EquationsofMotion Method and the Extended Shell Model
Abstract
This paper presents the equationsofmotion method as a useful and flexible tool in the study of nuclear spectroscopy. It is partly a review, but also it introduces a new and much more powerful equationsofmotion technique which supercedes the older linearization methods. The older methods worked with operator equations. To obtain closed expressions they had to be linearized in a rather arbitrary manner. The present approach works with the groundstate expectation of operator equations and thereby avoids all problems of linearization. Thus, like the Green's function method, the equationsofmotion method becomes potentially exact. It has many advantages over Green's function methods, however, among which are its greater compactness, simplicity, and the physical insight it yields. The method is first applied to rederive the random phase approximation (RPA) and the quasiparticle RPA (QRPA) and to show precisely what terms they neglect. It is demonstrated that some of these terms have coherent phases. A higher RPA and QRPA are then derived to include these terms. The corrections have some interesting effects: notably, there is a reduction of the effective interaction strength and a stabilization of the nucleus against sudden phase transitions. The equationsofmotion method is also used to generalize, in a very simple and natural way, the HartreeFock (HF) and HartreeBogolyubov (HB) concepts of independent particles and quasiparticles to nonsimple ground states. The equationsofmotion method is presented as a simple extension of the shell model to the treatment of excitationg of a correlated ground state. By concentrating on the quantities of direct physical interest, the complexity of workins with correlated wavefunctions is avoided.
 Publication:

Reviews of Modern Physics
 Pub Date:
 January 1968
 DOI:
 10.1103/RevModPhys.40.153
 Bibcode:
 1968RvMP...40..153R