Momentum and density dependence of the mean field in nuclear matter

Abstract

The momentum and density dependence of the mean field in nuclear matter has been studied with phenomenological effective interactions with particular emphasis on the influence of the functional form of the interaction in determining the high density and high momentum behaviour of the mean field. Emphasis is also given to choosing the effective interaction in a form simple enough to permit analytical calculations of various properties of nuclear matter with a minimum number of adjustable parameters. These simple effective interactions are found to have a zero-range density-dependent part similar to Skyrme interactions and a long-range density-independent part of conventional form, such as Yukawa, Gaussian and exponential. It is observed that the high density and the high momentum behaviour of the mean field in nuclear matter is essentially governed by the nature of the density dependence and the precise functional form of the long-range part of the exchange component of the effective interaction. The parameters of these interactions can be constrained to obtain a mean field in nuclear matter which is independent of the functional form of the exchange interaction in the range of momentum k = 0- and up to a density four times the standard nuclear matter density. However, beyond this range the functional form of the exchange interaction becomes important in determining the momentum and density dependence of the mean field in nuclear matter.