The geometry and phase transition behavior of configuration mixing in the interacting boson model

In the last 20 years there has been much interest in the study of nuclear coexistence phenomena, understood as the possibility of a simultaneous excitation of nuclear configurations which may lead to shape phase transitions [1]. The structural changes in the properties of physical systems are called phase transitions. These changes have long been studied in systems such as water in its gaseous, liquid and solid forms, the so-called thermodynamic phase transitions, where the control parameter is the temperature T . Phase transitions may occur as some of the control parameters that constrain the system are varied. In the late 70’s, Gilmore et al. [2] introduced phase transitions in which the control parameter g, is a parameter appearing in the quantum Hamiltonian describing the system. These “ground state energy phase transitions”, are in some ways similar to thermodynamic phase transitions and are known today as “quantum phase transitions”. In the context of the nuclear shell model the origin of coexistence can be traced back to many-particle many-hole excitations across shell gaps, which become energetically favourable as a result of the interplay between shell effects and the neutron-proton interaction [3]. For example, in the neutron-deficient lead isotopes, shape coexistence was predicted by May et al. [4] in a Nilsson framework including shell corrections.