arXiv subjects

V. R. Pandharipande

Publications and source records attributed to V. R. Pandharipande.

34 records · Page 2Linked to original sources

arXiv1999

Kaon Condensation in Dense Matter

The kaon energy in neutron matter is calculated analytically with the Klein-Gordon equation, by making a Wigner-Seitz cell approximation and employing a $K^-N$ square well potential. The transition from the low density Lenz potential, proportional to scattering length, to the high density Hartree potential is found to begin at fairly low densities. Exact non-relativistic calculations of the kaon energy in a simple cubic crystal of neutrons are used to test the Wigner-Seitz and the Ericson-Ericson approximation methods. All the calculations indicate that by $\sim 4$ times nuclear matter density the Hartree limit is reached, and as the Hartree potential is less attractive, the density for kaon condensation appears to higher than previously estimated. Effects of a hypothetical repulsive core in the $K^-N$ potential are also studied.

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arXiv1999

Neutron Star Structure

A review of properties of matter in the interior of neutron stars is given. Particular attention is paid to recent many-body theory calculations of the properties of dense matter. Among topics discussed are the strong increase of tensor correlations at relatively low densities, the "relativistic boost term" in the interaction, and the sensitivity of properties of neutron star models to three-body forces.

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arXiv1998

Weak capture of protons by protons

The cross section for the proton weak capture reaction $^1H(p,e^+ν_e)^2H$ is calculated with wave functions obtained from a number of modern, realistic high-precision interactions. To minimize the uncertainty in the axial two-body current operator, its matrix element has been adjusted to reproduce the measured Gamow-Teller matrix element of tritium $β$ decay in model calculations using trinucleon wave functions from these interactions. A thorough analysis of the ambiguities that this procedure introduces in evaluating the two-body current contribution to the pp capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral $Λ^2(E=0)$ for the pp capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered.

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arXiv1998

Quantum Monte Carlo Studies of Relativistic Effects in Light Nuclei

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in 3H (4He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.

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arXiv1998

Center-of-mass effects on the quasi-hole spectroscopic factors in the 16O(e,e'p) reaction

The spectroscopic factors for the low-lying quasi-hole states observed in the 16O(e,e'p)15N reaction are reinvestigated with a variational Monte Carlo calculation for the structure of the initial and final nucleus. A computational error in a previous report is rectified. It is shown that a proper treatment of center-of-mass motion does not lead to a reduction of the spectroscopic factor for $p$-shell quasi-hole states, but rather to a 7% enhancement. This is in agreement with analytical results obtained in the harmonic oscillator model. The center-of-mass effect worsens the discrepancy between present theoretical models and the experimentally observed single-particle strength. We discuss the present status of this problem, including some other mechanisms that may be relevant in this respect.

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arXiv1998

The equation of state for nucleon matter and neutron star structure

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.

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arXiv1998

Many-body theory of nuclear and neutron star matter

We present results obtained for nuclei, nuclear and neutron star matter, and neutron star structure obtained with the recent Argonne v18 two- nucleon and Urbana IX three-nucleon interactions including relativistic boost corrections. These interactions predict that matter will undergo a transition to a spin layered phase with neutral pion condensation. We also consider the possibility of a transition to quark matter.

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arXiv1997

Quantum Monte Carlo calculations of nuclei with A \leq 7

We report quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A \leq 7 using a realistic Hamiltonian containing the Argonne v18 two-nucleon and Urbana IX three-nucleon potentials. A detailed description of the Green's function Monte Carlo algorithm for systems with state-dependent potentials is given and a number of tests of its convergence and accuracy are performed. We find that the Hamiltonian being used results in ground states of both 6Li and 7Li that are stable against breakup into subclusters, but somewhat underbound compared to experiment. We also have results for 6He, 7He, and their isobaric analogs. The known excitation spectra of all these nuclei are reproduced reasonably well and we predict a number of excited states in 6He and 7He. We also present spin-polarized one-body and several different two-body density distributions. These are the first microscopic calculations that directly produce nuclear shell structure from realistic interactions that fit NN scattering data.

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arXiv1996

Femtometer Toroidal Structures in Nuclei

The two-nucleon density distributions in states with isospin $T=0$, spin $S$=1 and projection $M_S$=0 and $\pm$1 are studied in $^2$H, $^{3,4}$He, $^{6,7}$Li and $^{16}$O. The equidensity surfaces for $M_S$=0 distributions are found to be toroidal in shape, while those of $M_S$=$\pm$1 have dumbbell shapes at large density. The dumbbell shapes are generated by rotating tori. The toroidal shapes indicate that the tensor correlations have near maximal strength at $r<2$ fm in all these nuclei. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron, the quasi-deuteron model, and the $dp$, $dd$ and $αd$ $L$=2 ($D$-wave) components in $^3$He, $^4$He and $^6$Li. The toroidal distribution has a maximum-density diameter of $\sim$1 fm and a half-maximum density thickness of $\sim$0.9 fm. Many realistic models of nuclear forces predict these values, which are supported by the observed electromagnetic form factors of the deuteron, and also predicted by classical Skyrme effective Lagrangians, related to QCD in the limit of infinite colors. Due to the rather small size of this structure, it could have a revealing relation to certain aspects of QCD.

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arXiv1995

Neutron Drops and Skyrme Energy-Density Functionals

The J$^π$=0$^+$ ground state of a drop of 8 neutrons and the lowest 1/2$^-$ and 3/2$^-$ states of 7-neutron drops, all in an external well, are computed accurately with variational and Green's function Monte Carlo methods for a Hamiltonian containing the Argonne $v_{18}$ 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.

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arXiv1995

Kaon Energies in Dense Matter

We discuss the role of kaon-nucleon and nucleon-nucleon correlations in kaon condensation in dense matter. Correlations raise the threshold density for kaon condensation, possibly to densities higher than those encountered in stable neutron stars.

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arXiv1995

Three-body correlations in few-body nuclei

A detailed comparison of Faddeev and variational wave functions for $^3$H, calculated with realistic nuclear forces, has been made to study the form of three-body correlations in few-body nuclei. Three new three-body correlations for use in variational wave functions have been identified, which substantially reduce the difference with the Faddeev wave function. The difference between the variational upper bound and the Faddeev binding energy is reduced by half, to typically $<2\%$. These three-body correlations also produce a significant lowering of the variational binding energy for $^4$He and larger nuclei.

nucl-th↗

arXiv1995

Quantum Monte Carlo Calculations of $A\leq6$ Nuclei

The energies of $^{3}H$, $^{3}He$, and $^{4}He$ ground states, the ${\frac{3}{2}}^{-}$ and ${\frac{1}{2}}^{-}$ scattering states of $^{5}He$, the ground states of $^{6}He$, $^{6}Li$, and $^{6}Be$ and the $3^{+}$ and $0^{+}$ excited states of $^{6}Li$ have been accurately calculated with the Green's function Monte Carlo method using realistic models of two- and three-nucleon interactions. The splitting of the $A=3$ isospin $T=\frac{1}{2}$ and $A=6$ isospin $T=1$, $J^π = 0^{+}$ multiplets is also studied. The observed energies and radii are generally well reproduced, however, some definite differences between theory and experiment can be identified.

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arXiv1994

Pedagogical Studies of Relativistic Hamiltonians

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energies, two- and many-body interactions and their boost corrections. We review the calculation of the boost correction of the two-body interaction from commutation relations of the Poincare group and show that its important terms can be easily understood from classical relativistic mechanics. The boost corrections for scalar- and vector- meson-exchange interactions, obtained from relativistic field theory, are shown to be in agreement with the results of the classical calculation. These boost corrections are also shown to be necessary to reproduce the known results of relativistic mean-field theories. We conclude with comments on the relativistic boost operator for the wave function of a nucleus. Several of the results presented in this pedagogical article are known. We hope that a better understanding of relativistic Hamiltonians and their relation to relativistic field theory is obtained by putting them together with a few new relations.

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arXiv1994

Variational Monte Carlo Calculations of $^3$H and $^4$He with a relativistic Hamiltonian - II

In relativistic Hamiltonians the two-nucleon interaction is expressed as a sum of $\tilde{v}_{ij}$, the interaction in the ${\bf P}_{ij}=0$ rest frame, and the ``boost interaction'' $δv({\bf P}_{ij})$ which depends upon the total momentum ${\bf P}_{ij}$ and vanishes in the rest frame. The $δv$ can be regarded as a sum of four terms: $δv_{RE}$, $δv_{LC}$, $δv_{TP}$ and $δv_{QM}$; the first three originate from the relativistic energy-momentum relation, Lorentz contraction and Thomas precession, while the last is purely quantum. The contributions of $δv_{RE}$ and $δv_{LC}$ have been previously calculated with the variational Monte Carlo method for $^3$H and $^4$He. In this brief note we report the results of similar calculations for the contributions of $δv_{TP}$ and $δv_{QM}$. These are found to be rather small.

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arXiv1994

Many-body effects in 16O(e,e'p)

Effects of nucleon-nucleon correlations on exclusive $(e,e'p)$ reactions on closed-shell nuclei leading to single-hole states are studied using $^{16}O(e,e'p)^{15}N$ ($6.32$ MeV, $3/2^-$) as an example. The quasi-hole wave function, calculated from the overlap of translationally invariant many-body variational wave functions containing realistic spatial, spin and isospin correlations, seems to describe the initial state of the struck proton accurately inside the nucleus, however it is too large at the surface. The effect of short-range correlations on the final state is found to be largely cancelled by the increase in the transparency for the struck proton. It is estimated that the values of the spectroscopic factors obtained with the DWIA may increase by a few percent due to correlation effects in the final state.

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