Coherent states and the calculation of nuclear partition functions

Abstract

herent state. The solutions are constructed in the mean-field approximation, the random-phase approximation ~RPA!, and in a variational approach. The results of these approximations are compared with the exact solutions of each model, to determine their degree of validity. The paper has been organized as follows. The essentials about the use of coherent states in statistical mechanics are presented at the beginning of Sec. II. The partition function of the Lipkin SU~2! model is presented in Sec. II A. Section II A 1 describes the approximations introduced to calculate the matrix elements of the statistical operator acting on coherent states, namely, ~a! the exponential approximation and ~b! the Dyson boson mapping. Next, in Sec. II A 2 and Sec. II A 3 we show how to treat the Hamiltonian and the matrix elements of the density operator in the Weiss approximation and in a variational approach, respectively. In all cases the coherent states are used as trial states to perform the statistical sum. The critical behavior of the solutions is presented (