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We review recent progress in the theory of neutron matter with particular emphasis on its superfluid properties. Results of quantum Monte Carlo calculations of simple and realistic models of uniform superfluid neutron gas are discussed along with those of neutrons interacting in a potential well chosen to approximate neutron-rich oxygen isotopes. The properties of dilute superfluid Fermi gases that may be produced in atom traps, and their relations with neutron matter, are illustrated. The density dependence of the effective interaction between neutrons, used to describe neutron-rich systems with the mean field approximations, is also discussed., 7 pages, 2 figures

We review the present statiis of the many-body theory of nuclear and pure neutron matter based on realistic models of nuclear forces, The current models of two- and three-nucleon interactions are discussed along with recent results obtained with the Brueckner and variatioual methods. New initiatives in the variational method and quantuni Monte Carlo nicthods to study pure neutron matter are described, and finally, the analytic behavior of the energy of piire neutron matter at low densities is cliscussed.

The ground state energy of a six-neutron drop is computed with variational and Green{close_quote}s function Monte Carlo methods using the Argonne v{sub 18} two-nucleon and the Urbana three-nucleon potentials. Combined with earlier results from investigations of the drops {sup 8}n and {sup 7}n, this energy gives a 1p-shell pairing energy of (1.8{plus_minus}0.4)MeV. The generalized Skyrme effective interaction discussed in the earlier work is applied to these nuclei by calculating, for the open-shell drops {sup 7}n and {sup 6}n, the matrix elements of the Skyrme t matrix directly for the states involved. The pairing energy obtained is 1.50 MeV, in reasonable agreement with the accurate calculations. {copyright} {ital 1997} {ital The American Physical Society}

We show that, as a consequence of the requirement that nucleons in the bulk and in the surface of a nucleus be treated in a thermodynamically consistent way, the neutron skin thickness in neutron rich nuclei is simply related to the dependence of the surface tension on neutron excess. This relationship thus provides constraints on physically acceptable microscopic interactions and mass formulae for neutron rich nuclei, whose properties are of interest in both laboratory and cosmic situations.

Over the past quarter of a century, the challenge of understanding the properties of neutron stars has been a powerful stimulus to studies of neutron-rich matter. This review considers neutron-rich m�ltter at subnuclear densities. Under these conditions, the basic constituents of matter are neutrons, protons, and electrons, and their interactions are well characterized. In addition, theoretical many-body techniques are sufficiently well developed that properties of matter can be esti­ mated with a useful degree of precision. Among the topics addressed are the bulk and surface properties of neutron-rich matter, the prediction of nonspherical nuclei in neutron-star crusts, superfi uidity, the effects of fi nite temperature and departures from equilibrium, and the structure of the outer parts of neutron stars.

The phase boundary between the liquid matter of the interior of a neutron star and the solid matter that comprises the crust is studied. The matter is assumed to consist of electrons and non-relativistic neutrons and protons in beta equilibrium. The characteristic used to identify the phase boundary is the onset of instability of the uniform matter against proton clustering, and it is examined for four interactions either used previously in astrophysical studies — Skyrme 1′, SkM and FPS - or proposed here as an improvement — FPS21. The relationship of this important property of neutron-star matter to the neutron-matter character of each interaction is explored. Characteristic densities associated with proton drip and with the liquid-gas boundary of one- and two-fluid models of the matter are compared with the instability density. Properties of some other effective interactions, relativistic and non-relativistic, are compared with those of the interactions discussed. The desirability of more calculations of neutron-matter properties, and of the utilization of those that do exist when formulsting dense-matter equations of state, is emphasized. For the improved interaction FPS21, the crust fraction of the moment of inertia of a neutron star is estimated.

We have calculated the wave functions and energy levels of a two‐dimensional mesoscopic electron system having four‐fold symmetry and multiply connected topology, in both zero and finite magnetic fields (B fields). The electron distribution can be controlled in the multiply connected structure by changing the peripheral channel thickness. The energy levels oscillate as a function of the B field, with pronounced gaps, and the electronic states are classified into four kinds of eigenstates under the 90° rotation operation. The three‐dimensional wave functions of cylindrical and helical structures having this cross section are constructed.

We calculate properties of neutron star matter at subnuclear densities using an improved nuclear Hamiltonian. Nuclei disappear and the matter becomes uniform at a density of about 0.6n(s), where n(s) of about 0.16/cu fm is the saturation density of nuclear matter. As a consequence, the mass of matter in the crusts of neutron stars is only about half as large as previously estimated. In about half of that crustal mass, nuclear matter occurs in shapes very different from the roughly spherical nuclei familiar at lower densities. The thinner crust and the unusual nuclear shape have important consequences for theories of the rotational and thermal evolution of neutron stars, especialy theories of glitches.

Conditions in neutron stars are more extreme than almost any encountered on Earth: densities exceed those of atomic nuclei, and matter has a large neutron excess. During the past quarter of a century, the challenge of understanding neutron stars has stimulated physicists to confront conditions far different from those normally encountered terrestrially. Laboratory studies have in turn yielded important input for the studies of neutron stars. We discuss a number of examples of this continuing interplay between physics and astrophysics. The first is the equation of state of dense matter, which is the basis for all theoretical models of neutron stars. The second is the composition of dense matter. This has profound influence on neutrino generating processes in neutron stars, and hence on their cooling. A third example is nuclei with a large neutron excess, such as are expected to be present in the crusts of neutron stars. Properties of similar nuclei play an important role in theories of element production.

In a quantum dot the magnetic moment, proportional to the persistent currents, is given by the derivative with respect to the magnetic field of the energy of the system, which for noninteracting electrons is just the sum of the lowest filled one-particle levels. These quantities are calculated for round and square dots, with and without interior holes, using hard wall boundary conditions. The relation is traced between the old results of Landau for a large system and what may be expected in current experiments on small quantum dots of various sizes and shapes. For the square ring geometry at low and moderate magnetic fields we note and discuss the appearance of gaps separating braids of groups of four levels.

A computer program that permits the rapid simulation of electron motion in two-dimensional mesoscopic circuits of a certain type, in the presence of a magnetic field, is described. As an illustration, a preliminary comparison is made with experimental results of a loop circuit. The introduction of ‘gate’ into the computer version of the circuit can be used to find the connection between the properties of the circuit and the states of the isolated loop. Impurity elastic scattering can be simulated.

We review how inclusion of Landau damping of virtual exchanged quanta in the transverse interactions of particles in relativistic plasmas leads to finite rates of transport processes. We also summarize results of recent Boltzmann kinetic equation calculations, to leading order in the coupling strength, of the transport coefficients of relativistic plasmas.

A theoretical study is made of charged-particle motion in planar circuits made up of narrow wires, in the presence of a magnetic field of arbitrary strength, in the ballistic approximation. The basic element is a four-terminal junction of narrow wires, and its detailed properties are calculated. Its scattering probabilities strongly reflect the influence of quantum effects of the junction, including subband thresholds and virtual, resonant states, and the Hall resistance calculated from them may depart considerably from the classic wide-wire result. Physical features are related to the emergence of pinned Landau levels as the field strength increases. By suitably modifying the four-terminal method, it is extended to include elbow (``ssL'') and tee (``ssT'') junctions. The results are then used to construct linear six- and eight-terminal junctions, whose resistive properties are discussed. The Hall resistance is predicted to depend on which arms are used and on the stub spacing. The application of the method to the general linear series of junctions is then outlined. The four-terminal results are also applied to a square eight-terminal junction, to show the presence and the consequences of the Aharonov-Bohm effect in circuits with closed loops.

Uniform neutron matter is approximated by a cubic box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne $\vep $ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large nn scattering length, and does not begin with the Fermi-gas kinetic energy as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is ~ half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations employing Fermi hypernetted and single operator chain summation methods to study nucleon matter over a larger density range, with more realistic Hamiltonians including three-nucleon interactions., 25 pages, 10 figures

Variational calculations of nucleon matter, either symmetric nuclear or pure neutron matter, use Fermi hypernetted chain and single-operator chain summation methods to sum approximately the contributions of clusters of $g~3$ nucleons to the energy expectation value. The cluster contributions summed by these methods are discussed in detail, and it is shown that for realistic interactions the 3-body cluster contribution is larger than the sum of $g~4$-body contributions. We present a new method, based on representing cluster wave functions by multidimensional vectors in spin-isospin space, as is common in quantum Monte Carlo calculations of light nuclei, to calculate exactly the 3-body cluster contribution including 3-body forces and all but spin-orbit correlations. The variational energies obtained with the Argonne $v18$ 2- and Urbana IX 3-nucleon interactions, using the exact 2- and 3-body cluster contributions and the approximate $g~4$-body contributions summed with chain summation techniques are lower, closer to the empirical values for symmetric nuclear matter than in previous calculations using the operator chain summation approximation for the large 3-body cluster. In pure neutron matter the operator chain summation approximation is found to be fairly accurate for the 3-body cluster; the present results are only slightly higher than the previous ones. We also report on the results for the Argonne $v14$ 2-nucleon interaction without any 3-body interaction. This case has been studied with Brueckner's method including 2, 3, and parts of 4-hole line terms by Day and Wiringa [Phys. Rev. C 32, 1057 (1985)]. Our results are significantly lower than theirs.

Properties of dense nucleon matter and the structure of neutron stars are studied using variational chain summation methods and the new Argonne v18 two-nucleon interaction. The neutron star gravitational mass limit obtained with this interaction is 1.67 M_{solar}. Boost corrections to the two-nucleon interaction, which give the leading relativistic effect of order (v/c)^2, as well as three-nucleon interactions, are also included in the nuclear Hamiltonian. Their successive addition increases the mass limit to 1.80 and 2.20 M_{solar}. Hamiltonians including a three-nucleon interaction predict a transition in neutron star matter to a phase with neutral pion condensation at a baryon number density of 0.2 fm^{-3}. We also investigate the possibility of dense nucleon matter having an admixture of quark matter, described using the bag model equation of state. Neutron stars of 1.4 M_{solar} do not appear to have quark matter admixtures in their cores. However, the heaviest stars are predicted to have cores consisting of a quark and nucleon matter mixture. These admixtures reduce the maximum mass of neutron stars from 2.20 to 2.02 (1.91) M_{solar} for bag constant B = 200 (122) MeV/fm^3. Stars with pure quark matter in their cores are found to be unstable. We also consider the possibility that matter is maximally incompressible above an assumed density, and show that realistic models of nuclear forces limit the maximum mass of neutron stars to be below 2.5 M_{solar}. The effects of the phase transitions on the composition of neutron star matter and its adiabatic index are discussed., Comment: 39 pages RevTeX including 12 tables. 21 postscript figures. Submitted to Phys. Rev. C

The {ital J}{sup {pi}}=0{sup +} ground state of a drop of 8 neutrons and the lowest 1/2{sup {minus}} and 3/2{sup {minus}} states of 7-neutron drops, all in an external well, are computed accurately with variational and Green{close_quote}s function Monte Carlo methods for a Hamiltonian containing the Argonne {ital v}{sub 18} two-nucleon and Urbana IX three-nucleon potentials. These states are also calculated using Skyrme-type energy-density functionals. Commonly used functionals overestimate the central density of these drops and the spin-orbit splitting of 7-neutron drops. Improvements in the functionals are suggested. {copyright} {ital 1996 The American Physical Society.}

An overview is given of important aspects of the physics of dense matter below nuclear matter density. Among topics discussed axe electronic properties, the surface tension of neutron-rich and hot nuclei, the reduction of the Coulomb energy as a consequence of the close packing of nuclei, and the possibility of non-spherical nuclei. For the most part, the discussion of nuclear properties is based on generalizations of the liquid-drop model, but results of calculations based on more microscopic approaches are also given.

In calculating the transport properties of relativistic electromagnetic or quark-gluon plasmas microscopically, one encounters the problem of divergent constituent cross sections arising from the exchange of transverse photons or gluons. Inclusion of Landau damping of the virtual quanta exchanged provides an effective long-wavelength cutoff. Dominance of Landau damping over a possible magnetic mass in QCD is demonstrated in the weak-coupling limit. The viscosities of a pure gluon plasma and a quark-gluon plasma are calculated in weak coupling from a variational solution to the Boltzmann equation.

An approximation for the moment of inertia of a neutron star in terms of only its mass and radius is presented, and insight into it is obtained by examining the behavior of the relativistic structural equations. The approximation is accurate to approximately 10% for a variety of nuclear equations of state, for all except very low mass stars. It is combined with information about the neutron-star crust to obtain a simple expression (again in terms only of mass and radius) for the fractional moment of inertia of the crust.

In high-energy electron-nucleus scattering, a new quantity for characterizing the additional information about the structure of a nuclear transition contained in the current distributions is defined, the vorticity density. It is symmetrical between the states involved in the transition, and it is completely unconstrained by the transition charge distribution. It is evaluated and discussed for single-particle harmonic oscillator transitions, for hydrodynamic collective transitions, and then for 3− transitions in 208Pb as described by the random phase approximation. Its relationship to collectivity is discussed.

Discrepancies among experiments and theory on electron scattering from oriented holmium are partially resolved. An estimate is presented which suggests that the distorted-wave Born-approximation orientation effect calculated by Wright is too large by about a factor of 2. Distorted-wave Born approximation calculations (made with a coupled-channel program) are presented which confirm this suggestion. They agree well with the Stanford data for orientation perpendicular to the scattering plane. The previous discrepancy for orientation along the recoil-momentum direction is reduced, but is not removed. The sensitivity of these results to the charge shape is examined although a fit to the data is not made. Results are given of a complete coupled-channel calculation for the first three nuclear states. Suggestions are made for future work, and cross sections and orientation effects for energy-resolved scattering from holmium at 200 MeV are given. (AIP)

Optimum properties of particle inertial impactors for a two-dimensional ideal fluid are derived using conformal mapping techniques and improved numerical methods. Results of sequential calculations of one-dimensional contour integrals are matched with analytical expressions for fluid properties near the stagnation point. Particle trajectories are numerically simulated for a range of jet-to-plate spacings and fluid deflecting plate angles. These results are compared with the calculations of Davies and Aylward for a deflecting plate angle beta =90 degrees . It is found that an unconventional angle beta not=90 degrees exists for a given jet-to-plate spacing which maximises the slope of the particle efficiency curves. Although the conclusions are derived for an ideal fluid (Re= infinity ), similar results should apply for impactors operating at finite Reynolds numbers.

We have computed the energy and the wave function for an electron caught at the intersection of two narrow channels. There are two bound energies for the case with fourfold rotational symmetry. For impenetrable walls the energies are ${E}_{1}$=0.66${E}_{t}$ and ${E}_{2}$=3.72${E}_{t}$, where the threshold for propagation of electrons in one channel is ${E}_{t}$=h${\ifmmode\bar\else\textasciimacron\fi{}}^{2}$${\ensuremath{\pi}}^{2}$/2${m}^{\mathrm{*}}$${w}^{2}$ and w is the width of the channel. The state at ${E}_{2}$ is bound only because it has odd parity and thus cannot decay into the even-parity propagating wave at the same energy. (The odd-parity propagation threshold is at 4${E}_{t}$.) We have also computed the transmission and reflection probabilities in the propagating case for a range of energies up to slightly above the odd-parity threshold.

We explore some properties of dense matter in Skyrme's chiral soliton model and show that at high densities the energy density varies as ${n}^{\frac{4}{3}}$, where $n$ is the baryon density. This is quite different from the behavior of conventional nuclear models, but is very similar to that of quark matter. The maximum mass of neutron stars constructed of such matter is significantly lower than that for most other versions of dense matter and may account for the absence of neutron stars in many extended supernova remnants. The phase transition to quark matter is expected to be softened considerably by such a nuclear-matter model.

We analyze the process of fragmentation in heavy-ion interactions from the viewpoint of growth of instabilities in hot expanding nuclear matter. The growth rates of modes in a medium unstable to small density perturbations of finite wavelength are calculated from a kinetic equation. This enables us to treat the case where the nucleon mean free path is comparable to or greater than the wavelength of the fluctuation, and the temperature is arbitrary. We estimate for hot nuclear matter the initial conditions which, after expansion, will result in fragmentation, evaporation, or vaporization.

Fragmentation in heavy-ion collisions is studied theoretically by examining the conditions under which density fluctuations may grow during the expansion of a sphere of heated or superdense nuclear matter. Matter is described by the realistic equation of state of Friedman and Pandharipande. The growth rates and accumulated growth factors depend sensitively on the wavenumbers of the fluctuations. Growth rates are examined in the limiting regimes of hydrodynamic and of collisionless motion, and the effects of viscous damping and thermal conduction are also considered.

We have performed optical-model calculations using the Klein-Gordon and the Dirac equations for the 600 MeV p-/sup 4/He scattering experiments of Boschitz et al., and the 1050 MeV p-/sup 4/He scattering experiments of Baker et al. We have compared these analyses with our previous analysis of the 1000 MeV p-/sup 4/He experiment of Palevsky et al. In comparing the results at the three energies we find that the experiments require a slightly energy-dependent optical potential rms radius. The average value is in good agreement with the /sup 4/He matter radius obtained from electron scattering, and substantially smaller than the low energy /sup 4/He optical potential rms radius. On the other hand, the experiments require quite different values for the optical potential strength parameters. (AIP)

Characteristic 4.44-MeV $\ensuremath{\gamma}$ rays from the first excited state of carbon were observed in coincidence with scattered 4.5-GeV/c ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons in counters and wire spark chambers. The $\ensuremath{\gamma}$-ray angular distribution in the momentum-transfer frame confirms the electric quadrupole nature of the transition and reveals the polarization of the recoiling $^{12}\mathrm{C}*$ nucleus so that density matrix elements can be determined. A simple model with no adjustable parameters, which employs the distorted-wave impulse approximation and uses electron scattering data to obtain the nuclear transition matrix elements, predicts the angular distribution of the pions and the polarization of the $^{12}\mathrm{C}*$ recoils very well. However, the absolute values of the measured cross sections are only half as large as the predicted ones.

It is found that just below nuclear saturation density more stable forms of dense matter exist than the near-spherical nuclei or bubbles customarily assumed. Because of the large effect of the Coulomb lattice energy, cylindrical and planar geometries can occur, both as nuclei and as bubbles. It is suggested that in order to approximate more complicated kinds of short-range order, the dimensionality should be regarded as a continuous variable ranging from d = 3 (spheres) to d = 1 (planes). The dependence of d on density is illustrated, and its dependence on nuclear models discussed.

A simple phenomenological analysis of the scattering and absorption of low energy K -mesons by protons is presented. An effective range expansion is used to describe the complex phase shifts;s-wave interactions are assumed dominant; only the crudest approximation, that of zero effective range, is illustrated. The scattering and absorption of K--mesons by protons and the scattering of K+-mesons by protons are consistent with this zero range approximation. The appreciable fall-off of the K- elastic scattering cross-section with increasing energy as cornpared to the essential constancy of the K+ cross-section is attributable in large part to the presence of the absorption in flight for K- mesons. The connection between the cross-sections for absorption in flight from states of definite angular momentum and the capture rates from the corresponding bound states is explicitly stated and the possibility of correlating the data from the two sources is discussed.

A critical examination is made of the hypothesis of model independence in high-energy electron scattering from nuclei. Results are presented which indicate that, contrary to this hypothesis, any differences in nuclear charge distributions result in differences in the electron angular distributions which become more and more pronounced as the energy is increased. The fallacies of the arguments leading to this hypothesis are noted, and comments are made on the scattering process.

The details of a phase-shift calculation of high-energy electron scattering by nuclei are given, together with some preliminary results. A new method for summing the Legendre series for the Coulomb scattering amplitude is described. The results indicate that the first Born approximation does not give cross sections accurate enough for a reliable interpretation of the experiments. From a comparison of the few theoretical cross sections already obtained with the experiments in gold at 125 Mev, very tentative conclusions about the nuclear charge distribution are drawn. It is pointed out that an analysis of results at two or more energies will be a much more sensitive test of possible charge distributions.

New information is reported on differences between the charge distributions of Ca40 and of Ca44, obtained by means of elastic scattering of 250 MeV electrons. Attention is focused, experimentally and theoretically, on the difference in scattering between the two isotopes.

A relativistic wave equation for helium-like systems which gives energy levels correct to within α 2 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.

Assumptions and approximations made in the analysis of experiments on electron scattering are discussed. From the detailed shape of the differential cross section vs. angle curve, information is deduced about nuclear charge distributions. (W.D.M.)

A general treatment of the phase approach to scattering theory is presented. Equations are given for the difference in phase between the solutions of two general differential equations. The method is applied to potential scattering of Schrodinger and Dirac particles. By suitable choice of these differential equations phase equations of the kind obtained previously are obtained, and also some new ones. A remarkably simple result is obtained for the Dirac case in the extreme-relativistic limit. A method is given for matching the solutions to known exterior functions. A numerical comparison of the accuracies of this approach and of the usual one is given for two special cases.

The scattering of high-energy electrons from ${\mathrm{C}}^{12}$, reported previously, has been extended to 420 Mev. The elastic and inelastic scattering from the first excited level at 4.43 Mev has been studied between 33\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{}. The new data are in good agreement with what one would expect from the earlier measurements on ${\mathrm{C}}^{12}$ performed at 187 Mev. Additional measurements of the elastic ${\mathrm{O}}^{16}$-scattering cross sections of 240-, 360-, and 420-Mev electrons as functions of the scattering angle furnish information on the size and shape of the ${\mathrm{O}}^{16}$ nucleus. Pronounced diffraction minima in the angular distributions were observed for ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$. The experimental results are compared with the predictions of a theoretical phase-shift analysis derived for the harmonic-well independent-particle model of the nucleus. Preliminary best fits confirm the shell-model predictions for the charge density distribution of these $p$-shell nuclei. The preliminary analysis of the data shows that the length parameter of the well is 1.66\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for ${\mathrm{C}}^{12}$, and 1.76\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for ${\mathrm{O}}^{16}$, thus indicating a slight variation of the curvature of the harmonic well as the $p$ shell is filled in.

A simple relationship between elastic scattering amplitudes and monopole excitation amplitudes is pointed out and illustrated. It applies to potential scattering, and can be used for the nucleon-nucleus problem as well as electron-nucleus scattering. The example of scattering of electrons by carbon and calcium is used to illustrate the method.

Partial-wave calculations of electron and positron scattering by cobalt and bismuth are presented, and compared with the experimental results of Goldemberg, Pine, and Yount. A physical description of the scattering process is given which throws light on the general behavior of the calculational cross sections. Their dependence on incident energy, and on the assumed nuclear charge distribution is discussed. (auth)