Low-order variational calculations for model nuclear matter with the healing condition

Abstract

Low order calculations for the energy and density of model nuclear matter are carried out which make use of correlation functions $f(r)$ obtained by means of a differential equation. This is derived by variation of the two-body energy functional subject to the well known healing condition ($\ensuremath{\rho}\ensuremath{\int}{[1\ensuremath{-}f(r)]}^{2}D(r)d\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}=c, c$ a small constant). The problem of the determination of the corresponding Lagrangian multiplier has been investigated and we have concluded to determine it from the less deep minimum of the ratio $|\frac{{E}^{(3)}}{{E}^{(2)}}|$ of the third to the second term of the factorized Iwamoto-Yamada expansion of the energy. In addition, the corresponding condition for the minimum has been studied. Results for the values of the energy (which has been approximated by the first three terms of the factorized Iwamoto-Yamada expansion), the density, and several convergence quantities have been obtained with the test potentials of Iwamoto and Yamada and Ohmura, Morita, and Yamada. Compared to other results from low and high order calculations, it is seen that those of the density are similar, but those for the energy are smaller in our case, suggesting that correlation functions quite constrained have been obtained. The possibility of improvements is finally considered.NUCLEAR STRUCTURE Correlation function, binding energy, and Fermi momentum of nuclear matter. Low order calculation, healing condition.