A classical two-body Hamiltonian model and its mean field approximation

We extend a recent billiard model of the nuclear N -body Hamiltonian to consider a finite two-body interaction. This permits a treatment of the Hamiltonian by a mean field theory, and also allows the possibility to model reactions between nuclei. The density and the mean field potential can be accurately described by a scaling function which shows the qualitative features of the liquid drop picture of the nucleus. Typeset using REVTEX 1 The nuclear many-body problem is often approximated by phenomenological mean field or liquid drop models which serve as good starting points to study the shape and the spectrum of low lying single particle and collective excitations [1–3]. This well-known approach is a consequence of the inadequate knowledge of the microscopic nuclear Hamiltonian, and the difficulty in dealing with the many-body problem. The mean field approximation is commonly employed to make the many-body problem tractable. Therefore it is of interest to question of how well mean-field theory works for a given microscopic Hamiltonian that can be solved exactly. A promising model for such a program may readily be obtained from a recent billiard model of the nuclear N -body Hamiltonian. This is an interacting N -body system with two-body interactions that is rich enough to show various features of self-bound many-body systems yet simply enough to allow for practical calculations and an understanding [4]. Generalizing the model of ref. [4], we consider the Hamiltonian H = N ∑