From Nuclei to Stars

The following sections are included:

• PREFACE

• A NOTE FROM PROFESSOR CHEN NING YANG

• CONTENTS

The following sections are included:

• Family Background and Early Life

• The First Eagle: Gregory Breit

• The Second Eagle: Rudolf Peierls and Birmingham

• Copenhagen, Princeton and Stony Brook

• The Third Eagle: Hans Bethe

• References and Endnotes

Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time. Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.

We summarize our current understanding of the connection between the QCD phase line and the chemical freeze-out curve as deduced from thermal analyses of yields of particles produced in central collisions between relativistic nuclei.

In “Bird of Passage”, Rudolf Peierls summarizes the situation of nuclear theory in the 1940's: “The success of the concept of the compound nucleus, consisting of strongly interacting nucleons, which Niels Bohr introduced in 1936, had mesmerized everybody into believing that there was no chance of describing nuclei in terms of the more or less independent motion of individual nucleons, the so-called shell model. Therefore the success of this model in 1949 came as a great surprise. Some of us, notably Brian Flowers and later Gerry Brown, studied various applications of the model.” The many applications that Gerry developed laid the foundations for the development of nuclear theory…

The state of the art in the study of π⁻, K⁻ and ∑⁻ atoms, along with the in-medium nuclear interactions deduced for these hadrons, is reviewed. A special emphasis is placed on recent developments in -nuclear physics, where a strongly attractive density dependent K⁻-nuclear potential of order 150–200MeV in nuclear matter emerges by fitting K⁻-atom data. This has interesting repercussions on quasibound nuclear states, on the composition of strange hadronic matter and on condensation in self bound hadronic systems.

We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.

The state of the art in dibaryons with strangeness is reviewed, including the K⁻pp dibaryon which signals the onset of –nuclear binding. A new type of strange dibaryons is highlighted, where the primary binding mechanism is provided by strong p-wave pion interactions, as demonstrated by a quasibound dibaryon calculation.

We derive an energy-independent and non-local potential for the baryon-baryon interaction from the Nambu-Bethe-Salpeter amplitude on the lattice. The method is applied to the nucleon-nucleon interactions with the (2+1)-flavor lattice QCD simulations. The central and tensor potentials are obtained as leading order terms of the velocity expansion of the non-local potential. The central potential has a repulsive core surrounded by an attractive well, while the tensor potential has intermediate and long range attractions. Validity of the velocity expansion is tested by the nucleon-nucleon interaction with finite relative momentum. Interactions among octet-baryons in the flavor SU(3) limit are also studied in full QCD simulations to unravel the origin of the repulsive core.

We study the role of density-dependent low-momentum nucleon-nucleon interactions in describing the anomalously long beta decay lifetime of ¹⁴C. We approach this problem both from the perspective of chiral effective field theory, in which genuine three-body forces generate an effective density-dependent two-body interaction, as well as from the perspective of Brown-Rho scaling, in which the masses and form factor cutoffs in one-boson-exchange interactions are modified in a dense nuclear medium due to the partial restoration of chiral symmetry. The beta decay transition of ¹⁴C to the ground state of ¹⁴N is calculated within the shell model using a model space consisting of two 0p-shell holes within a closed ¹⁶O core. The effective 0p-shell interaction is calculated up to second order in perturbation theory with single-particle energies extracted from experiment. We find that both three-nucleon forces and Brown-Rho scaling medium modifications give qualitatively similar results not only for the ground state to ground state Gamow-Teller transition but also for Gamow-Teller transitions from excited states of ¹⁴C to the ground state of ¹⁴N. In this way, it is observed that at a low-momentum scale of Λ_low−k = 2.1 fm⁻¹, medium-modifications of the nuclear force play an essential role in increasing the lifetime of ¹⁴C from a few minutes to an archaeologically long one of 5730 years.

High-precision calculations of electroweak processes in light nuclei are of great importance for multiple reasons. Gerry Brown together with Dan-Olof Riska published in 1972 a famous calculation on radiative capture of a thermal neutron on a proton, and their work was a precursor of subsequent great developments in high-precision calculations of electroweak processes in light nuclei. The application of effective field theory to nuclear systems is a prominent example of these developments. We present an overview of it with main emphasis placed on those topics in which we ourselves have been involved.

I have been working with Gerry for a long time, over 40 years, on a number of topics concerning the nucleon-nucleon interaction and the nuclear many-body problem. Time really goes by fast. In celeberating Gerry's birthday, I would really like to write here an extensive article recollecting the various projects which we have had fun to work on. But for practical reasons, let me here just review one recent topic which is also of interest to Gerry, namely the low-momentum interaction V_low−k and its application to finite nuclei and neutron stars. The V_low−k interaction works well for finite nuclei. But to satisfactorily describe the properties of large systems such as neutron stars, one may need to include the medium corrections from the Brown-Rho scaling and/or the three-nucleon force.

The determinations of neutron star masses are reviewed in light of a new measurement of 1.97M_⊙ for PSR J1614-2230 and an estimate of 2.4M_⊙ for the black widow pulsar. Using a simple analytic model related to the so-called maximally compact equation of state, model-independent upper limits to thermodynamic properties in neutron stars, such as energy density, pressure, baryon number density and chemical potential, are established which depend upon the neutron star maximum mass. Using the largest well-measured neutron star mass, 1.97M_⊙, it is possible to show that the energy density can never exceed about 2 GeV, the pressure about 1.3 GeV, and the baryon chemical potential about 2.1 GeV. Further, if quark matter comprises a significant component of neutron star cores, these limits are reduced to 1.3 GeV, 0.9 GeV, and 1.5 GeV, respectively. We also find the maximum binding energy of any neutron star is about 25% of the rest mass. Neutron matter properties and astrophysical constraints additionally imply an upper limit to the neutron star maximum mass of about 2.4M_⊙. A measured mass of 2.4M_⊙ would be incompatible with hybrid star models containing significant proportions of exotica in the form of hyperons, Bose condensates or quark matter.

Gerry Brown has been known more as nuclear theorists. However, last ten years we have been working on the formation and evolution of black hole (BH) binaries. Two different types of BH binaries were being considered in our works; (1) BH-neutron star (NS) binaries, and (2) soft X-ray transient sources that are BH binaries with companions from main sequence to giant. In this review, I will summarize our recent works on black hole binaries. For the black hole neutron star binaries, due to the supercritical accretion, we found a possibility that there might be more BH-NS binaries than NS-NS binaries. This possibility can be tested by the future gravitational wave observations. These binaries are also the possible sources of short-hard gamma-ray bursts. For the soft X-ray black hole binaries, we found the mass-period relation. As a byproduct, we predicted the spin of black holes in these systems, and a few of them were confirmed by the recent black hole spin observation. We also found that these black holes are the possible sources of long gamma-ray bursts that are caused by the rapidly spinning black holes.

We summarize the current status of our understanding of nuclear forces based upon chiral symmetry — an idea that was advocated by Gerry Brown already several decades ago.

These are personal recollections of how Gerry Brown's work and thinking influenced the development of the chiral effective Lagrangian based theory of nuclear forces.

The coefficients of diffusion, thermal conductivity, and shear viscosity are calculated for a system of non-relativistic particles interacting via a delta-shell potential V(r) = −υδ(r − R) when the average distance between particles is smaller than R. The roles of resonances and long scattering lengths including the unitary limit are examined. Results for ratios of diffusion to viscosity and viscosity to entropy density are presented for varying scattering lengths.

The history of how chiral symmetry has entered in nuclear physics, in which Gerry Brown and I have participated from 1970 up to today, is described from my personal viewpoint. The route of development we have traversed together goes from meson exchange currents, to “little chiral bag,” to chiral effective field theory, to “Brown-Rho scaling” and then to dense matter and chiral phase transition. It has been a great fun and exciting, some right and some wrong in what we have done together, but none that can be dismissed as “not even wrong.” We have found all along that whatever signal there may be for the manifestation of chiral symmetry in nuclear medium, be it at low density in meson exchange currents or at high density approaching the chiral phase transition, is rich in its intricacy and subtlety.

As an amusing incarnation of Nuclear Physics, the gauge bosons W, Z and the top quarks may form collective states bound by Higgs-based attraction. Since Higgs vacuum expectation value (VEV) is significantly modified inside them, they are called “bags”. We argue that creation of such objects can explain certain numerical studies of cosmological baryogenesis. Using as an example a hybrid model, combining inflationary preheating with cold electroweak transition, we identify “spots of unbroken phase” found in numerical studies of this scenario with such W–Z bags. We argue that the baryon number violation should happen predominantly inside these objects, and show that the rates calculated in numerical simulations can be analytically explained using finite-size pure gauge sphaleron solutions, developed previously in the QCD context by Carter, Ostrovsky and Shuryak (COS). Furthermore, we point out significant presence of the top quarks/antiquarks in these bags (which were not included in those numerical studies). We find that tops help to stabilize them for a longer time. Another enhancement of the transition rate comes from the “recycling” of the tops in the topological transition. Although we do not discuss it here, it is highly probable that this scenario would produce CP violation by the usual CKM matrix mechanism large enough to explain the observed baryon asymmetry.

The Landau-Migdal theory describes the linear response of strongly interacting Fermi systems by weakly interacting quasi particles. Gerry Brown initiated the first successful derivation of the quasi particle interaction from the ground state energy of nuclear matter. He realized the importance of the pion, which determines the long range part of the quasi-particle interaction and suggested to treat the pion exchange as an explicit part of the quasi particle interaction, which has to be complemented by Landau's contact interaction. The resulting quasi particle interaction has a strong momentum dependence which proved to be essential for a quantitative description of nuclear excitation modes with unnatural parity which are discussed in this review.

In a common method of constructing a single nucleon wave function in a given potential well, its energy is taken to be equal to its separation energy. This prescription is examined in view of Hartree-Fock theory where the potential well results from mutual interactions of the nucleons. It is shown that a more appropriate single nucleon energy of a valence nucleon is obtained by adding to the separation energy the rearrangement energy. This leads to a better prescription for constructing single nucleon wave functions in a given potential well.

Recent developments in holography have provided a new vista to the nucleon composition. A strongly coupled core nucleon tied with vector mesons emerge in line with the Cheshire cat principle. The cat is found to hide in the holographic direction. We discuss the one, two and many baryon problem in this context and point at the striking similarities between the holographic results and recent lattice simulations at strong coupling.