IMPROVED LOW-DENSITY EXPANSIONS FOR THE BINDING-ENERGY OF NUCLEAR-MATTER

We discuss recent formal and numerical progress which has been achieved in the investigation of the binding energy of nuclear matter in the framework of low-density expansions. We concentrate our study on the Brueckner-Hartree-Fock approximation. We show that it is the first order term of two different hole-line expansions, derived respectively from Green function theory and from Goldstone's linked cluster series. The existence of these two approaches is helpful for the determination of suitable choices for the single-particle energy, and for exhibiting the analogy and difference with the variational methods. Numerical results are confronted with upper bounds estimated from the Fermi hypernetted chain method, and with the binding energy obtained from the correlated basis functions approach. The Brueckner-Hartree-Fock approximation is satisfactory if one introduces a continuous single-particle potential which is attractive for intermediate states located near the Fermi momentum. It is found that the usual procedure of setting this potential to zero is not satisfactory at the two-hole-line level. The three-hole-line approximation of the Bethe-Brueckner approach, and the two-hole-line approximation of the Green function expansion, are not sensitive to the choice of the single-particle potential. © 1979.