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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., 7 pages, 2 figures

The Auxiliary Field Diffusion Monte Carlo method has been applied to simulate droplets of 7 and 8 neutrons. Results for realistic nucleon-nucleon interactions, which include tensor, spin--orbit and three--body forces, plus a standard one--body confining potential, have been compared with analogous calculations obtained with Green's Function Monte Carlo methods. We have studied the dependence of the binding energy, the one--body density and the spin--orbit splittings of $^7n$ on the depth of the confining potential. The results obtained show an overall agreement between the two quantum Monte Carlo methods, although there persist differences in the evaluation of spin--orbit forces, as previously indicated by bulk neutron matter calculations. Energy density functional models, largely used in astrophysical applications, seem to provide results significantly different from those of quantum simulations. Given its scaling behavior in the number of nucleons, the Auxiliary Field Diffusion Monte Carlo method seems to be one of the best candidate to perform {\sl ab initio} calculations on neutron rich nuclei., Comment: 8 pages, 3 figures

The Fermi hypernetted chain theory is reformulated to perform calculations with a finite number of fermions in a periodic box. The proposed method is expected to be useful to estimate the finite size effects in Quantum Monte Carlo simulations. Moreover, it can deal with anisotropic correlations as well as with different shaped boxes. Results are given for the neutron matter Bethe homework Hamiltonian and for nuclear matter with spin–isospin dependent central interactions. It is found that finite size effects come from both the kinetic and the potential energy expectation values.

Differences between the quasiparticle and the bare particle, as constituents of Fermi systems, mainly result from the effects of correlations. Comparative studies performed in liquid helium and indicating interesting similarities in the single particle properties of Bose and Fermi liquids will be discussed, also in connection with the theoretical and experimental quasihole strength in nuclei. A new Quantum Monte Carlo method for nuclear systems is also outlined.

Using a potential model, constrained by the hadron spectrum, for the confinement of relativistic quarks we explore the consequences of the substructure of nucleons for the binding energy and ground state wavefunction of 4 He. In its simplest form, this model gives a binding energy of 19 MeV. Quark wavefunctions differ from those associated with free nucleons by less than 10%, the rms quark radius is 1.34 fm and the resulting structure differs considerably from that of an expansion beginning from the (0s) 4 shell model. Considerable contributions to the binding energy, attractive from quark delocalization and repulsive from the quark hyperfine interaction, appear unavoidable. We conclude that these effects cannot be excluded from a detailed understanding of the properties of nuclear ground states.

We review variational calculations with a Jastrow wave function and show they are inadequate to calculate the zero-temperature equation of state E ( ρ ) for liquid helium. The importance of the Feynman-Cohen backflow around a moving particle is then discussed, and a variational wave function incorporating backflow is proposed. Results with this wave function are discussed for 3 He, 4 He and the v 2 potential model of nuclear matter. In both 4 He and 3 He the new wave function gives an energy and equilibrium density much closer to the experimental values than the Jastrow form. In the v 2 model the addition of the backflow terms to the Jastrow correlation lowers the energy by 2–3 MeV. Spin-isospin correlations can simulate the state dependence of the backflow correlation at small momenta. However, at nuclear-matter densities they can produce only about half of the lowering due to backflow.