Lowest order constrained variational and local density approximation approach to the hot alpha particle

Abstract

The free energy of an alpha particle is calculated using the local density approximation in the harmonic oscillator basis. The effective two-body interactions are generated from the lowest order constrained variational (LOCV) calculation for nuclear matter at finite temperature, with the Reid and Δ-Reid potentials. The Fermi–Dirac distribution is used to calculate the entropy and the occupation probability of each state of alpha particle at a given temperature. The effective mass is treated as a variational parameter. Our zero temperature results with the Δ-Reid interaction agree well with the experimental saturation data of alpha particle and the other many-body techniques. The flashing temperature of ≈5 MeV is found, which is consistent with experimental evidence. It is concluded that a similar liquid–gas phase transition to that of nuclear matter is most probable in the alpha particle and heavier nuclei. PACS Nos.: 21.65+f, 21.10-k, 21.10Dr, 21.60-n