Pairing correlations and transitions in nuclear systems

Abstract

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. A simple pairing interaction model is used in order to study and classify an eventual pairing phase transition in finite fermionic systems such as nuclei. We show that systems with as few as ∼ 10−16 fermions can exhibit clear features reminiscent of a phase transition.

Free energy and criticality in the nucleon pair breaking process

“…1 The ongoing breaking of further Cooper pairs overlapping in excitation energies above 2 MeV is therefore contrary to what is found in the schematic model of Ref. [18]. This is probably due to strong residual interactions in real nuclei, like the quadrupole-quadrupole interaction, which were not taken into account in the model calculation.…”

“…Now, the evolution of ∆F c with increasing system size L may determine the order of a possible phase transition [16,17]. These ideas have, e.g., recently been applied to analyze phase transitions in a schematic pairing model [18]. Figure 2 displays a schematic description of the entropy for even-even, odd-mass and odd-odd nuclei as function of excitation energy.…”

Exact mesoscopic correlation functions of the Richardson pairing model

“…This is the most interesting model from the condensed matter point of view. However for the description of pairing in nuclei other choices of the parameters ǫ α are more natural 9,40,41,44 . These could be treated by a simple adaptation of our results.…”

Level densities andγ-strength functions in148,149Sm

“…Negative heat capacity is usually taken as a signal of a first order phase transition [28] suggesting that the process of breaking a nucleon pair around E ∼ 2∆ appears like a phase transition of first order. Others claim that negative heat capacity in a small system like the nucleus is compatible with a second order phase transition [29].…”