Abstract
A method is developed to derive simple relations among the reduced matrix elements of the quadrupole operator between low-lying collective states. As an example, the fourth order scalars of Q are considered. The accuracy and validity of the proposed relations is checked for the ECQF Hamiltonian of the IBM-1 in the whole parameter space of the Casten triangle. Furthermore these relations are successfully tested for low-lying collective states in nuclei for which all relevant data is available.
Highlights
Microscopic shell model wave functions of collective nuclear states need a huge configurational space
The wave functions of some excited states can be described by actions of one-body operators on the ground state wave function with good accuracy
In even-even nuclei, where the ground state is a 0+ state, the first 2+ state is given by the quadrupole operator Q acting on the ground state
Summary
Microscopic shell model wave functions of collective nuclear states need a huge configurational space. The Q-phonon structure of the low-lying collective states allows one to obtain quadrupole shape invariants [14,15,16,17] from rather few data. As an example we consider fourth order scalars obtained by coupling the four quadrupole operators in different ways.
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