arXiv subjects

J. Carlson

Publications and source records attributed to J. Carlson.

105 records · Page 6Linked 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

Particle Mixing and Charge Asymmetric $ΛN$ Forces

We calculate the contributions of a particular set of charge asymmetric $ΛN$ interactions to the difference of the separation energies of $^4_Λ$He and $^4_Λ$H. We use perturbation theory with four-body variational Monte Carlo wave functions calculated from a Hamiltonian with two- and three-hadron forces. We compare with the data and with an earlier calculation made by one of us which employed a two-body wave function of the $Λ$-nucleus type.

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arXiv1999

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.

cond-mat↗

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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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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arXiv1997

Pairing Correlations in the Two-Dimensional Hubbard Model

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path method. For small lattice sizes and weak interactions, we find that the $d_{x^2-y^2}$ pairing correlations are stronger than the extended $s$ pairing correlations and are positive when the pair separation exceeds several lattice constants. As the system size or the interaction strength increases, the magnitude of the long-range part of both correlation functions vanishes.

cond-mat.str-el↗

arXiv1996

New approach to $^4$He charge distribution

We present a study of the $^4$He charge distribution based on realistic nucleonic wave functions and incorporation of the nucleon's quark substructure. The central depression of the proton point density seen in modern four-body calculations is too small by itself to lead to a correct description of the charge distribution. We utilize six-quark structures calculated in the Chromodielectric Model for N-N interactions, and we find a swelling of the proton charge distribution as the internucleon distance decreases. These charge distributions are combined with the $^4$He wave function using the Independent Pair Approximation and two-body distributions generated from Green's Function Monte Carlo calculations. We obtain a reasonably good fit to the experimental charge distribution without including meson exchange currents.

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arXiv1996

A Constrained Path Monte Carlo Method for Fermion Ground States

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an over-complete basis of Slater determinants. By constraining the determinants according to a trial wave function $|ψ_T\rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|ψ_T\rangle$ is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to $16\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.

cond-mat↗

arXiv1996

The "Hole" In He

The measurement and analysis of electron scattering from He-3 and He-4 by Sick and collaborators reported 20 years ago remains a matter of current interest. By unfolding the measured free-proton charge distribution, they deduced a depression in the central point nucleon density, which is not found in few-body calculations based on realistic potentials. We find that using wave functions from such calculations we can obtain good fits to the He charge distributions under the assumption that the proton charge size expands toward the center of the nucleus. The relationship to 6-quark Chromo-Dielectric Model calculations, is discussed. The expansion is larger than than the predictions of mean field bag calculations by others or our CDM calculations in the independent pair approximation. There is interest here in the search for a "smoking gun" signal of quark substructure.

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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.

nucl-th↗

arXiv1995

A Constrained Path Quantum Monte Carlo Method for Fermion Ground States

We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wavefunction $|Ψ_T \rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|Ψ_T\rangle$ is exact. We report results on the two-dimensional Hubbard model up to size $16\times 16$, for various electron fillings and interaction strengths.

cond-mat↗

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

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

Quantum simulations of the superfluid-insulator transition for two-dimensional, disordered, hard-core bosons

We introduce two novel quantum Monte Carlo methods and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the methods is appropriate for zero temperature and is based upon Green's function Monte Carlo; the other is a finite-temperature world-line cluster algorithm. In each case we find that the dynamical exponent is consistent with the theoretical prediction of $z=2$ by Fisher and co-workers.

cond-mat↗

arXiv1993

The Coulomb Sum and Proton-Proton Correlations in Few-Body Nuclei

In simple models of the nuclear charge operator, measurements of the Coulomb sum and the charge form factor of a nucleus directly determine the proton-proton correlations. We examine experimental results obtained for few-body nuclei at Bates and Saclay using models of the charge operator that include both one- and two-body terms. Previous analyses using one-body terms only have failed to reproduce experimental results. However, we find that the same operators which have been used to successfully describe the charge form factors also produce substantial agreement with measurements of the Coulomb sum.

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