On collective two-phonon states in deformed nuclei

Abstract

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by t-2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3-4MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.

Description of low-lying vibrationalK ??0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

“…The mathematical apparatus of the QPNM for deformed nuclei has first been given in [10,11,14,16] and in more detail in [12,13]. Formulae allowing for p-h and p-p interactions are given in [19,21]; they will be used in the present paper.…”

“…The function ~K~ ~b 1 ix, 22 #z i2) is responsible for the effect of the Pauli principle in two-phonon terms of the wave function (6); its form is presented in [13,14,16].…”

“…Based on the calculations in the QPNM we have concluded in [14,16] (6) has been added by the three-phonon terms and the shifts of three-phonon poles have been calculated. It is shown that these shifts may exceed three or more times the shifts of two-phonon poles.…”

“…A new series of calculations is performed within the quasiparticle-phonon nuclear model (QPNM) [10][11][12][13] with the wave functions containing one-and two-phonon components and taking account of the Pauli principle of two-phonon components. The role of two-phonon components of the wave functions and the influence of the Pauli principle have been studied in [14][15][16], hexadecapole vibrational states in [17], influence of the quadrupole pairing on the energies of two-quasiparticle states in [18] and the influence of p-p interactions on the properties of K==2 + states in [19]. The importance of the monopole pairing is evident and it is interesting to study the influence of the quadrupole pairing.…”

Observation of aγband based on a two-quasiparticle configuration inGe70

“…Well developed γ−bands are known to exist in many transitional nuclei close to the ground-state which have been investigated using various phenomenological models [5,6]. In the framework of microscopic triaxial projected shell model (TPSM) approach [7], these γ− bands result from projection of the K=2 state of the triaxial selfconjugate vacuum configuration.…”