G.E. Brown

The Skyrme Model

We review the recent developments on the Skyrme model in the context of QCD, and analyze their relevance to low-energy phenomenology. The fundamentals of chiral symmetry and PCAC are presented, and their importance in effective chiral models of the Skyrme type discussed. The nature and properties of skyrmions are thoroughly investigated, with particular stress on the basic role of the Wess-Zumino term. The conventional Skyrme model is extended to the low-lying vector meson resonances, and the rudiments of vector meson dominance are elucidated. A detailed account of the static and dynamical properties of nucleons and δ-isobars is presented. The relevance of the Skyrme model to the nuclear many-body problem is outlined and its importance for boson exchange models stressed.

The little bag

Abstract A quark bag model for nucleons and isobars is made with pions existing only outside the bag. The pion field is introduced so as to ensure continuity of the axial-vector current at the boundary of the bag. It is argued that the bag can be quite small, of radius ∼ħ/ m n c where m n is the nucleon mass. The energy of the small bag is much larger than m n c 2 , but self-energy processes, especially those involving the pion, are invoked in order to bring the nucleon energy down to its physical value. The resulting theory looks very much like the old Yukawa theory for a pion with a small distributed source, the source now being described in terms of quarks.

On the interaction of two electrons

A relativistic wave equation for helium-like systems which gives energy levels correct to within α2 Ry is derived from quantum electrodynamics, care being taken in the handling of pair-production processes. Calculations made with it agree to this accuracy with Breit’s calculations.

Equation of State in the Gravitational Collapse of Stars

Abstract The equation of state in stellar collapse is derived from simple considerations, the crucial ingredient being that the entropy per nucleon remains small, of the order of unity (in units of k), during the entire collapse. In the early regime, ρ∼1010−1013 g/cm3, nuclei partially dissolve into α-particles and neutrons; the α-particles go back into the nuclei at higher densities. At the higher densities, nuclei are preserved right up to nuclear matter densities, at which point the nucleons are squeezed out of the nuclei. The low entropy per nucleon prevents the appearance of drip nucleons, which would add greatly to the net entropy. We find that electrons are captured by nuclei, the capture on free protons being negligible in comparison. Carrying the difference of neutron and proton chemical potentials μn−μp in our capture equation forces the energy of the resulting neutrinos to be low. Nonethelesd, neutrino trapping occurs at a density of about ρ = 1012 g/cm3. The fact that the ensuing development to higher densities is adiabatic makes our treatment in terms of entropy highly relevant. The resulting equation of state has an adiabatic index of roughly 4 3 coming from the degenerate leptons, but lowered slightly by electrons changing into neutrinos and by the nuclei dissolving into α-particles (although this latter process is reversed at the higher densities), right up to nuclear matter densities. At this point the equation of state suddenly stiffens, with Γ going up to Γ ≈ 2.5 and bounce at about three times nuclear matter density. In the later stages of the collapse, only neutrinos of energy ⪅10 MeV are able to get out into the photosphere, and these appear to be insufficient to blow off the mantle and envelope of the star. We do not carry our description into the region following the bounce, where a shock wave is presumably formed, and, therefore, we cannot answer the question as to whether the shock wave, in conjunction with neutrino transport, can dismantle the star, but a one-dimensional treatment shows the shock wave to be very promising in this respect.

Pion scattering and isobars in nuclei

Abstract General features of pion scattering by systems with equal numbers of neutrons and protons are discussed. To begin with, it is pointed out that most phenomena can be understood within the framework of a simple formalism in terms of an index of refraction for pions traversing nuclear matter. The pion-nucleon scattering amplitude is of resonance type, the resonance being identified with the Δ (1230 MeV) resonance. The Lorentz-Lorenz correction to the scattering, arising from short-range nucleon-nucleon correlations, is first discussed in classical terms, and then later in terms of isobar dynamics. It is found that there are only small differences in descriptions of pion-nucleon scattering in nucleon medium : a) in which the isobar is considered as a composite system of nucleon and pion, b) in which the isobar is considered to be an elementary particle. Self-energy interactions of the isobar with the nuclear medium are estimated, and found to be nearly as attractive as those of a nucleon. In the final section we outline a dynamical approach towards pion scattering from finite nuclei and give instruction on “How to know an isobar when you see one”.

Enhancement of low-mass dileptons in heavy ion collisions

Using a relativistic transport model for the expansion stage of S+Au collisions at 200 GeV/nucleon, we show that the recently observed enhancement of low-mass dileptons by the CERES Collaboration can be explained by the decrease of vector meson masses in hot and dense hadronic matter. {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}.

Meson exchange effects in n + p → d + γ

Abstract It is shown that an exchange-current correction of ≈ 10% to the threshold neutron capture n + p → d + γ can arise in a straightforward way from one-pion-exchange terms, most of it coming from the exchange moments written down by Villars in 1947. A large part of the correction comes from 1 S o to 3 D 1 terms, which have generally been overlooked.

Evolution of Binary Compact Objects That Merge

Beginning from massive binaries in the Galaxy, we evolve black hole-neutron star (BH-NS) binaries and binary neutron stars, such as the Hulse-Taylor system PSR 1913+16. The new point in our evolution is a quantitative calculation of the accretion of matter by a neutron star in a common-envelope evolution that sends it into a black hole. We calculate the mass of the latter to be ~2.4 M☉. The black hole fate of the first neutron star can only be avoided if the neutron star does not go through common-envelope evolution. This can be realized if the two massive binaries are sufficiently close in mass, not more than ~5% apart, so that they burn helium at the same time. Then their common hydrogen envelope is expelled by the tightening in the double He star system, with attendant hydrodynamical coupling to the envelope. In this way, we obtain a rate of 10-5 per yr per galaxy for production of the narrow neutron star binaries, such as Hulse-Taylor 1913+16 or Wolszczan 1934+12. This is in agreement with estimates based on the observed number of such systems extrapolated to the entire Galaxy, with beaming factors and corrections for the ~90% of binary pulsars estimated to be unobservable. Our chief conclusion is that the production rate for BH-NS binaries (in which the neutron star is unrecycled) is ~10-4 per yr per galaxy, an order of magnitude greater than that of neutron star binaries. Not only should this result in a factor of ~10 more mergings for gravitational wave detectors such as LIGO, but the signal should also be larger. We include some discussion of why BH-NS binaries have not been observed, but conclude that they should be actively searched for.

From kaon-nuclear interactions to kaon condensation

Abstract An effective chiral lagrangian in heavy-fermion formalism whose parameters are constrained by kaon-nucleon and kaon-nuclear interactions next to the leading order in chiral expansion is used to describe kaon condensation in dense “neutron star” matter. The critical density is found to be robust with respect to the parameters of the chiral lagrangian and is found to be ρ c ~ (3–4)ρ 0 . Once kaon condensation sets in, the system is no longer composed of neutron matter but of nuclear matter. Possible consequences on stellar collapse with the formation of compact “nuclear stars” or light mass black holes are pointed out.

Giant multipole resonances

Abstract The positions and the transition strengths of the giant multipole resonances of the spherical nuclei ( 16 O, 40 Ca, 90 Zr and 208 Pb) are calculated with large configuration spaces in the random phase approximation based on the Hartree-Fock ground states of a newly developed Skyrme interaction. Positions of many giant resonances are reproduced within 5 % of the experimental values. Most of the energy-weighted sum rules calculated from the double commutators are exhausted to within 13 % by the contribution from the RPA response function.