ROTATIONAL-INVARIANT MODEL OF THE STATES WITH K^π=1⁺ AND THEIR CONTRIBUTION TO THE SCISSORS MODE

Abstract

Within the Random-Phase Approximation the method of self-consistent determination of the isoscalar and isovector effective separable interactions restoring a broken symmetry of the deformed mean-field is given. The method allows to treat more rigorously without free parameters the properties of the scissors mode and is used to develop the rotational invariant microscopic model of the states with K π = 1 + . The spurious state separates out and has zero energy. An important consequence of this separation is the fragmentation of the scissors mode and the collectivization of the low-lying 1 + states. In addition to the isoscalar restoring interactions the consideration of the isovector restoring forces in calculations causes the splitting of the states with large B(M1) strength at low energy. The model contains a single parameter of isovector spin-spin interactions and it allows one to describe satisfactorily the fragmentation of the scissors mode and the dependence of the summed B(M1) strength on δ 2 and A in deformed nuclei.

Fine structure of the dipole excitations of the even-even 160Gd nucleus in the spectroscopic region

“…[13], and in framework of this theory we investigated the low-lying dipole mode for nuclei from different areas [8,[13][14][15][16]. Therefore, we restrict ourselves here to a short description of the applications to low-lying M1 and E1 excitations.…”

“…of the nucleus is taken at rest. According to [13,17], the translational invariance of the single-quasiparticle Hamiltonian can be restored with the aid of a separable isoscalar effective interaction of the form…”

“…There, by selection of suitable separable effective isoscalar and isovector forces, without introducing any additional parameters, we can restore rotational invariance of the model Hamiltonian within QRPA for the description of the M1 modes, as well as translational and Galilean invariance for the calculation of E1 excitations in 160 Gd nucleus. (A detailed description of the method was given in Ref [13].) We calculate mean excitation energies and the summed B(M1) value and groundstate transition widths of the dipole excitations.…”

Investigation of low-lying magnetic dipole excitations in the $^{153}$Eu nucleus

“…The fragmentation of M 1 strength in odd-mass nuclei can be explained using microscopic models such as quasiparticle random phase approximation (QRPA) or the more general quasiparticle phonon nuclear model (QPNM). However, in these models the rotational symmetry of the single particle Hamiltonian simultaneously is violated by the HartreeFock-Bogoliubov (HFB) approaches in the mean field [5][6][7]. The violation of the rotational invariance results in admixtures (spurious states) connected with rotational degree of freedom in K π = 1 + excitation states of eveneven core [7,8].…”

“…However, in these models the rotational symmetry of the single particle Hamiltonian simultaneously is violated by the HartreeFock-Bogoliubov (HFB) approaches in the mean field [5][6][7]. The violation of the rotational invariance results in admixtures (spurious states) connected with rotational degree of freedom in K π = 1 + excitation states of eveneven core [7,8]. One has to remove these spurious contributions to determine exactly the energies of excitation states and the M 1 strength distribution in odd-mass nuclei.…”