Description of proton-neutron mixed-symmetry states with Skyrme interaction
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NUCLEI Theory
Description of Proton–Neutron Mixed-Symmetry States with Skyrme Interaction* A. P. Severyukhin1), N. N. Arsenyev1) , V. V. Voronov1), N. Pietralla2), and Nguyen Van Giai3) Received November 23, 2010
Abstract—Starting from an effective Skyrme interaction we study the effects of the phonon–phonon coupling on the M 1 transitions between quadrupole states. The finite rank separable approach for the quasiparticle random phase approximation is used. Choosing as an example the nucleus 94 Mo, we demonstrate an ability of the method to describe the properties of the low-lying states. DOI: 10.1134/S106377881108014X
1. INTRODUCTION Properties of the quadrupole–collective isovector excitations of the valence shell of heavy nuclei reflect three main aspects: the many-body property (collectivity), the quantum nature (shell structure), and the two-fluid character (isospin degree of freedom), and the balance between these aspects can be studied. These isovector excitations, so-called mixedsymmetry states [1, 2], are sensitive to the proton– neutron interaction. On the other hand, the dominance of the proton–neutron attraction is one of the main characteristics of the effective nucleon–nucleon interaction. It can be traced back to the cooperation of its T = 0 and T = 1 channels. This is a good possibility to examine theoretical approaches using the effective nucleon–nucleon interaction. One of the successful tools for nuclear structure studies is the quasiparticle random phase approximation (QRPA) with the self-consistent mean-field derived by making use of the nonrelativistic two-body force [3–5]. There is the significant role of the selfconsistency conditions [6, 7]. Such the QRPA calculations do not require to introduce new parameters since the residual interaction is derived from the same energy density functional as that determining the mean-field. Many properties of the nuclear collective states can be described correctly within such models, see, for example, [8–13]. A complexity of calculations taking into account a coupling between one-phonon and more complex ∗
The text was submitted by the authors in English. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia. 2) ¨ Kernphysik, Technische Universitat ¨ Darmstadt, Institut fur Germany. 3) ´ Institut de Physique Nucleaire, CNRS–IN2P3, Universite´ Paris-Sud, Orsay Cedex, France.
states increases rapidly with the size of the configuration space. The separable form of the residual interaction is the practical advantage of the well-known quasiparticle phonon model (QPM) [14] which allows one to perform structure calculations in very large configuration spaces. However, it is difficult to extrapolate the model parameters to new regions of nuclei. Among developments for nuclear structure studies with a Skyrme interaction, a finite rank separable approximation [15–17] for the residual interaction is particularly promising. The approach is generalized to take into account a coupling between the one- and two-phonon components of the wav
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