Variations on a theme of nuclear matter

TLDR

The authors review new techniques for applying the variational method to the nuclear matter problem. They employ a correlated variational wave function and use diagrammatic cluster expansion and chain‑summation techniques to compute expectation values, while also reviewing other methods for calculating binding energies of quantum fluids. Recent calculations for simplified nuclear matter models have converged, but realistic models including spin‑orbit forces still yield either insufficient binding or overly high equilibrium densities.

Abstract

The authors review new techniques developed to apply the variational method to the nuclear matter problem. The variational wave function is taken to be ($S{\ensuremath{\Pi}}_{i<j}{\mathrm{F}}_{\mathrm{ij}}$) $\ensuremath{\Phi}$; the correlation operators ${\mathrm{F}}_{\mathrm{ij}}$ can in principle induce central, backflow, spin isospin, tensor, etc. correlations, and $\ensuremath{\Phi}$ is the ideal Fermi gas wave function. The application of diagrammatic cluster expansion and chain summation techniques to calculate expectation values with such wave functions is discussed in detail. The authors also give a brief overview of various other approaches to the calculation of the binding energies of quantum fluids, and a comparison of results for simple systems such ad helium liquids. Results obtained by various methods for simplified models of nuclear matter, which include central, spin, isospin, and tensor forces, have converged significantly in recent months. Results obtained with more realistic models which include the spin-orbit potentials are also discussed. The potential models considered so far either give too little binding or too high equilibrium density.