Boson expansions and the cranking model

Eugene R. Marshalek

Heng Wu

By utilizing the 1/N expansion technique, the SU(3)-symmetry breaking caused by boson energies is discussed for the sdg Interacting Boson Model, and the analytical expressions of the intrinsic states are given under the approximation in the order of 1/N. It is also shown that the many body theories for a interacting boson system, such as Hartree-Bose method, Tamm- Dancoff approximation and Cranked Hartree approximation, are all special cases of the 1/N expansion technique.

Abraham Klein

W. van Dijk, F. Masafumi Toyama

We develop an approach to solving numerically the time-dependent Schrödinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an Euler-MacLaurin expansion for the time-integrated nonhomogeneous term. By comparing the numerical results with exact solutions of analytically solvable models, we find that the method leads to precision comparable to that of the generalized Crank-Nicolson method applied to homogeneous equations. Furthermore, the systematic increase in precision generally permits making estimates of the error.

M. C. Cambiaggio, J. Dukelsky, Guillermo R. Zemba

An extension to bosons of a constrained Hartree variational method is developed in which an angular momentum constraint is imposed. The method is applied to a soluble bosonic model, the Q-consistent Hamiltonian of Warner and Casten (1982). The results are compared not only with the exact ones but also with those obtained from the cranked Hartree variational approximation.

Peter Ring, Peter Schuck