On the Problem of “Phase Transitions” in Nuclear Structure

Abstract

In the setting of Brice, so evocative of Homeric adventures, it may be appropriate to state that the nuclear physicist is forced to steer perpetually between the Scylla of inductive and the Charybdis of deductive reasoning. The first approach consists in attempting to organize the empirical facts in as model independent a fashion as possible with the aim of describing them analytically in order to gain deeper insight. The second approach consists in model building, where the model, although usually based on vastly simplifying assumptions, is expected to yield completeness and accuracy in its predictions. The nuclear structure talks we have heard so far during this workshop have proven very effectively the success of an approach which belongs in the second category, namely that associated with the Interacting Boson Model (IBM), in classifying the complex band structure of even-even nuclei. On the other hand the inductive method yielded the Variable Moment of Inertia (VMI) equations,^1,2 which give a precise description of ground state band energies of non-magic nuclei in terms of the rotational energy expression:

Research supported by the U. S. Department of Energy under Contract Nos. DE-AC02-76CH00016 and DE-AC02-80ER10576.