In What Sense Does the "Phonon" Picture Persist in Spherical Even-Even Nuclei?

Abstract

For the purpose of obtaining the microscopic description of one-, two- and three-phonon states in spherical even-even nuclei, n-quasi-particle collective excited states (with n = 2, 4, 6) are obtained by diagonalizing the quadrupole force in the Tamm-Dancoff calculation in the single-j-shell model. The characteristics of the “collectivity” which these eigenstates exhibit through energy eigenvalues and B(E2) values are investigated. The results are compared with the “phonon” (boson) picture and the breaking and persistency of the picture are made clear. It is also studied whether the collective excited states obtained are well approximated by states of simpler structure or not. It is revealed that the use of the states which are constructed by using the J = 2-coupled pair operators as building blocks is fairly good approximation, if spurious components due to the nucleon number fluctuation are removed out of the states.