Extensions of the Variational Method with an Explicit Energy Functional for Nuclear Matter with Spin-Orbit Force

Abstract

Two extensions of the variational method with explicit energy functionals (EEFs) with respect to the spin-orbit force were performed. In this method, the energy per nucleon of nuclear matter is explicitly expressed as a functional of various two-body distribution functions, starting from realistic nuclear forces. The energy was then minimized by solving the Euler–Lagrange equation for the distribution functions derived from the EEF. In the first extension, an EEF of symmetric nuclear matter at zero temperature was constructed using the two-body central, tensor, and spin-orbit nuclear forces. The energy per nucleon calculated using the Argonne v8’ two-body nuclear potential was found to be lower than those calculated using other many-body methods, implying that the energy contribution caused by the spin-orbit correlation, whose relative orbital angular momentum operator acts on other correlations, is necessary. In a subsequent extension, the EEF of neutron matter at zero temperature, including the spin-orbit force, was extended to neutron matter at finite temperatures using the method by Schmidt and Pandharipande. The thermodynamic quantities of neutron matter calculated using the Argonne v8’ nuclear potential were found to be reasonable and self-consistent.

Keywords

• nuclear matter
• variational method
• nuclear force