Determination of nuclear level densities from experimental information.

A novel Information Theory based method for determining the density of states from prior information is presented. The energy dependence of the density of states is determined from the observed number of states per energy interval and model calculations suggest that the method is sufficiently reliable to calculate the thermal properties of nuclei over a reasonable temperature range. 21.10.Ma Typeset using REVTEX 1 The simplest expression for the nuclear level density has been obtained in the Fermi-gas model by Bethe [1–3] and later modified by Bloch [4–6]. There are, however, a number of shortcomings in this approach. For example, the lack of coupling to the collective part of the nuclear spectrum leads to an energy-independent level density parameter. Recently there has been considerable theoretical activity in the determination of the nuclear manybody density of states, taking into account shell, pairing, and deformation effects [7,8], finite size effects [9], and thermal and quantal effects [10,11] as well as improvements in the determination of the spin cut-off factors [12]. Furthermore, the multiple inverse Laplace transform used to determine the nuclear density of states from the Grand-Canonical partition function of a Fermi gas appears to lead to certain inconsistencies in the folding of nuclear level densities [13]. In spite of these deficiencies Bloch’s formula is widely used, particularly as a means of parameterizing the experimentally determined nuclear level densities [14]. Generally the level density parameter is taken to be constant. Should it be energy dependent, an a priori form for the energy dependence must be assumed. In the present work we will demonstrate a simple means of extracting the nuclear level density from the experimental information, based on Information Theory [15]. We wish to determine the distribution of states or level density, ρ(E), for a nucleus such that