would occur at the average energy differences and the resonances would not be broadened. Thus, I invented the separated oscillatory fields method described in Paper 1.2. This new method was first used in 1951 (Paper 2.4) and worked very well. Another improvement was the use of lower external magnetic fields so that field errors and instabilities would have less effect on the determination of the internal interactions. With these improvements, the various interaction parameters for H₂ and D₂ were determined 11.4 times more accurately in this work than reported in the earlier Paper 1.1. Later, N. J. Harrick, R. G. Barnes, P. J. Bray and I [Phys. Rev. 90, 260–266 (1953)] used this apparatus to study the radiofrequency spectra at intermediate magnetic fields.

The separated oscillatory fields method first used in this experiment has been used in many subsequent experiments at radio and microwave frequencies and has been extended to laser frequencies, as discussed in Paper 1.16.

Since the molecules H₂, D₂ and HD are the simplest polyatomic molecules and since we could measure many of their parameters with unprecedented accuracy, I decided that they deserved to be studied thoroughly. After completing the precision studies on the H₂ and D₂ nuclear resonances, my students and I used the same apparatus to study the spectra associated with the reorientation of the rotational magnetic moments of H₂ and D₂. We observed the variations of rotational magnetic moments with rotational quantum numbers and isotopic masses and determined the electron distribution in the hydrogen molecule [N. J. Harrick and N. F. Ramsey, Phys. Rev. 88, 228–232 (1952) and R. G. Barnes, P. J. Bray and N. F. Ramsey, Phys. Rev. 94, 893–902 (1954)].

We next wanted to study HD, but there are twice as many resonances in the first rotational state for HD as for H₂, so the observed intensities were too low for precision measurements. By then G. Wessel and H. Lew had developed an electron bombardment detector that worked well with condensable vapors, so my associates and I developed an electron bombardment detector and vacuum system that also worked with noncondensable gases such as H₂, D₂ and HD [W. E. Quinn, A. Pery, J. M. Baker, H. R. Lewis, N. F. Ramsey and J. T. LaTourette, Rev. Sci. Instrum. 29, 935–943 (1958)]. This detector was first used to study HD (Paper 2.5). We measured the radiofrequency spectra in both the zeroth and first rotational states. The results were consistent with previous measurements and with the theory given in Paper 5.7.

Thirteen years after Paper 2.5, R. F. Code and I [Phys. Rev. A4, 1945–1959 (1971)] remeasured HD and D₂ with even better accuracy by using a very low magnetic field, the improved apparatus described in Paper 2.6, an electron bombardment detector and a 20 K source cooled by gaseous helium [Rev. Sci. Instrum. 42, 896–898 (1971)]. That experiment gave more accurate interaction parameters and a confirmation of the electron-coupled spin–spin interaction theory of Paper 5.5.

Prior to 1961, molecular beam magnetic resonance studies had been limited to the molecular hydrogens or to molecules containing at least one atom, such as an alkali, easily detected with a surface ionization detector. Electron bombardment detectors (commentary for Paper 2.5) allowed the study of almost any molecule. We, therefore, built a new molecular beam resonance apparatus with an electron bombardment detector and with alternative heated, cooled and jet beam sources.

The apparatus was built by H. M. Nelson, J. A. Leavitt, M. R. Baker and me [Phys. Rev. 121, 807–815 (1961)] and was first used to study HF. The experimental results agreed well with a theory we developed, giving us average values for the spin–spin magnetic interaction and the two spin-rotational interactions.

Paper 2.6 describes similar studies with DF. The theory is more complicated than for HF because of the deuteron quadruple interaction and the larger number of rotational states, requiring numerical calculations with a programmed computer. When this is done and the parameters are adjusted for the best fit, the magnetic and quadruple interaction parameters are well determined.

The same authors [Phys. Rev. 124, 1482–1486 (1961)] also used their apparatus to study HCl and obtained the interaction parameters by a similar analysis. Later, H³⁵Cl and H³⁷Cl were studied at very low magnetic fields where the interaction parameters could be more accurately determined [R. F. Code, A. Khosla, I. Ozier, N. F. Ramsey and P. N. Yi, J. Chem. Phys. 49, 1895–1901 (1968)].

In addition, this apparatus was used to measure the internal spin-dependent interactions in N₂ [S. I. Chan, M. R. Baker and N. F. Ramsey, Phys. Rev. 136, A1224–A1228 (1961)] and to settle a dispute on the structure of CO by measuring the sign and magnitude of its rotational magnetic moment [I. Ozier, P. N. Yi, A. Khosla and N. F. Ramsey, J. Chem. Phys. 46, 1530 (1967)]. The signs and magnitudes of the spin-rotation constant and the rotational magnetic moment of ¹³C¹⁶O were determined [I. Ozier, L. M. Crapo and N. R Ramsey, J. Chem. Phys. 49, 2314–2321 (1968)].

To measure different molecules, T. R. Lawrence, C. H. Anderson and I changed the detector of the apparatus described in Paper 2.5 to a surface ionization detector with a mass spectrometer. Paper 2.7 describes the use of this apparatus to determine the rotational magnetic moments of LiH and LiD. Some asymmetry was observed in the LiH resonance curve, but it could be attributed to a small variation of the rotational magnetic moment with the rotational quantum number. The magnitudes of the resonances demonstrated the occurrence of multiple quantum transitions and suggested the use of such transitions to study rotational transitions of molecules with even smaller rotational g factors.

By comparing the rotational magnetic moments of the LiH and LiD molecules with the theory of the isotopic shift of rotational magnetic moments given in Papers 2.2 and 5.2, we determined, for the first time, the sign of the electric dipole moment of the LiH molecule.

This apparatus and method was later used by R. A. Brooks, C. H. Anderson and me [Phys. Rev. 136, A62–A68 (1964)] to measure the rotational magnetic moments of Li₂, Na₂, K₂, Rb₂ and Cs₂. We found empirically that electronic contributions to the rotational magnetic moments are approximately proportional to the reciprocals of the molecules' masses. R. Brookes and N. Kaufman also used the apparatus to measure the rotational magnetic moment of BaO, which showed that A. M. Russel's two-spherically-symmetric-ion model could only account for less than half of the experimental result. F. Mehran, R. A. Brooks and I [Phys. Rev. 141, 93–104 (1966)] also measured the rotational magnetic moments of five alkali-halide molecules and found the results to be in agreement with a theory developed by H. M. Foley. R. A. Brooks, C. H. Anderson and I [J. Chem. Phys. 56, 5193–5194 (1972)] used the same apparatus to measure the rotational magnetic moments of the mixed alkalis KNa and LiNa.

The atomic hydrogen hyperfine separation can be accurately calculated from theory, so comparison to the experimental value provides a crucial test of fundamental theory. Historically, it was the disagreement between the theoretical and experimental values of this quantity that stimulated J. Schwinger's development of relativistic quantum electrodynamics (QED). Dan Kleppner and I invented the atomic hydrogen maser primarily to measure this quantity more accurately. The description and theory of the hydrogen maser are in Papers 1.10 and 1.11 while the results are in Paper 2.8. At the time of these measurements, the largest uncertainty came from the primary cesium time standard with the second largest from the correction for the H-maser wall collisions. Since both cesium and atomic hydrogen are used as time standards, many national centers for time measurements have remeasured the hydrogen hyperfine separation in terms of the internationally defined second. At present the preferred value is Δν(H) = 1,420,405,751.7667 ± 0.0009 Hz.

Until the Josephson effect determinations of the fine structure constant α, the principle uncertainty in comparing this experimental value to the QED prediction was in the value of α. In fact α could be determined by assuming the QED calculation to be correct and then determining the value of α from our hyperfine experiment. The value of α so obtained differed significantly from Lamb's determination from fine structure measurements. Because of the fewer theoretical calculations involved, the Lamb value was generally accepted. However, when α was determined from the Josephson effect it disagreed with the Lamb value and agreed completely with the value derived from our hyperfine measurements. Now, with the Josephson value of α, the principal uncertainty in comparing hyperfine theory and experiment comes from the proton structure, and the hydrogen hyperfine experiment is used to evaluate the proton structure.

Paper 2.9 describes the first measurement of the Stark shift of the hyperfine interaction. The electric field was applied parallel to the axis of quantization (H). This measurement has the advantage of there being a theoretical calculation to which the experimental results can be compared. The experiment agrees with theory to within the 6% experimental error.

Some years later, P. Gibbons and I [Phys. Rev. A5, 73–78 (1964)] and J. G. Stuart, D. J. Larson and I [Phys. Rev. A22, 2092–2097 (1980)] measured the Stark shift when the electric field was applied perpendicular to the axis of quantization. Our measurements agreed with theory to within the 2.5% experimental error.

The suggestion was reported in Paper 2.7 that multiple quantum transitions are important in the study of resonant rotational transitions of molecules with large rotational angular momenta. It would be a formidable task to do exact quantum calculations for the large number of states involved in multiple quantum transitions at large angular momentum; J. W. Cederberg and I [Phys. Rev. 136, A39–A43 (1964) developed a hybrid procedure — part classical and part quantum — for calculating the observed resonance shapes with both single and separated oscillatory fields. The theory agreed well with the observed rotational magnetic moment spectrum of OCS, for which the most probable angular momentum J is 22.

Paper 2.10 describes the use of this multiple quantum transition method to obtain the rotational magnetic moments of heavy molecules, including CO₂, OCS, CS₂, C₂H₂, Fe(CO)₅, Ni(CO)₄ and CF₄.

Although the proton magnetic moment is fundamental in nuclear and atomic physics, all its measurements prior to this paper were in molecules where externally applied magnetic fields induced circulations of the electrons that magnetically shielded the proton. I had developed a theory of the shielding correction (Paper 5.1), but it was of limited accuracy and had never been tested. We therefore made a direct measurement of the absolute value of the proton magnetic moment, both to have a better value for this fundamental constant and to test my magnetic shielding theory. We successfully did this (Paper 2.11) by operating the hydrogen maser at a high magnetic field and observing both the proton and the electron spin flip frequencies. In the hydrogen atom, the relativistic correction for the electron spin flip and the magnetic shielding of the nucleus are known, so the proton moment is measured directly in terms of the electron moment. From the previously measured value of the electron moment, the value of the proton magnetic moment in Bohr magnetons is obtained. From this absolute value of the magnetic moment and the NMR measurements of the proton resonance frequency in H₂, the magnetic shielding theory of Paper 5.1 was experimentally confirmed to within the estimated error.

Since the hyperfine separation of atomic tritium is only 7% larger than that of hydrogen, a hydrogen maser apparatus can, in principle, be used as a tritium maser. Because tritium is scarce and highly radioactive, we designed a recirculation system for the tritium maser. After a short run, the tritium seemed to disappear and be partially replaced by hydrogen and other contaminants as a result of absorption of the tritium by the pyrex walls of the discharge bulb used to produce atomic from molecular tritium. The use of quartz walls alleviated this problem sufficiently to allow us to complete a successful experiment. But our final accuracy was limited to 5 parts in 10¹² by the short running times these difficulties imposed.

Having measured the hydrogen hyperfine separation, we were eager to measure the corresponding property for deuterium. Making a deuterium maser would be a formidable task, since the deuterium hyperfine separation is smaller by a factor of 4.3 so a deuterium maser needed to be 4.3 times larger. Therefore, we made our first deuterium measurements by operating a hydrogen maser with a mixture of atomic hydrogen and deuterium [S. B. Crampton, H. G. Robinson, D. Kleppner and N. F. Ramsey, Phys. Rev. 141, 55–66 (1966)]. Spin exchange collisions reduced the amplitude of the hydrogen maser oscillations and the magnitude of the effect depended on the hyperfine state of the deuterium. Therefore, when we introduced an additional oscillatory field and swept it through the deuterium resonance we determined the deuterium resonance frequency by the reduction of the hydrogen maser oscillations.

Paper 2.13 describes an improved version of this experiment with a more accurate result and a determination of the hydrogen-deuterium atomic magnetic moments ratio. Later, the deuterium maser described in Paper 1.13 was constructed with the most accurate value for the deuterium hyperfine separation given in Paper 1.13.

D. J. Larson and I [Phys. Rev. A9, 1543–1548 (1974)] also used the spin exchange technique to measure the hydrogen-tritium atomic magnetic moments ratio and hyperfine transitions of other atoms such as ¹⁴N. In this way S. B. Crampton, H. C. Berg, H. G. Robinson and I measured the quadrupole coupling constant in the ¹⁴N ground state for the first time [Phys. Rev. Lett. 24, 195–197 (1970)]. In a later experiment, J. M. Hirsch, G. H. Zimmerman, D. J. Larson and I [Phys. Rev. A16, 484–487 (1977)] used the same method to measure the atomic nitrogen g factor and to obtain more accurate values for the dipole and quadrupole coupling constants A and B. Our value for A agrees well with theory, but the theoretical value of P. G. H. Sandars for B is 16 times bigger than the experimental value and of the opposite sign.

We have used the hydrogen maser spin exchange technique to measure the Rb atomic magnetic moment to an accuracy of one part in 10⁷ [P. A. Valberg and N. F. Ramsey, Phys. Rev. A2, 554–565 (1971)].

Because of the great interest in methane (CH₄) and other spherical top and tetrahedral molecules, we made a series of magnetic resonance measurements on these and similar molecules using the apparatus described in Paper 2.7 and its commentary. The first was by C. H. Anderson and me [Phys. Rev. 149, 14–24 (1966). We used the apparatus described in Paper 2.6. to study the spectrum associated with the reorientations of the total nuclear spin and the rotational angular momentum relative to a strong external magnetic field in CH₄ and CHD₃. We measured the average spinrotational constants for the protons and the g value of the rotational magnetic moments.

Paper 2.14 reports the first direct observation of the normally forbidden ortho–para transition in CH₄. The ortho–para transitions result from spin conversion transitions in a magnetic field where there is an anticrossing between ortho and para levels, and the results give information on the distortion electric dipole moment.

W. Itano and I. Ozier [J. Chem. Phys. 72, 3700–3711 (1980)] have studied in our laboratory the avoided crossing spectrum of methane in the J = 2 rotational state and W. M. Itano and I [J. Chem. Phys. 72, 4941–4945 (1980)] have studied the corresponding spectrum of SiH₄ and GeH₄. The analysis of the experiments gave the hyperfine constants and rotational g factors of the molecules.

Our magnetic resonance experiments on molecules with low moments of inertia were very productive, because few rotational states were excited and the spectral lines could be individually distinguished. The experiments (Papers 2.6 and 2.10) with heavier molecules, like DCl, CO and CH₄, gave valuable but less detailed information since the observed spectrum had to be compared with that predicted by averaging over many rotational states. For experiments with even more complex molecules, we needed to select the rotational state by using electric instead of magnetic fields (the effective electric dipole moment of the molecule depends on the rotational state). T. F. Gallagher, R. C. Hilborn, T. C. English and I designed and built a molecular beam electric focusing apparatus with a jet source, electric quadrupole focusing fields giving both parallel and single crossing focusing, a 2.5-m-long resonance region and an iridium hot wire detector. This apparatus, and the initial measurements with it, are described by T. F. Gallagher, R. C. Hilborn and me [J. Chem. Phys. 56, 5972–5979 (1972)] and in Paper 2.1. ⁷Li^35,37Cl and ⁷Li^79,81Br were studied and accurate values obtained for the nuclear electric quadrupole interactions, the spin-rotational interactions and the spin–spin interactions in the J = 1 rotational state and in various vibrational states of the molecules. A. R. Jacobson and I, with the same apparatus, obtained similar results with LiI [J. Chem. Phys. 65, 1211–1213 (1976)].

J. L. Cecchi and I later installed a 2.27 m electromagnet along the resonance region in order to study Zeeman and Stark shifts in the same apparatus [J. Chem. Phys. 60, 53–65 (1974)], the first studies being with ⁷Li^79,81Br. The experiments were done with no external electric field (the effective electric field induced by the motion of the molecule through the magnetic field was sufficient to produce the parity-mixing field that is necessary for observing ΔJ = 0, ΔmJ = ±1 transitions). We accurately measured a number of parameters for these molecules including their nuclear magnetic moments, the tensor terms in their magnetic shieldings and the tensor terms in the diamagnetic susceptibility. R. R. Freeman, D. W. Johnson and I [J. Chem. Phys. 61, 3471–3478 (1974)] used the same apparatus to determine similar quantities for isotopes of LiCl in the zeroth and first rotational states.

Since the original apparatus had an iridium detector, it was limited to molecules containing at least one alkali atom. To extend its use to HBr and similar molecules, D. W. Johnson and I [J. Chem. Phys. 67, 941–947 (1977)] installed an HBr negative ion ionizer to measure the hyperfine interaction parameters of H⁷⁹Br, H⁸¹Br, D⁷⁹Br, D⁸¹Br and D³⁵Cl in the first and second rotational states.

In this paper, we describe our addition of an electric field to the apparatus of Paper 2.6 and studies of the changes in the rotational spectrum as the electric field is increased from zero to 50 KV/cm. From these measurements we could calculate the anisotropy of the molecular electric polarizability. We obtained accurate values for this parameter for both H₂ and D₂. The experimental values test different molecular theories and, to within 0.3%, agree with the theory of W. Kolos and L. Wolniewicz [J. Chem. Phys. 46, 1426–1430 (1967] for the tensor polarizability of H₂. The confirmation of this theory is particularly useful since it is used to calibrate Raman intensities, to calculate orientation-dependent van der Waals forces and to analyze spectral shifts induced by electric fields and pressure. We also did experiments in which we varied both the electric and magnetic fields and compared these results to theory.

L. A. Cohen, J. H. Martin and I [Phys. Rev. A19, 433–437 (1979)] used a modification of this apparatus with rotating fields and multiple quantum transitions to measure the signs of the rotational magnetic moments of acetylene and a number of spherical top molecules, like CF₄.

The deuteron electric quadrupole moment is determined from measurements of the quadrupole interaction energy, which is the product of the quadrupole moment and the gradient of the electric field. Therefore the quadrupole moment measurement can only be as accurate as the calculation of the field gradient. Although Papers 2.1 and 2.5 describe accurate measurements of the deuteron quadrupole moment interactions in D₂ and HD, all suffer from uncertainties in the calculation of the gradient of the electric field because of the near cancellation of the nuclear and electron contributions to the gradient. Although the LiD calculation is more complicated, the near cancellation does not occur and the accuracy of the LiD calculation is comparable to that of HD. To obtain an independent determination of the deuteron quadrupole moment, we used Cecchi's apparatus, described in the commentary on Paper 2.15, to measure the quadrupole interaction in LiD. We then used the theoretical value [K. K. Docken and R. R. Freeman, J. Chem. Phys. 61, 4217–4223 (1975)] for the gradient and obtained a value for the deuteron electric quadrupole moment that agreed with the value from D₂ and HD to within 1.5%. We also measured other spin-dependent interaction parameters in LiH and LiD in different rotational and vibrational states.

Because of the interest in our studies of tetrahedral molecules (Paper 2.14 and in the papers referred to in its commentary), P. N. Yi, I. Ozier and C. H. Anderson developed, in our laboratory, the theory of nuclear hyperfine interactions in tetrahedral molecules [Phys. Rev. 165, 92–109 (1968)]. I. Ozier, L. M. Crapo and S. S. Lee [Phys. Rev. 172, 63–82 (1968)] used this theory to determine, from their measurements, the average spin-rotation constants and the anisotropy in the spin rotation matrices of the molecules CH₄, SiH₄, GeH₄, CF₄, SiF₄ and GeF₄. P. N. Yi, I. Ozier and I [J. Chem. Phys. 55, 5215–5227 (1971)] used the theory to interpret the low field hyperfine spectrum of CH₄ which we measured with the apparatus described in Papers 2.6 and 2.14. We obtained values for the average spin-rotation constant c_a and for the anisotropy c_d of the spin-rotation interaction.

Paper 2.18 extends our measurements to the rotational magnetic moment spectra of the above series of tetrahedral molecules and provides values of g_J, c_a and c_d for all the molecules in the series. These values are used in theories of NMR nuclear spin relaxation.

I. I. Ozier, P. N. Yi and I [J. Chem. Phys. 66, 143–146 (1977)] used the same apparatus to measure the magnetic moment spectrum of SF₆ and to obtain values for g_J, and c_a.

Although most of our spectroscopy with separated coherent oscillatory fields was with atoms or molecules, the method is equally effective for neutrons in an external magnetic field. As will be discussed in Section 3, most of our neutron experiments have been searches for a neutron electric dipole moment as tests of parity and time reversal symmetry. However, the same apparatus has also been suitable for precision measurements of the neutron magnetic moment. The first accurate measurements of the neutron magnetic moment by L. Alvarez and F. Bloch in 1940 used a neutron beam resonance method with a single oscillatory field.

In 1956, V. W. Cohen, N. Corngold and I [Phys. Rev. 104, 283–291 (1956)] measured the neutron magnetic moment, at the Brookhaven reactor, with neutron polarizing mirrors, a 1.5-m-long magnet and separated oscillatory fields. Our determination became the accepted value for the next 23 years.

In 1979 our group at Grenoble made a new neutron beam measurement with improvements such as the use of a liquid deuterium moderator to provide an intense beam of slow neutrons and the transmission of the neutrons through hollow tubes with total reflection of the neutrons on the inner walls of the tubes (Paper 2.19). The principal error in previous experiments had been the uncertainty as to whether the field averaged in discrete steps with a small NMR water probe was the same as for the moving neutrons. For this reason we used a flowing water magnetometer with the neutrons and water passing in succession through the same tube. After we made suitable corrections for various small effects [Metrologia 18, 93–94 (1982)], such as the diamagnetic susceptibility of water, we obtained the ratios of the magnetic moment of the free neutron to those of the electron, the Bohr magneton and the nuclear magneton to 0.25 parts per million.

Please refer to full text.

This was the first published paper to question the validity of the assumption, then universally held by physicists, that all particle forces must conserve parity. The origin of our idea that this assumption might be invalid for nuclear forces is discussed in Section 6(f) of "Autobiographical Notes."

We proposed a search for a neutron electric dipole moment as a test of parity symmetry, noting that a search for an electric dipole moment of a charged particle like the proton would be much less sensitive because the dipole moment is observed through its interaction with an electric field and the application of an electric field to a free charged particle will accelerate it out of the apparatus. We analyzed past experiments to see what limits they set on a particle electric dipole moment and found them extremely insensitive for the above reason. The most sensitive were the 1947 experiments of W. Havens, I. I. Rabi, J. Rainwater, E. Fermi and L. Marshall on the neutron–electron interaction, which showed that the electric dipole moment of the neutron should be less than 3 × 10^-18 e cm. We concluded we could set a much lower limit and did the experiment described in Paper 3.2.

In some respects, Paper 3.1 suffered from being ahead of its time. It was published at a time when all physicists except the authors were so convinced there was parity symmetry that our paper received little attention. Seven years later, when the parity assumption was experimentally disproved, this paper was mostly forgotten. It is the only one to which T. D. Lee and C. N. Yang refer in their great parity paper, but they combine the reference with the results of Paper 3.2, so our paper appears to present evidence in favor of parity conservation rather than being the first paper to question it.

This paper describes our first search for a neutron electric dipole moment as a test of parity. With our graduate student, James Smith, we designed a neutron beam experiment at an Oak Ridge reactor using thermal neutrons, polarized by total reflection from a magnetized mirror and analyzed by transmission through saturated iron. Transitions were induced by the separated oscillatory fields method and the electric dipole moment obtained by comparing the resonance frequencies with the electric and magnetic fields being parallel or antiparallel. In this experiment we showed that the electric dipole moment of the neutron had to be less than 5 × 10^-20 e cm, much less than could be inferred from any previous experiment.

The experiment was completed in 1951, but publication in The Physical Review was delayed until 1957. However, the result was well known before the discovery of parity nonconservation in the weak interaction from Smith's 1951 thesis, our colloquia and my book Molecular Beams (Oxford University Press, 1956).

Initially the negative result in this experiment was explained away by theorists as a result of parity conservation. Later, after the failure of parity conservation in the weak interaction, it was attributed to time reversal symmetry, but, when CP conservation failed in the decay of the long-lived neutral kaon, an electric dipole moment of one size or another was expected by most particle theories consistent with the kaon results. We have made renewed electric dipole searches when major improvements in sensitivity appeared possible.

V. W. Cohen, R. Nathans, E. Lipworth, H. B. Silsbee and I [Phys. Rev. 177, 1942–1947 (1969)], in a neutron beam experiment at Brookhaven, lowered the neutron electric dipole moment limit to 1 × 10^-21 e cm.

W. B. Dress, J. K. Baird and I [Phys. Rev. 170, 1200–1205 (1968) and 179, 1285–1291 (1969)] used a new apparatus at Oak Ridge with the neutrons confined to rectangular pipes to increase the effective neutron intensity. In this way we reduced the upper limit to 5 × 10^-23 e cm. W. B. Dress, P. D. Miller and I [Phys. Rev. D&, 3147–3149 (1973)] later modified the apparatus so it could be rotated to allow the beam to pass successively through it in two opposite directions and thereby reduce the uncertainty from the effective magnetic field v × E/c created by the motion of the neutrons through the electric field. This experiment reduced the limit to 1.0 × 10^-23 e cm. Continuations of this experiment at the ILL in Grenoble, France, are described in the commentary on Paper 3.3.

As mentioned in the commentary on Paper 3.2, our apparatus for the neutron electric dipole moment was moved in 1974 to the much more intense cold neutron beam from the liquid deuterium moderator at the Institut Laue-Langevin (ILL) at Grenoble, France. With that beam and other improvements, W. B. Dress, P. D. Miller, J. M. Pendlebury, P. Perrin and I [Phys. Rev. D15, 9 (1977)] reduced the upper limit to 3 × 10^-24 e cm. Our principal source of error was from B and E not being exactly parallel to each other so that the effective magnetic field v × E/c produced by the motion of the neutron would have a component parallel to B which would change the neutron resonance frequency and therefore falsely look like an electric dipole moment.

We had realized for many years that trapping the neutrons by total reflection inside a suitable bottle would overcome this problem since the average value of v/c would then be very small. However, the neutrons must be slower than 7 m/s. We had tried unsuccessfully at Oak Ridge many years earlier to make a bottle for neutrons, but there were too few slow neutrons. At the ILL there were enough low energy neutrons, even from a water converter, at 320 K to make a successful trap, so Pendlebury, Smith, Golub, Byrne, McComb, Sumner, Taylor, Heckel, Green, Morse, Kilvington, Baker, Clark, Mampe, Ageron, Miranda and I [Phys. Lett. 136B, 327–330 (1984)] constructed a bottle in which the neutrons could be stored and the electric dipole moment measured. We found that the neutron electric dipole moment was less than 1 × 10^-24 e cm.

Paper 3.3 is the latest publication on our searches. We used essentially the same apparatus as in the previous paper, but took advantage of a hundredfold increase in the neutron intensity from the ILL liquid deuterium moderator. We showed that the neutron electric dipole moment must be less than 12 × 10^-26 e cm to a 95% confidence level and by combining with the latest St. Petersburg result we conclude that the neutron electric dipole moment is less than 9 × 10^-26 e cm to a 95% confidence level.

Although none of these searches have found a nonzero electric dipole moment, in lowering the upper limit by a factor of more than 10⁷, we have eliminated the theories that predicted larger electric dipole moments. Currently (1997) a new and more sensitive search is being started with a ¹⁹⁹Hg magnetic field monitor in the same storage volume as the neutrons. This experiment may be able to test different predictions by the standard model, supersymmetric theories and superstring theories.

When T. D. Lee, C. N. Yang, C. S. Wu, E. Ambler and others discovered that parity was not conserved in the weak interaction, Lee, Yang, I. Landau, J. Schwinger and others predicted that there still should be no observable particle electric dipole moment due to time reversal symmetry (T). In Paper 3.4, I pointed out that time reversal symmetry is an unproved assumption which does not justify the abandonment of searches for electric dipole moments or other manifestations of T symmetry failure. I called attention to a way in which there could be a neutron electric dipole moment; if magnetic poles exist, either really or virtually; a circulating magnetic pole will create an electric dipole moment just as a circulating electric pole creates a magnetic dipole moment. I also observed that, if magnetic monopoles exist, the fundamental PCT symmetry would be replaced by PCTM symmetry, where M is magnetic pole conjugation. At that time, it was argued that, even though there was neither C nor P symmetry, there would be combined CP symmetry. I noted that T and M could also go together to provide TM symmetry even if there were no T symmetry. In preparing this paper, I had extensive arguments and discussions with T. D. Lee. Though I benefitted from these discussions, they delayed publication by almost a year. Many years later, I learned that J. D. Jackson, S. B. Treiman and H. W. Wyld [Phys. Rev. 106, 517 (1957)] also published a paper noting that T symmetry was an assumption that had to be experimentally tested. Both their paper and mine suffered from being too far ahead of the conventional thinking. As a result, by the time a failure of CP symmetry was experimentally observed in the decay of the long-lived neutral kaon, most physicists had forgotten our early warnings of the possibilities of CP and T symmetry nonconservation.

1964, F. C. Michel [Phys. Rev. 133, B329–B332 (1964)] published a thought-provoking paper on the possibility of there being a small parity-nonconserving spin rotation of a neutron passing through matter, but it appeared in the then new Physical Review B and was not seen by physicists who might have been interested in doing the experiment. In 1974 L. Stodolsky independently had the same idea at CERN, but experimentalists there considered the rotation angle to be much too small to be observed. Stodolsky told me of this work and I was immediately interested, for two reasons: my long term interest in parity non-conservation tests and my realization that our neutron electric dipole moment experiments were extremely sensitive tests of a small rotation of the neutron spin. I did a simple calculation and concluded that we could adapt our neutron electric dipole methods to measuring the proposed parity-nonconserving spin rotation. When M. Forte learned of our experiment, he urged that we first study ¹²⁴Sn, since he had a theory according to which the spin rotation with ¹²⁴Sn should be about ten times greater than with most materials. We, therefore, asked him to join our group and we constructed the apparatus described in Paper 3.5.

In our first run we measured the neutron spin rotation in ¹²⁴Sn and used a measurement of isotopically unseparated Sn as a control. To our surprise, we found no spin rotation with ¹²⁴Sn, but we did find a significant rotation with our control of normal Sn. This clearly indicated that the effect existed, but in a different Sn isotope. We later obtained a sample of separated ¹¹⁷Sn and found with this isotope a neutron spin rotation of (+36.7 ± 2.7) × 10^-6 radians per cm of sample traversed. In later publications [Phys. Lett. 119B, 298–300 (1982) and Phys. Rev. C29, 2489–2492 (1984)], we reported values for the parity-nonconserving spin rotations of neutrons passing through isotopes of lead where the sign of the rotation was negative, and of lanthanum where the rotation was much larger. Currently (1997), Heckel and his associates are preparing experiments to measure the spin rotation of neutrons passing through liquid H₂ and He from which they should be able to derive the neutron–neutron parity-nonconserving interaction.

Although most of my electric dipole moment experiments have been with neutrons, one was with TlF. E. A. Hinds and P. G. H. Sandars published a report (1980) on their ingenious experiment to observe an electric dipole interaction in the ²⁰⁵Tl nucleus with the nonuniform electric field within the molecule; even though the electric field averaged over the nuclear electric charge distribution had to be zero, it did not have to be so when averaged over the electric dipole moment distribution. By suitable molecular state selections, they were able to observe the difference between the ²⁰⁵Tl resonance frequencies when the effective electric and magnetic fields of the rotating molecule were changed from parallel to antiparallel and from this measurement infer the proton electric dipole moment. To obtain a sharp resonance they constructed an apparatus many meters long and as a result had such a weak resonance that they ran successfully only a few hours during more than several years. As a result, their electric dipole limit was less sensitive than hoped.

Since our electric resonance apparatus described in Paper 2.15 had both high resolution and high intensity, we decided (Paper 3.6) to modify that apparatus to do a more sensitive electric dipole moment search in TlF. The sensitivity of the experiment came up to our expectations. We lowered the limit and even had an exciting few weeks during which we seemed to be obtaining a nonzero result. However, we eventually found that, when we reversed the signs of our focussing electric quadrupole magnets, the sign of the result unexpectedly reversed. Although we never fully understood this spurious effect, we realized that our use of an existing apparatus had forced us to place the two different magnets excessively close together. Since the apparatus would have had to be entirely rebuilt to overcome this problem, we decided to terminate our experiment with our already improved limit and to encourage Hinds in his plans to build a new apparatus at Yale incorporating the best features of our apparatus. In subsequent years, Hinds and his students did construct their new apparatus and did not find an electric dipole moment, but did establish a still lower limit.

Before 1980 most electric dipole moment experiments were with neutrons, but since then there have also been a number with atoms and molecules. Because of my long association with searches for electric dipole moments I have often been asked to review all current and past experiments. Paper 3.7 is such a review, for the 14th International Conference on Atomic Physics. I discuss the history of electric dipole searches, describe the different experiments and compare their results using a phenomenological analysis first used by I. B. Khriplovich. He considered various interaction terms that could give rise to CP and T noninvariance, with each term having its own multiplying parameter. Different experiments are then compared by the limits they set on the different parameters. Paper 3.7 shows that the different parameters are most tightly constrained by one of the following three experiments: the neutron electric dipole experiments of our group at Grenoble and the group at St. Petersburg, the ¹⁹⁹Hg experiments of the group led by Fortson in Seattle and the ²⁰⁵Tl experiment of E. D. Commins and his collaborators at Berkeley. All groups are planning improved experiments in the coming years. Although the "standard model" predicts such low values for electric dipole moments that none of the experiments are likely to reach those limits in the near future, most of the alternatives to the "standard model," such as supersymmetry and superstrings, are compatible with the possibility of observing a nonzero electric dipole moment during the next round of experiments.

Please refer to full text.

This paper was motivated by my desire to calculate the magnetic shielding corrections for our accurate measurements with H₂, D₂ and HD molecules. The shielding depends on both first order diamagnetic and second order paramagnetic effects. Due to the generality of the fundamental portions of the theory, they continue to be the basis of the theory for magnetic shielding in all molecules. With most molecules it is difficult to carry out calculations to obtain accurate numerical results since second order perturbations summed over all excited states of the molecule are required. I showed that an approximation could be obtained by replacing the individual excitation energies with a single average energy and then using closure to evaluate the sums. Subsequently many molecular theorists have devised ingenious approximate methods for such calculations.

Since hydrogen molecules have no inner core electrons to contribute to the shielding, the molecular contributions are a large fraction of the total shielding. Fortunately, these molecules are simple and I was able to show that the difficult second order paramagnetic terms could be evaluated in terms of the spin-rotational interactions we had measured (Papers 2.1, 2.2 and 2.4). In this way, I obtained (Paper 4.1) a specific value for the shielding constant which enabled us for the first time to obtain the magnetic moment of the free proton. Sixteen years later, in Paper 2.11, with the atomic hydrogen maser, we were able to measure the proton magnetic moment directly and found complete agreement with the molecular beam value only after it had been corrected, thus demonstrating experimentally the validity of the theory.

Because of the extensive use of this theory in NMR chemical analysis, biology and medicine, this paper has been one of my most frequently cited publications.

In Paper 4.1, I averaged the magnetic shielding calculations over all orientations of the molecule, since this is needed in most NMR experiments where the molecules are in either a liquid or dense gas and are subject to many collisions that average their orientations. But orientation effects are important in molecular beam experiments and some NMR experiments with crystals. In Paper 4.2, I calculated the orientation dependence of the magnetic shielding and averages over different rotational angular momentum quantum states.

Paper 4.3 holds my personal record for the shortest interval of time — six hours — between conception and completion.

Since Felix Bloch — primarily a theorist — had been doing experiments on magnetic shielding and I — primarily an experimentalist — was doing the theory of magnetic shielding, Bloch in jest called me for a time his "Haus Theoretiker." One day he came to my office to tell me with glee that he had experimental disproof of my magnetic shielding theory. He showed me the results of Packard and Arnold's experiment on ethyl alcohol (CH₃CH₂OH). They had found three resonances with intensity ratios of 3:2:1 and two of them were approximately temperature-independent, as expected from my theory, but the third and weakest one, corresponding to OH, was markedly temperature-dependent. I had no immediate answer and left the chemical formula on my blackboard as a reminder to worry about the problem further. Several days later Urner Liddel, whom I knew only as the excellent ONR administrator of my research contract, came to my office and, on seeing the chemical formula for ethyl alcohol on the blackboard, asked if I was drinking it or studying it. He then went on to explain that his Ph.D. in chemical engineering had been on molecular association in liquid alcohol. His mere mention of molecular association was sufficient to suggest that as the explanation of the temperature dependence. We immediately did a few calculations to confirm the reasonableness of the hypothesis and sat down to write a joint paper which was typed that afternoon and mailed to The Journal of Chemical Physics. In addition to providing an explanation for the temperature dependence, it showed experimentally that the known molecular association was through the OH.

In this paper, I describe extensions of my earlier magnet shielding and chemical shift theories to provide easier and better calculations with heavy molecules. Contributions from the innermost electrons are considered separately so they can be treated with essentially an atomic theory. The chemical shift is treated as a second rank tensor which can be averaged in whatever manner is appropriate. The possibility of temperature dependence is also explicitly included.

In addition, I develop an analogous theory for molecular diamagnetic susceptibilities, including possible orientation and temperature dependences of the susceptibilities.

In this paper we extended to HF, F₂, and N₂ the method of Paper 4.1 for obtaining the second order paramagnetic terms in magnetic shielding from the experimentally measured nuclear spin-rotation interactions. By combining this with reliable calculations of the diamagnetic parts we obtained the value of the total shielding constant for HF and F₂. For F₂ we were able to do this provided we made a reasonable assumption for the unmeasured sign of the spin-rotational interaction. It is interesting to note that the shielding constants for F₂ and N₂ are negative. From these shielding constants and from previous uncorrected NMR measurements without the shielding correction we obtained the corrected nuclear magnetic moments.

Please refer to full text.

The theory of molecular H₂, D₂ and HD presented in Papers 1.1, 2.1 and 2.2 was adequate for our first molecular beam magnetic resonance experiments at high magnetic fields, but, as we aimed for more accurate experiments with our new separated oscillatory field apparatus, it was clear we needed a more accurate general theory. This improved theory is applicable at low, intermediate and high fields as well as including nuclear magnetic shielding. This paper was used in a number of experiments, including those in Papers 2.4 and 2.5.

Several years later, when we were planning experiments with HD, H. B. Lewis and I wrote a similar theoretical paper on HD [Phys. Rev. 108, 1246–1250 (1957)]. It was used in the analysis of the experiments described in Paper 2.5 and the experimental paper by R. F. Code and me [Phys. Rev. A4, 1945–1959 (1971)].

As the accuracy of our measurements increased, zero point vibrational and centrifugal effects became important, so I wrote this paper concerning their effects on the spin–spin magnetic interaction, the spin-rotational magnetic interaction, the rotational magnetic moment, the magnetic shielding of the nucleus and the molecular diamagnetic susceptibility. Although the general results apply to any molecule, the detailed discussions are limited to ¹Σ diatomic molecules and specifically to H₂, D₂ and HD. I showed, for example, that the ratio of the rotational magnetic moments of H₂ and D₂ should be slightly different from the ratio of the masses. The theory also provides important corrections in determining the average value of 〈1/R³〉, which is needed to calculate the magnetic portion of the tensor interaction to see if there is a nonmagnetic tensor interaction between two protons, as discussed in Paper 6.3.

In preparation for more accurate measurements of the molecular hydrogen rotational transitions, I did theoretical analyses for extracting basic information from the data. As discussed in Paper 2.2, the value of the rotational magnetic moment gives the high frequency or second order paramagnetic terms in the magnetic susceptibility and the experiment also directly determines the orientation dependence of the magnetic susceptibility. In Phys. Rev. 78, 221–222 (1950) I showed, theoretically, that high frequency terms, determined from the rotational magnetic moment measurement, can be used to eliminate the high frequency term in the orientation-dependent magnetic susceptibility, leaving only a term corresponding to the quadrupole moment of the electron distribution of the H₂ molecule. N. J. Harrick and I [Phys. Rev. 88, 228–232 (1952)] then did a better experiment, from which we determined the experimental value for the quadrupole moment or 〈3z² - r²〉 of the electron distribution. It agreed with that calculated from the James–Coolidge wave functions within experimental error.

A few months after completing this work, I found a precision measurement of the magnetic susceptibility of H₂ by G. G. Havens in Phys. Rev. 43, 992–996 (1933). Although his result did not directly give the average 〈r²〉 because of the then unknown high frequency terms, I used it in Paper 5.3 along with our determination of the high frequency term to determine 〈r²〉. From this value and the value for 〈3z² - r²〉, I obtained 〈x²〉 = 〈y²〉 and 〈z²〉. The results agreed well with calculations from the James–Coolidge wave functions.

Unfortunately, in the publication of this paper the references were omitted, but they are given properly here.

The nuclei in a rotating molecule are moving with a velocity v and an acceleration (dv/dt), so their spins are subject to a kinematical relativistic precession just like the Thomas precession of the electron spins in atoms. Prior to our experiments, this precession for nuclear spins in molecules had been too small to be observable and had never been discussed. But, with the greater accuracy of our new experiments, it became significant, so I developed the theory of the effect for molecules in Paper 5.4. The added kinematical precession angular frequency is ω_T = (dv/dt) × v/2c². I showed that this precession contributes 1059 Hz to the spin-rotational interaction in H₂. In connection with this work, I developed a simple and straightforward means for deriving the Thomas precession, later published in Journal of Physics Education 1, 46 (1971).

Most of my theoretical papers on nuclear interactions in molecules originated from our own experiments. However, some, like Paper 5.5, were to interpret puzzling observations by others. In 1951 Gutowsky, McCall, Slichter, Hahn and Maxwell discovered splittings of NMR resonance lines in molecules that are independent of the strength of the external magnetic field, in contrast to the usual NMR splittings that are due to magnetic shielding. They pointed out that their observations could be interpreted as the effect of an interaction between two nuclei with spins I_N and I_N', of the form h δ I_N · I_N', but no one could invent a theoretical mechanism for making the interaction constant d as large as observed. Purcell and I (Paper 5.5) proposed a new electron-coupled nuclear spin–spin interaction. The spin of one nucleus would interact magnetically with the spin of a nearby electron, which would affect the spin of another distant electron in a ¹Σ diatomic molecule because the total electron spin has to be zero. This distant electron would then interact magnetically with a nearby nuclear spin to give a net nuclear spin–spin interaction of the required form. This mechanism produces a much bigger effect at long distances than do direct magnetic interactions since the electron spins are exchange-coupled. We calculated this effect for HD and found a sufficiently large coupling constant to justify extending this interpretation to the reported experiments. We also suggested that the interaction be measured for HD to provide a better comparison of experiment to theory.

Measurements on HD were soon made, so I developed the theory further [Phys. Rev. 91, 303–307 (1953)] to show that, if the mean energy of the molecular excited states is given the reasonable value 1.4 Rydbergs, the electron-coupled spin interaction constant would be +43 Hz, in agreement with its measured magnitude [there is a minor misprint in my second theoretical paper and the sign of the last term in square brackets of Eq. (23) should be minus, with a corresponding change in Eq. (24)]. The theory has been confirmed by NMR experiments and by HD molecular beam resonance experiments [R. F. Code and N. F. Ramsey, Phys. Rev. A4, 1945–1959 (1971)]. As discussed in that paper, the latest theoretical calculation of δ is 42.57 Hz, in reasonable agreement with the latest NMR measurement of + 42.94 ± 0.10 Hz.

Subsequent to our original papers, electron-coupled spin interactions have been found to be important in many studies of both molecules and solids.

As a result of this work on electron-coupled nuclear spin–spin interactions, I wrote a report [Phys. Rev. 89, 527 (1953)] pointing out that such interactions would make dominant contributions to calculations of pseudoquadrupole effects for nuclei in molecules.

Please refer to full text.

As discussed in the commentary on Paper 1.4, Pound, Purcell and I spent one weekend studying the NMR of a nuclear spin system with the high energy states occupied more than the low, which we recognized as corresponding to the spin system being in a state of negative absolute temperature. In 1955, when I was at Oxford as a Guggenheim Fellow, Sir Francis Simon tried to convince me that we were wrong in thinking we had a negative temperature, but, after extensive discussion, I convinced him that we were right and that our thermodynamic system was as valid as any other system; he then urged me to write a complete theory (Paper 6.1).

Initially, I discuss spin temperatures and the conditions which must apply for temperature to be a valid concept. From the point of view of thermodynamics the only requirement for the existence of a negative temperature system is that the entropy S should not be restricted to a monotonically increasing function of the internal energy. This is clearly the case for a thermodynamically isolated nuclear spin system in a solid since there is only one way in which the spins can be aligned in the lowest energy state and only one way in the highest energy state but many ways, and hence higher entropies, at intermediate energies. Since the temperature T is given by T = (dS/dU)^-1, negative absolute temperatures correspond to the regions where the slope of the curve of entropy as a function of internal energy is negative. I wrote most of the thermodynamic section of the paper with Zeemansky's text Thermodynamics on one knee and a pad of paper on the other while I was riding the train from Oxford to Cambridge. I essentially transcribed the relevant portions of the text but corrected for and noted the places where previous thermodynamicists had implicitly assumed, without saying so, that the entropy was a monotonically increasing function of the internal energy.

During this process I was shocked to find I was writing a paper contrary to one of the most popular statements of the second law of thermodynamics. My paper is consistent with most statements of the second law, like the principle of increasing entropy, but it is contrary to the Kelvin–Planck statement that it is impossible to operate an engine in a closed cycle that will do nothing other than extract heat from a reservoir with the performance of an equivalent amount of work. When the possibility of negative absolute temperatures is recognized, this statement must be restricted to positive temperature reservoirs and it is reversed for negative temperature reservoirs, i.e. it is impossible by doing work in a closed cycle to do nothing other than deposit heat in a negative temperature reservoir.

Negative temperature systems are the closest approximations to masers and lasers. Charles Townes has told me that a colloquium I gave at Columbia on negative temperatures was a stimulus to his invention of the maser.

In 1959 Y. Aharonov and D. Bohm [Phys. Rev. 115, 485–490 (1959)] shocked most of the physics community by inventing two "gedanken" (thought) experiments for which the electrons in a beam never exposed to an electric or magnetic field would have their interference fringes shifted by differences of either electrostatic scalar potential V or vector potential A between the two paths that produced the interference pattern. Most physicists disbelieved the paper since, in classical electromagnetic theory, the physical phenomena are all produced by the fields and the potentials are introduced as mathematical functions from which the fields are obtained by differentiation.

Wendell Furry and I at first doubted the Aharonov–Bohm (AB) paper but tried to understand it. Eventually we convinced ourselves that their paper was correct and the AB effects were essential for assuring the consistency of quantum mechanics and of complementarity. We showed (Paper 6.2) that the two gedanken devices invented by Aharonov and Bohm could, with modifications, be used to detect along which of the two interfering paths the electron traveled. But, by complementarity, it must be impossible both to observe interference fringes and to know through which path the electron passed. This contradiction is prevented by the AB effects of potentials since the zero point oscillations of the potentials, through the AB effects, destroy the interference pattern just as the device becomes sufficiently sensitive to detect the electron path. We pointed out that a key difference between a classical and a quantum particle is that a quantum particle, through its wave function, can be affected simultaneously by potentials along two different paths while this is impossible for a classical point particle. This peculiarity gave me the opportunity to project, at scientific meetings, the then new Charles Addams cartoon of a skier coming down a slope with one track on one each side of a tree. I pointed out that for classical particles such a picture was a joke whereas a quantum particle could be affected by the potentials on both paths. This cartoon was later reproduced in one of my published papers [Quantum Coherence and Reality (p. 39), edited by J. S. Anandam, World Scientific Publishing Co., 1994].

The night before I first presented this work at a meeting, I learned that L. Marton and his associates had that day presented a postdeadline paper claiming to show that the AB effects did not exist. As an experimentalist presenting a theoretical paper, I felt uncomfortable on learning that our paper had possibly been disproved experimentally, so I arranged a meeting with Marton before my talk. Initially their experiment appeared convincing, but I discovered they had omitted a direct magnetic effect; with its inclusion their experimental results could be explained only by including both the direct and the AB effects. Later, Marton and his associates presented their experiment as evidence for, rather than against, the AB effect.

The magnetic interaction between the magnetic moments of the two protons in H₂ is in the form of a second rank tensor. Since we have measured the magnetic moments directly and know enough about the molecular wave function to make good corrections for the effects of zero point vibrations (Paper 5.2), we can accurately calculate the theoretical value of the magnetic spin–spin interaction. However, we measured the interaction accurately in Paper 2.5 and my paper with R. F. Code [Phys. Rev. A4, 1945–1959 (1971)], so the experimental and theoretical values can be directly compared. The excellent agreement strongly supports the theory. Alternatively, the sensitivity of the comparison can be used to set upper limits for any other moderately long range tensor interactions that could exist between two protons. I set such limits in Paper 6.3 and expressed the results both in terms of limiting values for additional interaction constants and in terms of the restrictions on field theories mediated by the exchange of low mass particles. Many years later these restrictions became important when field theories with tensor interactions were seriously proposed.

Philosophers and historians of science, when discussing the Heisenberg uncertainty principle, often imply that the principal effects of quantum mechanics on measurements are to reduce the attainable precision. In this paper I point out seven different ways in which quantum mechanics affects precision measurements and that six of these make highly precise measurements possible and meaningful while only one — the uncertainty principle — is a serious limitation to accuracy. The limitations of the uncertainty principle are valid and important, but they can often be partially overcome by various means, including measurements in long-lived states and observations of many atoms. The existence of quantized states and the identity principle — that two atoms in the same quantum state are not merely closely similar but truly identical — make highly precise measurements both possible and meaningful. Thus, in the commentary on Paper 2.8 the hyperfine separation of atomic hydrogen is measured to an accuracy of one part in a million million (10¹²). The identity principle assures that observers in France and the United States will get the same answer except for known relativistic corrections. On the other hand, a classical quantity, such as the height of the Eiffel Tower, cannot be measured nearly so accurately since it changes from one moment to the next.

At a conference honoring Y. Aharonov, I was urged to present a paper on my work with Wendell Furry (Paper 6.2) that had played such a major role in convincing the skeptical physics community of the validity of the original Aharonov–Bohm theory. However, I was reluctant to do so, since the field was far from my usual research. I then realized I might be able to develop analogous theorems for electrically neutral particles and for the sharp interference pattern with the separated oscillatory fields method. In Paper 6.5, I showed that in a neutron beam magnetic resonance experiment one can design an apparatus to determine the orientation state of the neutron in the intermediate region between the two oscillatory fields. However, if one does such an experiment, just as the sensitivity is good enough to determine the orientation state, the neutron resonance becomes sufficiently blurred by the Aharonov–Casher effect that a sharp interference pattern is no longer observable. This loss of the sharp resonance is analogous to the loss of the two-slit interference pattern in the AB effect. Although the two cases are analogous, there is an important difference. In the separated oscillatory fields method with a neutron spin there is a clear physical meaning to the linear superposition of states with spin up and spin down; it corresponds to a state with angular momentum orthogonal to the original orientations. As a result, the separated oscillatory fields method can be described classically by saying that in the first oscillatory field the spin vector is flipped π/2 radians, and if it precesses in the intermediate region by the same amount as the oscillator oscillates, the second oscillatory field will induce a similar π/2 rotation, giving rise to a sharp narrow resonance. Such an explanation is not possible with an electron two-slit experiment, since there is no classical analog of an electron being a superposition of two position states. The difference arises from the angular momentum being a three-dimensional vector so that a linear superposition of a spin up and a spin down state is a state of orthogonal angular momentum.