Encounters in Magnetic Resonances

The following sections are included:

• PREFACE

• TABLE OF CONTENTS

• Autobiographical Notes
  • Early Childhood
  • High School Days
  • College and the War Years
  • From Utrecht to Harvard
  • Graduate Studies at Harvard
  • Research in Leiden, 1947–1948
  • Harvard Society of Fellows, 1949–1951
  • Family Life in the United States
  • Member of the Harvard Faculty, 1951–1990
  • Outline of my Research
  • Graduate Students and Research Fellows
  • Teaching at Harvard
  • Administrative Duties at Harvard
  • Other Professional Activities
  • Professor Emeritus, 1990 —

Please refer to full text.

This note was submitted simultaneously with Paper 1.2 as a letter to the editor to the Physical Review. The two papers are my first contributions to nuclear magnetic resonance research and my first publications in the Physical Review. (I had three earlier papers published in the Dutch journal, Physica.) This note describes an experimental result which agrees with the then reigning concept of static local field distributions responsible for the line shape of a magnetic resonance line. The F¹⁹ nuclear spins occupy a simple cubic lattice in CaF₂. When the external magnetic field points along a body diagonal, the six nearest neighboring F¹⁹ spins do not contribute to a static local field component parallel to the external field. This was later called the "magic angle", when 3cos²ϑ - 1 = 0. The observed resonance is indeed narrowest in this direction…

Most observations on NMR in 1946 were in sharp contrast to then existing theoretical predictions regarding T₁ and T₂. We found that NMR lines in fluids and in many solids with motional degrees of freedom were much narrower than predicted by the second moment method. In these cases, the observed line width was determined by the inhomogeneity of the external magnetic field across the sample. We had found that our pole pieces were magnetically inhomogeneous and that a "sweet spot" occurred away from the center of the gap. The narrowest line we could obtain across a sample of about 5mm linear dimension had a width of 0.14 gauss. These crude observations rather naturally led to the concept of "local field averaging" or "motional narrowing." In the fall of 1946, Purcell, Pound and I would spend many evenings together in a basement room of the Lyman Laboratory of Physics where our magnet was located. We would move our index fingers, up or down, to describe the two spin states of the proton, quantized either parallel or antiparallel to the external field. The index fingers would move around in real space to pictorialize the temporal variations in the local field. It was clear that the local field produced by one proton at the location of the other proton(s) in the same water molecule would average close to zero due to rapid random rotation of the molecule in the fluid. We also pictured the mutual spin flip–flop process with our two index fingers flip-flopping in opposite directions. We realized that spin lattice relaxation would involve processes where only one spin would flip or two spins would flip in the same direction. These processes could be induced by local field components perpendicular to the external field with Fourier components at the resonant frequency or twice this frequency. During these bull sessions with six participating index fingers, a qualitative understanding of T₁ and T₂ processes in fluids was obtained. It was clear that T₂ should be "about equal" to T₁ for rapid motional narrowing. The real T₂ could not be determined because of inhomogeneity in our magnet, a 1905 Societe Genevoise model, powered by an assembly of truck batteries and a crude rheostat, but we could measure T₁…

While Purcell and Pound were primarily responsible for the experiment in hydrogen gas, I was concentrating on the problem of local field variations in liquids. I was familiar with the concept of the spectral density of a random function because I had prepared the lecture notes for a seminar series on Brownian motion given by Professor J.M.W. Milatz at the University of Utrecht in 1942. Purcell made the very helpful suggestion that I study Debye's book, Polar Molecules. He was obviously familiar with the relationship between dielectric losses at radio and microwave frequencies and the random rotation in polar liquids. I was able to derive a quantitative expression for the proton spin relaxation time in water, based on a calculation of the spectral density of the internal magnetic field caused by neighboring protons. I remember obtaining a final expression when I was confined in my dormitory with a severe cold between Christmas and New Year's Eve 1946. During November and December, I had measured the relaxation time T₁ in a large number of samples, including water, water-glycerin mixtures and hydrocarbons over a wide range of viscosities…

The first draft for this thesis was written during the summer of 1947 at Harvard University. Comments made by Professors E.M. Purcell and C.J. Gorter on my handwritten notes were incorporated. Gorter, who was visiting professor at Harvard during the summer of 1947, had offered me a research position at the Kamerlingh Ones laboratory in Leiden, which I accepted. It was clearly interesting to extend the NMR relaxation investigation to liquid helium temperatures. Besides this scientific reason, there was also the pull of my native country. The Ph.D. thesis defense at a Dutch university was a momentous social occasion, celebrated not only by academic colleagues, but also by family, relatives and friends. I had passed all my qualifying examinations in the Netherlands. If I were to obtain a Harvard Ph.D., I would have to take more exams, and I had neither the time nor the money to consider this less appealing option. Purcell was quite understanding of the situation, so I obtained the Dr. Phil. degree at the University of Leiden on research work carried out under his supervision at Harvard. Years later, the same situation happened to me in reverse. During the sixties, I supervised the research of three French students — Jacques Ducuing, Pierre Lallemand and Nicole Polonski. They all submitted their theses at the University of Paris…

The T₁ and T₂ mechanisms in fluids and solids with motional degrees of freedom other than lattice vibrations were understood in the summer of 1947. It was surmised that in ionic crystals such as CaF₂ or the alkalihalides, paramagnetic impurities were responsible for the fact that T₁ was many orders of magnitude shorter than predicted by Waller's theory. I decided that the best way to tackle this problem was to grow crystals with varying but known concentrations of paramagnetic ions. The relaxation T₁ was measured systematically in a series of crystals between liquid helium and room temperature. The results could be extrapolated to paramagnetic impurity concentrations of less than one part per million. The components of the electron spins S_z, parallel to external magnetic field, are not strictly time independent constants. Due to paramagnetic, electronic-spin-lattice processes, they flip at random times. This gives rise to time-varying local field components, perpendicular to the z-direction, which may flip the nuclear spins. Van Vleck liked this process so much that he labeled it the "Bloembergen dirt effect". This process is effective only for nuclear spins in the vicinity of a paramagnetic impurity. For low impurity concentrations, the bulk of the nuclear spins must transfer their Zeeman energy by "spin diffusion" to nuclei in the neighborhood of the impurity. This concept of heat conduction in a spin system with a local temperature gradient was first introduced in this paper…

Heitler and Teller predicted in 1936 quite reasonable relaxation times for nuclear spins in metals. It remained to verify the correctness of their theory. This was carried out for the first time in a sample of fine copper powder dispersed in paraffin in 1948. The relaxation time T₁ for the Cu⁶³ and Cu⁶⁵ is inversely proportional to the absolute temperature and proportional to the square of their hyperfine interactions with the conduction electrons, in good agreement with theory. Thus it could be concluded in the fall of 1948 that the basic T₁ and T₂ mechanisms in most classes of solids, liquids and gases were understood.

Please refer to full text.

In the summer of 1952, I received an invitation to speak at the first international physics conference to be held in Japan after World War II. It was to symbolize the reentry of Japanese physicists into the international community of scientists. In Japan we would be the guests of the Science Council of Japan. I accepted the invitation with the proviso that I could obtain transportation to and from Japan. I discovered to my surprise that Ed Purcell had not received a similar invitation. It occurred to me that the Japanese had (incorrectly) deduced from the order of the authors' names on the BPP paper that I was the senior author. When the Nobel Prize for Physics was announced in October 1952, the Japanese became aware of the facts and quickly sent an invitation to the new Nobel laureate, E.M. Purcell. Fortunately, they did not disinvite me. Purcell decided not to go, as it would involve a full month of additional travel added to his busy schedule…

During my first year in the Society of Fellows at Harvard, I had decided to familiarize myself with microwave techniques. I studied the magnetic resonance in nickel and supermalloy across the Curie point. The transition from paramagnetic to ferromagnetic resonance was found to be continuous (N. Bloembergen, Phys. Rev. 78, 572–280, 1950)…

My attention previously had been focused on the question of how the field of an electromagnetic oscillator drives the magnetic resonance. It occurred to me that a precessing magnetization conversely could drive an electromagnetic mode. This situation was also familiar to R.V. Pound, who together with E.M. Purcell had discussed the negative absorption in an inverted nuclear spin system in 1950. The same problem had already presented itself in the adiabatic rapid passage experiments of F. Bloch, W.W. Hansen and M. Packard in 1946. The NMR pulse techniques, originated by Erwin Hahn, and the 90° and 180° pulse developed by H.Y. Carr and E.M. Purcell, were also relevant to the coupling problem. It so happened that Professor R.H. Dicke from Princeton spent a sabbatical leave at Harvard in the spring of 1954. He had just published his quantum theoretical paper on superradiant states. These antecedents influenced Bob Pound and me to analyze the coupling between electromagnetic mode and a macroscopic precessing magnetization as a system of two coupled harmonic oscillators. We were vaguely aware of the fact that such a macroscopic magnetization could be considered as a coherent wave packet of Dicke superradiant states. Glauber later described the classical electromagnetic mode as a coherent superposition of Fock quantum states…

Following the ammonia beam maser concept and development by Gordon, Zeiger and Townes, there was widespread activity on maser action with two-level spin systems. The three methods to obtain an inverted or precessing magnetization were well known, as mentioned in the comments to the preceding paper. There was not much new physics involved in my opinion and I did not see the practical significance of such solid state masers, until I heard a colloquium talk at MIT by M.W.P. Strandberg. He did not say it during the lecture, but I asked him afterwards what motivated his interest and that of many others. He mentioned the possibility of a microwave amplifier with a very low noise temperature. This started me thinking about the problem. It was obvious that continuous wave operation for such an amplifier would be most desirable…

I never felt bad that we were somewhat slow in getting our maser to work. We learned a lot from our attempts, which first used the three levels of the Ni⁺⁺ ion in nickelfluosilicate. At the relatively long wavelength of the 21 cm^-1 it is very difficult to avoid cross-relaxation effects. The resonances between the Ni⁺⁺ energy levels were not sufficiently isolated. We therefore switched our attention to the four levels of the Cr³⁺ ions. Having started before synthetic ruby crystals became available to us, we grew our own crystals of magnetically dilute potassium cobalti-cyanide with a small percentage of Cr³⁺ replacing Co³⁺. We designed a cavity simultaneously resonant at X-band and at 21 cm. My postdoc Joe Artman, later professor of electrical engineering at Carnegie–Mellon in Pittsburgh, and my graduate student Sid Shapiro, later professor of electrical engineering at the University of Rochester, finally got the system to work while I was away on sabbatical leave at the Ecole Normale Superieure in Paris during the fall of 1957. Perhaps my presence at Harvard had retarded the successful outcome. At any rate, it was still the first maser demonstrated to operate at the astronomically important wavelength of the interstellar hydrogen line, although Bob Kingston at the MIT Lincoln laboratories succeeded at almost the same time to obtain maser action at 21 cm wavelength. In those years I was a consultant and had close interactions with the research group there, led by Benjamin Lax…

I was familiar with the problem of contact between different nuclear spin systems in LiF from the early experiments by Pound, Purcell and Ramsey at Harvard, and from the more recent experiments by Abragam and Proctor in Paris. I had also been exposed to so-called intermediate relaxation processes observed in the non-resonant relaxation experiments carried out by Gorter, de Vryer and others during my Leiden years. Spurred on by the problems of overlapping tails of different resonance lines in maser materials, a general sythesis of all these phenomena was achieved in the present paper. My graduate student, Peter S. Pershan, made a basic quantitative study of cross relaxation times in LiF. His results were incorporated on very short notice in the well-known text, Nuclear Magnetism by Anatole Abragam (Oxford University Press, 1960). Cross relaxation times intermediate between spin–spin relaxation times T₂ and spin-lattice relaxation times T₁ became firmly established as a result of this paper. Other cross relaxation effects involving multiple spin flip-flops were also introduced.

This paper summarizes the contents of Sidney Shapiro's Ph.D. thesis. It relates the background studies which were necessary for the successful operation of our 21 cm maser.

C.J. Gorter wanted a review of solid state masers in the series, "Progress in Low Temperature Physics," of which he was the editor. In order to maintain our cordial relations and to show my gratitude for my Leiden years, I consented to write this review in 1959 for his volume. In retrospect, it is clear that a serial publication aimed at low temperature physics did not catch the attention of the quantum electronics community. In a resource letter on masers published by the American Institute of Physics in the early sixties, my review is not even mentioned. Of course, a review written in 1959, eventually published in 1961, is not very effective in furthering a fast moving field of research…

This paper has been cited frequently because of widespread interest of chemists, biologists and medical researchers in the field of NMR. It is based on experimental data obtained by L.O. Morgan and A.W. Noble at the University of Texas in Austin. Professor Tom Morgan elected to spend a sabbatical leave at Harvard to collaborate with me on the theoretical interpretation. For me, it provided the opportunity to synthesize the work, started in 1947, and described in my Ph.D. thesis, with various other investigations on relaxation in paramagnetic solutions carried out during the decade of the fifties by me and others. This paper caps my research efforts in the field of magnetic relaxation…

Please refer to full text.

This brief note is an abstract of a ten-minute paper for the annual meeting of the American Physical Society in New York City in January 1949. The paper was never orally presented because my return from Leiden to Harvard, planned for early January 1949, was delayed by visa and transportation problems. The abstract is included because it describes the discovery of paramagnetic line shifts up to seven percent of the resonant frequency. This temperature dependent shift is much larger at liquid helium temperatures than the temperature independent shift due to paramagnetism in metals, discovered by Knight. His discovery was independent from, but somewhat later than, our work which was carried out in the fall of 1948. I believe it to be the first example of so-called chemical shifts.

This paper contains the full contents of my Leiden experiments, alluded to in the preceding abstract. I remember that in the room next to mine in the Kamerlingh Onnes Laboratory, R.P. Penrose, a visitor from Oxford, discovered the hyperfine structure in the electron paramagnetic microwave resonance in condensed matter. This hyperfine structure, discovered in a Tutton salt containing Cu²⁺ ions, is caused by the magnetic field produced by the nuclear magnetic moments of copper, interacting with the electron spin on the same ion. My fine structure was due to the magnetic field produced by the electron spins of the Cu⁺⁺ ions at the various locations of protons in the unit cell. We had several exciting conversations about these effects shortly after his discovery. His discovery was reported with some delay in a communication in Nature (R.P. Penrose, C.J. Gorter, A. Abragam and M.H.L. Pryce, Nature 163, 992–993, 1949)…

Nico Poulis worked with me as a graduate student in Leiden during the summer and fall of 1948. He was to take over the operation of my Leiden NMR experimental set-up after my return to Harvard, and would continue to work on NMR in magnetic materials for the remainder of his scientific career. He became a professor at Leiden in the late fifties. We teamed up briefly again in the summer of 1950, when I returned to the Netherlands to get married. I had obtained a single crystal of MnF₂ during a visit with Professor J.W. Stout at the University of Chicago. I had been invited to give a colloquium talk at Chicago in the spring of 1950 because they wanted to look me over for a possible faculty appointment there…

During my measurements on the nuclear relaxation time of Cu⁶³ and Cu⁶⁵ spins in metallic copper (see Paper 1.6), I had a quick look at a sample of brass filings. This unsuccesful result haunted me for several years and I discussed it with a graduate student T.J. Rowland, the only student in the Division of Engineering and Applied Sciences at Harvard with an interest in metal physics. When his advisor, Professor John Hobstetter, left Harvard in 1950, Ted Rowland was at a loss as to how to proceed with a Ph.D. thesis research program. He told me of his plight in 1951, just at the time when I had been appointed to the Harvard Faculty and was looking for my first graduate student. I proposed that we should look into the problem of nuclear magnetic resonance in alloys. Ted Rowland has more vivid and more detailed memories than I of the beginnings of this new field of investigation, and has described it in his contribution to the volume published in honor of my 70th birthday: T.J. Rowland, "Nuclear Magnetic Resonance in Metals: A Selective Review of the Beginning," Resonances, edited by M.D. Levenson, E. Mazur, P.S. Pershan and Y.R. Shen, World Scientific, Singapore 1990, pp. 21–27…

Already in 1953, the anomalous line widths of the Tl²⁰³ and Tl²⁰⁵ resonances in the pure metal had attracted our attention. Their nuclear magnetic moments differ by only one percent, but the Tl²⁰³ resonance was much broader than the Tl²⁰⁵ line, which itself was about ten times as large as the Van-Vleck type dipolar broadening. This suggested to us that the different isotopic abundances of two isotopes played a role. A scalar spin exchange interaction, leading to exchange narrowing between like isotopes and exchange broadening between unlike isotopes could then explain the anomaly…

Professor N.F. Mott invited me to a conference he had organized for July 1954 in Bristol. The use of magnetic resonance methods to study crystalline defects was the focal point of the conference. Mott even presaged that these techniques might become as valuable as x-ray diffraction. He clearly had more vision and foresight than I did at that time. I was allotted two slots on the program, during which I presented a broad overview of the influence of various types of imperfections on magnetic dipole and on electric quadrupole interactions of nuclear spins.

In September 1954, an International Conference on Electron Transport in Metals and Solids was held in Ottawa, Canada. I had been invited to present an overview of NMR work bearing on electronic structure of conductors. It was the only paper on this technique presented at the conference. It described the rapidly increasing experimental and theoretical interest in this topic…

This is another review article written eight years after my presentation at the Bristol conference in 1954. Professor Jacques Friedel had invited me to a conference on the electronic structure of metals held at his laboratory in Orsay of the University Paris Sud in the summer of 1962. My personal interests at that time had already shifted towards nonlinear optics, but I was glad to review this NMR topic, as I had had several stimulating conversations with Jacques Friedal about our work during the fifties. He later became more and more involved with the administration of science and he was serving as president of the Academie des Sciences when I last visited with him in Paris a few years ago. I was pleased to receive his autobigraphy, Graine de Mandarin, Odile-Jacob, Paris, 1994…

This paper is included in this selection despite its rather bland title and its easy accessibility because it introduces two important novel aspects in magnetic resonance, which are both subtle and complex. A clear discussion of one aspect has been given by Charles P. Slichter, who devotes a separate section, 7.11, in his well-known textbook Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1990) to this paper. The paper describes the contact between two nuclear spin systems with a large difference in their individual spin lattice relaxation times. The Cs¹³³ spins have a long relaxation time T₁. They are readily saturated by a resonant rf field H₁. By defining a second radiofrequency field for the resonance of the halogen spaced by an amount equal to γ_CsH₁, from its bare resonant frequency, a large transverse polarization of Cs¹³³ spins can be induced in a time much shorter than T₁. As Slichter explains, this is a precursor of the famous resonance condition introduced by E.L. Hahn and S. Hartman in the doubly rotating frame of two spin species in 1962…

In 1953, George B. Benedek obtained his Ph.D. degree for the study of relaxation times of protons in water and other fluids at high hydrostatic pressure. This work had been carried out under the supervision of Professors E.M. Purcell and P.W. Bridgman. It was a marriage of magnetic resonance and high pressure techniques. I was interested in extending such studies to solids, and it was easy to convince George Benedek to join my group as a research fellow. We also attracted a senior researcher from Japan, T. Kushida. They formed a highly productive team. My contribution was limited to the theoretical understanding of the equation of state and the pressure and temperature dependence of crystal fields. I was co-author of a paper which is readily accessible and is not reprinted in this volume: T. Kushida, G.B. Benedek and N. Bloembergen, "Dependence of the pure quadrupole resonance frequency on pressure and temperature," Physical Review 104, 1364–1377, 1956. Benedek soon became an assistant professor and, as a Harvard colleague, he pursued the studies of nuclear magnetic resonance at high pressure in many directions. The results of his work have been published in book form: G.B. Benedek, Magnetic Resonance at High Pressure, Interscience Publishers, New York, 1963. We have kept in touch with both the Benedek and the Kushida families throughout later years…

These five short communications all deal with the influence of an applied electric field on magnetic resonance lines. In a sense, it is a natural extension of the method of variation of external parameters such as hydrostatic pressure, uniaxial stress, temperature, etc. Earlier attempts had proved elusive. I remember several early discussions on the problem with T. Kushida. After he left Harvard to join the Ford Motor Company Research Laboratories in Dearborn, Michigan, he pursued the problem there. He independently found the effect in a crystal in NaBrO₃, while our first experimental result was obtained in a crystalline powder of NaClO₃. His result was published simultaneously with our paper 3.11: T. Kushida and T. Saiko, Physical Review Letters 7, 9–10, 1961…

These five short communications all deal with the influence of an applied electric field on magnetic resonance lines. In a sense, it is a natural extension of the method of variation of external parameters such as hydrostatic pressure, uniaxial stress, temperature, etc. Earlier attempts had proved elusive. I remember several early discussions on the problem with T. Kushida. After he left Harvard to join the Ford Motor Company Research Laboratories in Dearborn, Michigan, he pursued the problem there. He independently found the effect in a crystal in NaBrO₃, while our first experimental result was obtained in a crystalline powder of NaClO₃. His result was published simultaneously with our paper 3.11: T. Kushida and T. Saiko, Physical Review Letters 7, 9–10, 1961…

These five short communications all deal with the influence of an applied electric field on magnetic resonance lines. In a sense, it is a natural extension of the method of variation of external parameters such as hydrostatic pressure, uniaxial stress, temperature, etc. Earlier attempts had proved elusive. I remember several early discussions on the problem with T. Kushida. After he left Harvard to join the Ford Motor Company Research Laboratories in Dearborn, Michigan, he pursued the problem there. He independently found the effect in a crystal in NaBrO₃, while our first experimental result was obtained in a crystalline powder of NaClO₃. His result was published simultaneously with our paper 3.11: T. Kushida and T. Saiko, Physical Review Letters 7, 9–10, 1961…

These five short communications all deal with the influence of an applied electric field on magnetic resonance lines. In a sense, it is a natural extension of the method of variation of external parameters such as hydrostatic pressure, uniaxial stress, temperature, etc. Earlier attempts had proved elusive. I remember several early discussions on the problem with T. Kushida. After he left Harvard to join the Ford Motor Company Research Laboratories in Dearborn, Michigan, he pursued the problem there. He independently found the effect in a crystal in NaBrO₃, while our first experimental result was obtained in a crystalline powder of NaClO₃. His result was published simultaneously with our paper 3.11: T. Kushida and T. Saiko, Physical Review Letters 7, 9–10, 1961…

These five short communications all deal with the influence of an applied electric field on magnetic resonance lines. In a sense, it is a natural extension of the method of variation of external parameters such as hydrostatic pressure, uniaxial stress, temperature, etc. Earlier attempts had proved elusive. I remember several early discussions on the problem with T. Kushida. After he left Harvard to join the Ford Motor Company Research Laboratories in Dearborn, Michigan, he pursued the problem there. He independently found the effect in a crystal in NaBrO₃, while our first experimental result was obtained in a crystalline powder of NaClO₃. His result was published simultaneously with our paper 3.11: T. Kushida and T. Saiko, Physical Review Letters 7, 9–10, 1961…

The field of electrically induced effects in magnetic resonance grew very rapidly during the early sixties. In July 1962, I presented an overview at a meeting organized by the Colloque Ampère at Eindhoven in my native country. From there, I traveled via a conference in Paris where I reviewed the applications of magnetic resonance to alloy systems, to the First International Conference on Paramagnetic Resonance in Jerusalem, organized by Professor W. Low.

Since this was my first visit to Israel, I started my lecture with some of the earliest references to ruby. I had found these in the Oxford Dictionary of Quotations (Oxford University Press, 1955). They are both from the old testament: "The price of wisdom is above rubies" (Job 28.18), and "Wisdom is better than rubies" (Proverbs 8.11). I had checked these passages in the King James bible and in the classic Dutch bible, the Statenvertaling. Jewish scientists in the audience smiled and recognized the passages, but during social conversations in the evening it was pointed out to me that the original Hebrew text does not mention rubies in the quoted passages. The classical English, Dutch and French bible translations are all based on a faulty intermediate text. I later found that the New Oxford Bible translates the two passages as, "The price of wisdom is above pearls" and "Wisdom is better than jewels" respectively. Fortunately, my knowledge of physics was more appreciated in Jerusalem than my knowledge of religious literature.

When the editor-in-chief, D.D. Traficante, invited me to write an article for a special issue celebrating the fifth anniversary of his journal Concepts in Magnetic Resonance, I had to confess I was not familiar with the publication. After having seen a few issues, I agreed to write some historical comments on a field in which I had not been actively involved for about three decades. Many new journals had emerged to take care of the growing needs for communication in the rapidly expanding field. These include The Journal of Magnetic Resonance and more specialized journals dedicated to magnetic resonance in medicine or in biology or in solids. I had not kept abreast of all these developments, and therefore could only make some comments about the early history of the field and point out the connection between NMR and optical laser spectroscopy. My endeavors in nonlinear optics from its early beginnings in 1961 have always been guided or aided by my familiarity with the concepts of magnetic resonance and relaxation and with the Bloch equations. This note is a suitable endpoint for these encounters in magnetic resonance and points to a connection with another volume dedicated to encounters in nonlinear optics.