New projection method and generalized rotational spectrum

Abstract

Lanczos's algorithm for the matrix eigenproblem is used to project out angular momentum (J) components from a given deformed intrinsic wave function, containing N different values of J. Using this method, it is proved that the low-lying energy spectrum of a nucleus obtained by using the wave functions projected from a deformed intrinsic state (Hartree-Fock, Hartree-Fock-Bogoliubov, or random-phase approximation) has a general form suggested by Bohr and Mottleson in their macroscopic approach, E(J)=E(β)+ Σ1N-1A_n(β)Jⁿ(J+1)ⁿ. Expressions for E( β) and An( β) are derived. The first iteration gives Skyrme's formula for the nuclear moment of inertia. The above analytic form of E(J) is exploited to deduce certain conclusions about the nature of the projected energy as a function of J.