arXiv subjects

V. R. Pandharipande

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

At least 19 recordsLinked to original sources

arXiv2009

Superfluid Pairing in the Three Component Fermi Gas

We present an analysis of the SU(3) symmetric model of the strongly interacting three component Fermi gas in the continuum space using quantum Monte Carlo techniques. Three body effects predominate in the regime of interaction strength beyond that of threshold of the three particle bound state. However, we find that there is an interval of the interaction strength where the SU(2)$\otimes$U(1) broken symmetry superfluidity is possible. For a strong enough interaction, the SU(3) symmetry is restored and the superfluidity is suppressed. Within the interval of the broken symmetry, we also find that on average the particle pairs belonging to the species with superfluid pairing remain further separated than those without the superfluid pairing correlation.

physics.atom-ph↗

arXiv2006

Variational Theory of Hot Nucleon Matter

We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. In this paper we show that the correlated states of the microcanonical ensemble at a given temperature $T$ and density $ρ$ can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter.

nucl-th↗

arXiv2006

Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases

The ground state energy and pairing gap of the interacting Fermi gases calculated by the {\it ab initio} stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting ($1/ak_F <<0$) regime the BCS Hamiltonian should describe Landau quasi-particle energies and interactions, on the other hand in the strongly pairing regime, that is $1/ak_F \gtrsim 0$, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength $-\infty < 1/ak_F <0$ such as $ak_F \sim -1$. PACS: 05.30.Fk, 03.75.Ss, 21.65.+f

physics.atom-ph↗

arXiv2005

Delta Effects in Pion-Nucleon Scattering and the Strength of the Two-Pion-Exchange Three-Nucleon Interaction

We consider the relationship between P-wave pi-N scattering and the strength of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain why effective theories that do not contain the delta resonance as an explicit degree of freedom tend to overestimate the strength of the TPE3NI. The overestimation can be remedied by higher-order terms in these ``delta-less'' theories, but such terms are not yet included in state-of-the-art chiral EFT calculations of the nuclear force. This suggests that these calculations can only predict the strength of the TPE3NI to an accuracy of +/-25%.

nucl-th↗

arXiv2005

Ground State Properties of Fermi Gases in the Strongly Interacting Regime

The ground state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.

physics.atom-ph↗

arXiv2004

The Moment of Inertia of the Binary Pulsar J0737-3039A: Constraining the Nuclear Equation of State

We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate measurement (<~ 10 %) may be able to rule out some of these competing classes. Using the measured mass, spin and moment of inertia to identify the optimal model computed from different EOSs, one can determine the pulsar's radius.

astro-ph↗

arXiv2004

Virtual photon asymmetry for confined, interacting Dirac particles with spin symmetry

We study the Bjorken x dependence of the virtual photon spin asymmetry in polarized deep inelastic scattering of electrons from hadrons. We use an exactly solved relativistic potential model of the hadron, treating the constituents as independent massless Dirac particles bound to an infinitely massive force center. The potential is chosen to have spin symmetry and a linear radial dependence with spherical symmetry. The effect of interactions of the struck constituent with the remainder of the target on the longitudinal photon asymmetry is demonstrated. In particular, the small-x suppression of the photon asymmetry observed in polarized deep inelastic scattering from the proton is shown to be a consequence of these interactions. The effect of p--wave components of the Dirac wave function, long known to give an important contribution to the spin of hadrons, is explicitly demonstrated through their interference with the s--wave term.

nucl-th↗

arXiv2004

Quantum Monte Carlo Studies of Superfluid Fermi Gases

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length and the Fermi wave vector, $ak_F$. We report results for the ground state energy, the pairing gap $Δ$ and the quasiparticle spectrum. In the weak coupling regime, $1/ak_F < -1$, we obtain BCS superfluid and the energy gap $Δ$ is much smaller than the Fermi gas energy $E_{FG}$. When $ a > 0$, the interaction is strong enough to form bound molecules with energy $E_{mol}$. For $1/ak_F \gtrsim 0.5$ we find that weakly interacting composite bosons are formed in the superfluid gas with $Δ$ and gas energy per particle approaching $|E_{mol}|/2$. In this region we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS to BEC transition region, $-0.5 < 1/ak_F < 0.5$ is discussed.

physics.atom-ph↗

arXiv2004

Neutron Matter: A Superfluid Gas

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.

nucl-th↗

arXiv2003

Quadratic momentum dependence in the nucleon-nucleon interaction

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial-waves. In the Argonne v18 potential L**2 and (L.S)**2 operators are used to represent this dependence. The v18 potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in S-waves. However, p**2 rather than L**2 dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne v18pq, in which the L**2 and (L.S)**2 operators are replaced by p**2 and Qij operators, respectively. The quadratic momentum-dependent terms are smaller in the v18pq than in the v18 interaction. Results for the ground state binding energies of 3H, 3He, and 4He, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with the v18pq are slightly larger than those with v18 at interparticle distances < 1 fm. The two models provide essentially the same binding in the light nuclei, although the v18pq gains less attraction when a fixed three-nucleon potential is added.

nucl-th↗

arXiv2003

Superfluid Fermi Gases with Large Scattering Length

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be $(0.44 \pm 0.01)$ times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle.

physics.atom-ph↗

arXiv2003

Quantum Monte Carlo Calculations of Neutron Matter

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.

nucl-th↗

arXiv2002

Quenching of Weak Interactions in Nucleon Matter

We have calculated the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16 and 0.24 fm$^{-3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne v18 and Urbana IX two- and three-nucleon interactions. The squares of the charge current matrix elements are found to be quenched by 20 to 25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin up proton quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However $\geq$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.

nucl-th↗

arXiv2002

Elastic e-d Scattering Data and the Deuteron Wave Function

What range of momentum components in the deuteron wave function are available e d elastic scattering data sensitive to ? This question is addressed within the context of a model calculation of the deuteron form factors, based on realistic interactions and currents. It is shown that the data on the $A(q)$, $B(q)$, and $T_{20}(q)$ observables at $q \leq 6$ fm$^{-1}$ essentially probe momentum components up to $\simeq 4 m_π$.

nucl-th↗

arXiv2001

Cold Bose gases with large scattering lengths

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length $a$. At high densities, $n>>a^{-3}$, the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to $n^{2/3}$, as in Fermi systems.

cond-mat↗

arXiv2001

Realistic models of pion-exchange three-nucleon interactions

We present realistic models of pion-exchange three-nucleon interactions obtained by fitting the energies of all the 17 bound or narrow states of 3 <= A <= 8 nucleons, calculated with less than 2% error using the Green's function Monte Carlo method. The models contain two-pion-exchange terms due to pi-N scattering in S- and P-waves, three-pion-exchange terms due to ring diagrams with one Delta in the intermediate states, and a phenomenological repulsive term. The models have five parameters: the four strengths and the short-range cutoff. The 17 fitted energies are insufficient to determine all of them uniquely. We consider five models; they reproduce the observed energies with an rms error < 1% when used together with the Argonne v18 two-nucleon interaction. In one of the models the pi-N S-wave scattering interaction is set to zero; in all others it has the strength suggested by chiral effective field theory. One model also assumes that the pi-N P-wave scattering interaction has the strength suggested by effective field theories, and the cutoff is adjusted to fit the data. In all other models the cutoff is taken to be the same as in the AV18 interaction. The effect of relativistic boost correction is estimated. Results obtained with only Argonne v8' and v18 interactions are also reported. In addition, we present results for 7- and 8-body neutron drops in external potential wells.

nucl-th↗

arXiv2000

Many-body theory interpretation of deep inelastic scattering

We analyze data on deep inelastic scattering of electrons from the proton using ideas from standard many-body theory involving {\em bound} constituents subject to {\em interactions}. This leads us to expect, at large three-momentum transfer ${\bf{q}}$, scaling in terms of the variable $\tilde{y}=ν-{\bf |q|}$. The response at constant ${\bf |q|}$ scales well in this variable. Interaction effects are manifestly displayed in this approach. They are illustrated in two examples.

nucl-th↗

arXiv2000

Quantum Monte Carlo calculations of A=8 nuclei

We report quantum Monte Carlo calculations of ground and low-lying excited states for A=8 nuclei using a realistic Hamiltonian containing the Argonne v18 two-nucleon and Urbana IX three-nucleon potentials. The calculations begin with correlated eight-body wave functions that have a filled alpha-like core and four p-shell nucleons LS-coupled to the appropriate (J+/-;T) quantum numbers for the state of interest. After optimization, these variational wave functions are used as input to a Green's function Monte Carlo calculation made with a new constrained path algorithm. We find that the Hamiltonian produces an 8Be ground state that is within 2 MeV of the experimental resonance, but the other eight-body energies are progressively worse as the neutron-proton asymmetry increases. The 8Li ground state is stable against breakup into subclusters, but the 8He ground state is not. The excited state spectra are in fair agreement with experiment, with both the single-particle behavior of 8He and 8Li and the collective rotational behavior of 8Be being reproduced. We also examine energy differences in the T=1 and 2 isomultiplets and isospin-mixing matrix elements in the excited states of 8Be. Finally, we present densities, momentum distributions, and studies of the intrinsic shapes of these nuclei, with 8Be exhibiting a definite 2-alpha cluster structure.

nucl-th↗