Statistical fluctuations of ground–state energies and binding energies in nuclei

The statistical fluctuations of the ground–state energy and of the binding energy of nuclei are investigated using both perturbation theory and supersymmetry. The fluctuations are induced by the experimentally observed stochastic behavior of levels in the vicinity of neutron threshold. The results are compared with a recent analysis of binding–energy fluctuations by Bohigas and Leboeuf, and with theoretical work by Feshbach et al. Introduction. In this letter, we address the question: How does the interaction with high–lying configurations affect the properties of nuclear ground states? In particular, what are the ensuing uncertainties, given the fact that not much is known about both, the interaction and the high–lying configurations? The question has arisen within two seemingly different contexts. (i) In a purely theoretical framework, and inspired by the analogy with the theory of the optical model (where averaging over the random fluctuations of the compound– nucleus resonances is an essential element), the question was addressed using a statistical model for the high–lying states. To this end, Feshbach’s projection operator method [1] has been extended to the bound–state problem and used to estimate the resulting uncertainties in ground–state energies and wave functions [2]. (ii) A series of ever–refined nuclear mass formulas with a sizeable number of parameters has been used to fit the known binding energies. In spite of many years of dedicated effort, there remains a difference between mass formulas and data: The data fluctuate about the (smooth) best fits. The fluctuations have a width of about 0.5 MeV and have been interpreted as being due to chaotic nuclear motion [3]. Since the spectral fluctuations of nuclear levels near neutron threshold (and near the Coulomb barrier for protons) follow random–matrix predictions [4], the question arises whether this fact can be used to account for the observed fluctuations. We present a novel statistical approach to the question formulated above. In contrast to Refs. [2], it is not our aim to estimate the theoretical uncertainty of nuclear binding energies resulting from the use of a mean–field approach. Rather, we are interested in the statistical fluctuations of ground–state and binding energies which are induced by those of high–lying configurations.