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arXiv:nucl-th/9405005 · Physical Review Letters

Thermal Properties of F54e

David J. Dean, S. E. Koonin, Karlheinz Langanke, P. B. Radha, Y. Alhassid

Published Apr 10, 1995• 70 citations
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Abstract

We study the thermal properties of ${}^{54}\mathrm{Fe}$ with the Brown-Richter interaction in the complete $1p0f$ model space. Monte Carlo calculations show a peak in the heat capacity and rapid increases in both the moment of inertia and $M1$ strength near a temperature of 1.1 MeV that are associated with the vanishing of proton-proton and neutron-neutron monopole pair correlations; neutron-proton correlations persist to higher temperatures. Our results are consistent with a Fermi gas level density whose backshift vanishes with increasing temperature.

DOI
10.1103/physrevlett.74.2909

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We study the thermal properties of 54Fe{}^{54}\mathrm{Fe}54Fe with the Brown-Richter interaction in the complete 1p0f1p0f1p0f model space. Monte Carlo calculations show a peak in the heat capacity and rapid increases in both the moment of inertia and M1M1M1 strength near a temperature of 1.1 MeV that are associated with the vanishing of proton-proton and neutron-neutron monopole pair correlations; neutron-proton correlations persist to higher temperatures. Our results are consistent with a Fermi gas level density whose backshift vanishes with increasing temperature.
In the two-component Fermi gas with contact interactions a pseudogap regime, in which pairing correlations are present without superfluidity, can exist at temperatures between the superfluid critical temperature TcT_cTc​ and a temperature T∗>TcT^* > T_cT∗>Tc​. However, the existence of a pseudogap in the unitary limit of infinite scattering length is debated. To help address this issue, we have used finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the spin-balanced homogeneous unitary Fermi gas on a lattice. We present results for the thermal energy, heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility, and compare them to experimental data when available. Our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. We find that the energy-staggering pairing gap vanishes above TcT_cTc​ and that T∗T^*T∗ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.
Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the 1S0{}^{1}{S}_{0}1S0​ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The 1S0{}^{1}{S}_{0}1S0​ pairing gap at $T\ensuremath{\approx}0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature Tc{T}_{c}Tc​ of the normal-to-superfluid phase transition and the pairing temperature scale T∗{T}^{*}T∗ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.
We assume that the neutron-neutron potential is well-behaved and velocity-dependent. We can then apply perturbation theory to find the energy per particle of a neutron gas, in the range of Fermi wave numbers 0.5<kf<20.5<{k}_{f}<20.5<kf​<2 ${\mathrm{f}}^{\ensuremath{-}1}$. The energy through first order is found in closed form, or by a single numerical integration. We use two different velocity-dependent potentials adjusted to fit observed nucleon-nucleon 1S^{1}S1S and 1D^{1}D1D phase shifts. In the range of densities 0.5<kf<10.5<{k}_{f}<10.5<kf​<1 ${\mathrm{f}}^{\ensuremath{-}1}$, our two potentials give nearly the same energy/particle (within 0.5 Mev); our values tend to run an Mev below values found by Brueckner et al., for the Gammel-Thaler potential. Wider divergences appear at higher densities. Our values, and Brueckner's are higher than those found by Salpeter by a semiempirical approach. A crude estimate of the second-order energy for our potentials indicates that perturbation theory converges rapidly in the density range considered. Our results suggest that at moderately low densities the energy/particle in a many-body system is insensitive to the shape or nonlocal character of the assumed two-body potential.
I study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, I analyze its energy (${E}_{\ensuremath{\downarrow}}$), effective mass (${m}_{\ensuremath{\downarrow}}^{*}$), and quasiparticle residue (${Z}_{\ensuremath{\downarrow}}$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner-Hartree-Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N3LO{\mathrm{N}}^{3}\mathrm{LO}N3LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the 1S0{}^{1}{S}_{0}1S0​ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. It is shown that for Fermi momenta between $\ensuremath{\approx}0.25$ and $\ensuremath{\approx}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ the energy, effective mass, and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $\ensuremath{-}0.604\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.635\phantom{\rule{0.16em}{0ex}}{E}_{F}$, $1.300\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.085\phantom{\rule{0.16em}{0ex}}m$, and $0.741<{Z}_{\ensuremath{\downarrow}}<0.836$ in the case of the chiral interaction, and $\ensuremath{-}0.621\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.643\phantom{\rule{0.16em}{0ex}}{E}_{F}$, $1.310\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.089\phantom{\rule{0.16em}{0ex}}m$, and $0.739<{Z}_{\ensuremath{\downarrow}}<0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25\ensuremath{\lesssim}{k}_{F}\ensuremath{\lesssim}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.
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