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Physical review. B, Condensed matter

Ground-state properties of spin-aligned deuterium

M. F. Flynn, J. W. Clark, E. Krotscheck, R. A. Smith, Robert M. Panoff

Published Sep 1, 1985• 18 citations
Publisher

Abstract

Ground-state properties of nuclear-spin-aligned deuterium are studied within the method of correlated basis functions (CBF), using Fermi-hypernetted-chain (FHNC) techniques to evaluate the requisite matrix elements of the Hamiltonian and identity attendant to a Jastrow choice of correlation operator. Results are presented for the ground-state energies of three hypothetical species of this system, calculated to low order in CBF perturbation theory, taking account of two- and three-body CBF effective interactions. Also included are data on the Jastrow momentum distribution and radial distribution function, computed using the FHNC scheme. These findings are supplemented by benchmark variational Monte Carlo results on the energy and radial distribution function. The three deuterium species provide examples of strongly interacting Fermi fluids, intermediate in coupling strength between nuclear matter and liquid $^{3}\mathrm{He}$.

DOI
10.1103/physrevb.32.2945

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Physical review. B, Condensed matter•Apr 1, 1991•9 citations
Ground-state properties of nuclear-spin-aligned deuterium are studied within the method of correlated basis functions (CBF), using Fermi-hypernetted-chain (FHNC) techniques to evaluate the requisite matrix elements of the Hamiltonian and identity attendant to a Jastrow choice of correlation operator. Results are presented for the ground-state energies of three hypothetical species of this system, calculated to low order in CBF perturbation theory, taking account of two- and three-body CBF effective interactions. Also included are data on the Jastrow momentum distribution and radial distribution function, computed using the FHNC scheme. These findings are supplemented by benchmark variational Monte Carlo results on the energy and radial distribution function. The three deuterium species provide examples of strongly interacting Fermi fluids, intermediate in coupling strength between nuclear matter and liquid 3He^{3}\mathrm{He}3He.
Microscopic prediction of the ground-state phase of electron-spin-aligned bulk atomic deuterium (D\ensuremath{\downarrow}) is attempted, based on the variational Monte Carlo method. The accurate pair potential of Kolos and Wolniewicz is assumed, and three versions of D\ensuremath{\downarrow} are considered, which, respectively, involve one, two, and three equally occupied nuclear spin states. The most definitive results on the zero-temperature equations of state of these systems are obtained with optimized ground-state trial wave functions incorporating Jastrow pair correlations, triplet correlations, and momentum-dependent backflow effects. The species D${\ensuremath{\downarrow}}_{3}$ is bound already at the pure Jastrow level, while the energy expectation value of D${\ensuremath{\downarrow}}_{2}$ dips below zero upon supplementing the Jastrow description by triplets and momentum-dependent backflow. The variational energy of D${\ensuremath{\downarrow}}_{1}$ remains positive under all current refinements of the ground-state trial function. We conclude that the systems D${\ensuremath{\downarrow}}_{3}$ and D${\ensuremath{\downarrow}}_{2}$, if they could be manufactured and stabilized at relevant densities, would be Fermi liquids at sufficiently low temperature; on the other hand, it is likely that D${\ensuremath{\downarrow}}_{1}$ would remain gaseous down to absolute zero.
Correlated-basis-function (CBF) theory, which has provided a firm foundation for ab initio calculations of the properties of quantum fluids such as liquid 4He^{4}\mathrm{He}4He, is adapted and applied at the Jastrow-Feenberg variational level to give an optimized description of the structure and of the elementary excitations of the Ising-spin model in a transverse magnetic field. A set of trial wave functions of Hartree-Jastrow form is assumed to describe the spatial correlations present in the ordered as well as the disordered ground states, and the Feynman Ansatz is consistently adopted to represent the elementary magnon states. The CBF analysis of the spin system employs the hypernetted-chain (HNC) formalism for a substitutional binary mixture of bosons and derives HNC equations for the spatial distribution functions which determine the ground-state energy expectation value. Functional variation of this quantity with respect to the magnetic order parameter and the trial states leads to two Euler-Lagrange equations, which may be interpreted as a renormalized Hartree equation for the optimal magnetization and as a paired-magnon equation for the magnetic correlation function that is analogous to the familiar paired-phonon equation for conventional quantum fluids.Numerical calculations are based on simple cubic lattices and an optimized nearest-neighbor Ansatz for the generating pseudopotential. Results are reported on the order parameter, the energy per lattice site, the transverse magnetization, and the magnon excitation energies as functions of the coupling parameter 0\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}\ensuremath{\infty} measuring the strength of the transverse magnetic field. We also present numerical results on the magnetic correlation function, the static structure function, and the correlation length. The system exhibits a second-order phase transition at a critical value ${\ensuremath{\lambda}}_{\mathit{c}}$ of the coupling strength. Our numerical calculations of the optimal order parameter yields ${\ensuremath{\lambda}}_{\mathit{c}}$\ensuremath{\simeq}5.17 for a simple cubic lattice and ${\ensuremath{\lambda}}_{\mathit{c}}$\ensuremath{\simeq}3.12 for a square planar lattice. The calculated data are in very good agreement with results derived from perturbation expansions in conjunction with Pad\'e techniques. \textcopyright{} 1996 The American Physical Society.
The first variational Monte Carlo calculations of the ground-state energy of spin-aligned deuterium D\ensuremath{\downarrow} are presented. Using Slater-Jastrow trial wave functions, the calculations are based on the accurate theoretical pair potential of Kolos and Wolniewicz for the $b{^{3}\ensuremath{\Sigma}_{\mathrm{u}}}^{+}$ state. For D\ensuremath{\downarrow} with equal population of the three nuclear-spin states, the minimum theoretical ground-state energy is found to be negative, implying that this system is a liquid at zero temperature under zero external pressure.
The generalized momentum distribution n(p,Q), related to the half-diagonal two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2\mathrm{h}}$(r1{\mathbf{r}}_{1}r1​,r2{\mathbf{r}}_{2}r2​,${\mathbf{r}}_{1}^{\ensuremath{'}}$) by Fourier transformation in the variables r1{\mathbf{r}}_{1}r1​-${\mathbf{r}}_{1}^{\ensuremath{'}}$ and r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​, plays a key role in the description of final-state interactions in the nuclear medium and other strongly interacting many-body systems. The function n(p,Q) is explored for two Jastrow-correlated models of infinite nuclear matter within a Fermi hypernetted-chain procedure. Significant departures from ideal Fermi gas behavior in certain kinematic domains provide signatures of the strong short-range correlations contained in these models. However, such deviations are less prominent than in earlier calculations based on low-order cluster truncations; correspondingly, violations of the sequential relation are greatly reduced. Simple prescriptions for improved low-cluster-order approximations to n(p,Q) are suggested by analysis of the results of the Fermi hypernetted-chain evaluation. These results are also used to assess the quality of Silver's approximation n(p,Q)\ensuremath{\approx}n(p)[S(Q)-1] for the generalized momentum distribution in terms of the ordinary momentum distribution n(p) and the static structure function S(Q), with findings that have potential implications for the interpretation of data from inclusive electron scattering by nuclei at high momentum transfers.
A method for the accurate evaluation of the diagonal and off-diagonal matrix elements of the Hamiltonian operator within the correlated basis function scheme is presented. Considering a basis consisting of Slater determinants, correlated with a Jastrow correlation factor, the expectation value of the kinetic energy operator has been expressed in the Jackson-Feenberg form. A diagrammatic analysis is presented for the construction and evaluation of the cluster expansions of the required quantities incorporating the Fermi hypernetted chain theory.
Deuterium atoms form a fascinating spin-one Fermi fluid of moderate density. Several properties of this fluid are evaluated using the self-consistent Green-function method of many-body theory. The aim is both to determine the properties and to see how well Green-function methods can be implemented in a moderately dense Fermi liquid. Approximations begin with the self-energy. This is separated into Brueckner-Hartree-Fock terms and correlation or two-hole--one-particle (HHP) terms. We find ground-state energies E in reasonable agreement with Monte Carlo values. While the HHP terms are not so important for E, they lead to a significant enhancement of the effective mass m∗{\mathit{m}}^{\mathrm{*}}m∗ at the Fermi surface ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$. The particle-hole interaction is calculated from the self-energy using the conserving Baym-Kadanoff method. This leads to Landau parameters F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​ that are positive and an F1s{\mathit{F}}_{1}^{\mathit{s}}F1s​ that is consistent with m∗{\mathit{m}}^{\mathrm{*}}m∗.