S. Fantoni

Momentum distribution of nucleons in nuclear matter

Abstract We calculate the momentum distribution n(k) of nucleons in nuclear matter from a realistic hamiltonian. First the n(k) is calculated from a variational wave function containing central, spin, isospin, tensor and spin-orbit pair correlations. The non-central correlations are found to give the major part of the deviation of n(k) from the θ(kF-k) of a Fermi gas. Next we use second-order correlated-basis perturbation theory to study the effect of correlated 2p2h admixtures in the ground state. These admixtures give significant corrections to the variational n(k), particularly in the region k ∽ kF. They are necessary to obtain the correct behavior of n(k ∽ kF). The discontinuity of n(k) at k = kF is found to be 0.7 and its relations to the effective mass, the one-particle Green function and the difference between charge densities of 206Pb and 205Tl are discussed. The density dependence of n(k) is studied, and the n(k∽kF) is found to be relatively insensitive to density in the region ρ = 1 4 ρ 0 to ρ 0 .

Spectral function of finite nuclei and scattering of GeV electrons

Abstract We employ the local-density approximation to derive the spectral function P( k , E) of finite nuclei. For various densities of nuclear matter we calculate P( k , E) , and split it into the single-particle and correlated parts. For finite nuclei P( k , E) is calculated by combining the nuclear-matter correlated part, evaluated in local-density approximation, with the finite-nucleus single-particle part obtained from mean-field calculations or (e, e′p) experiments. These spectral functions are used to calculate cross sections for inclusive electron-nucleus scattering at large momentum transfer. The recoil-nucleon final-state interaction is treated in the local-density approximation as well.

A quantum Monte Carlo method for nucleon systems

Abstract We describe a quantum Monte Carlo method for Hamiltonians which include tensor and other spin interactions such as those that are commonly encountered in nuclear structure calculations. The main ingredients are a Hubbard-Stratonovich transformation to uncouple the spin degrees of freedom along with a fixed node approximation to maintain stability. We apply the method to neutron matter interacting with a central, spin-exchange, and tensor forces. The addition of isospin degrees of freedom is straightforward.

Microscopic calculation of the longitudinal response of nuclear matter

Abstract The orthogonalized version of correlated basis theory is used to evaluate the longitudinal response of nuclear matter from realistic nuclear interaction. The correlated 1plh excited states have been fully retained in the calculation. The 2p2h correlated states entering the self-energy insertions, have also been treated exactly. The calculated response results to be in good agreement with previous similar calculations of the density response of symmetrical nuclear matter which included the effect of 2p2h correlated states approximately via the optical potential. Its comparison with the response calculated along the Brueckner theory in the y -scaling region is also discussed. At moderately high values of the momentum transfer, the longitudinal response is compared with the available experimental data from quasi-free electron scattering off medium-heavy nuclei. Our theoretical estimates are in fair agreement with the data on 40 Ca, 48 Ca, 56 Fe and 238 U, except at the highest values of both the momentum transfer and missing energy.

Structure functions and correlations in nuclei

Abstract The static longitudinal structure function S L ( k ) and the static structure function S ( k ) of 3 H, 3 He and 4 He nuclei and nuclear matter are calculated using realistic wave functions obtained from Faddeev and variational calculations. In order to study the variation of the structure function with the number of particles in the system we also calculate S ( k ) of atomic helium liquid drops containing 4, 8, 20, 40, 70, 168 and 240 atoms. Monte Carlo integration is used to calculate the structure functions of finite systems, while those of nuclear matter are calculated with chain summation methods. The behavior of S ( k ) and S L ( k ) at small values of k is discussed. We find that the recent Saclay data on S L ( k ) of the 3 He nucleus are in agreement with theory. Though the data indicate the existence of correlations between the two protons in the 3 He nucleus, they are not accurate enough to draw interesting conclusions about the repulsive core in the nucleon-nucleon interaction. The structure functions of atomic helium liquid drops indicate a smooth variation of S ( k ) with the number of atoms in the drop. The S L ( k ) of the 4 He nucleus and nuclear matter are very similar for k > 1.5 fm −1 , and it appears plausible that S L ( k ) of nuclei having A > 3 may not depend significantly on A when k > 1.5 fm −1 .

Quantum Monte Carlo calculation of the equation of state of neutron matter

We calculated the equation of state of neutron matter at zero temperature by means of the auxiliary field diffusion Monte Carlo (AFDMC) method combined with a fixed-phase approximation. The calculation of the energy was carried out by simulating up to 114 neutrons in a periodic box. Special attention was given to reducing finite-size effects at the energy evaluation by adding to the interaction the effect due to the truncation of the simulation box, and by performing several simulations using different numbers of neutrons. The finite-size effects due to kinetic energy were also checked by employing the twist-averaged boundary conditions. We considered a realistic nuclear Hamiltonian containing modern two- and three-body interactions of the Argonne and Urbana family. The equation of state can be used to compare and calibrate other many-body calculations and to predict properties of neutron stars.

Equation of State of Superfluid Neutron Matter and the Calculation of the 1S0 Pairing Gap

We present a quantum Monte Carlo study of the zero-temperature equation of state of neutron matter and the computation of the 1S0 pairing gap in the low-density regime with rho < 0.04 fm(-3). The system is described by a nonrelativistic nuclear Hamiltonian including both two- and three-nucleon interactions of the Argonne and Urbana type. This model interaction provides very accurate results in the calculation of the binding energy of light nuclei. A suppression of the gap with respect to the pure BCS theory is found, but sensibly weaker than in other works that attempt to include polarization effects in an approximate way.

Introduction to modern methods of quantum many-body theory and their applications

Density functional theory microscopic description of quantum liquids the coupled cluster method and its application experiments with a Rubidium Bose-Einstein condensate theoretical aspects of Bose-Einstein condensation elementary excitations and dynamic structure of quantum fluids theory of correlated basis functions the magnetic susceptibility of liquid 3He the hyperspherical harmonic method - a review and some recent developments the nuclear many-body problem.

Model calculations of doubly closed shell nuclei in CBF theory (I)

Abstract Correlated basis function theory and Fermi hypernetted chain theory are extended to treat finite Fermi systems. In this first paper, the effects of the scalar nucleon-nucleon correlations are investigated by studying some model N = Z nuclei. Results of calculations performed using central nucleon-nucleon potentials, without tensor components, are presented and are compared with results from other theories.

Momentum distribution of liquid helium

We have obtained the one-body density matrix and the momentum distribution of liquid He atT=0 from Diffusion Monte Carlo simulations, using trial functions optimized via the Euler Monte Carlo (EMC) method. for4He we find a condensate fraction smaller than in previous calculation. For3He, which we have studied within the fixed-node approximation we analyze the momentum distribution around the Fermi surface. We also show that an approximate factorization of the one-body density matrix, ρ(r)≃ρu(r)ρB(r) holds, with ρu(r) and ρB(r) respectively the density matrix for the ideal (uncorrelated) Fermi gas and the density matrix or a mass 3 Bose system.