ISSN 1063-7788, Physics of Atomic Nuclei, 2007, Vol. 70, No. 8, pp. 1402–1406. c  Pleiades Publishing, Ltd., 2007. NUCLEI Theory Low-Lying Electric Dipole Transitions in Tin Isotopic Chain within the RPA Model * D. Tarpanov 1)** , C. Stoyanov 1)*** , N. Van Giai 2) , and V. V. Voronov 3) Received October 31, 2006 Abstract—A nuclear structure model based on a finite rank approximation of Skyrme interaction is applied to calculate the distribution of dipole strength in tin isotopes. The model is based on the quasiparticle random phase approximation. The results obtained with the three types of parametrizations of the Skyrme forces (SLy4, SkM * , and SIII) are compared. The low-lying part of dipole strength distribution reveals the existence of a group of slightly collective states, and the corresponding E1 transition strength increases with the enlargement of neutron excess. The group is associated with the pygmy resonance. PACS numbers: 21.60.Jz, 21.30.Fe, 23.20.Lv DOI: 10.1134/S1063778807080133 1. INTRODUCTION In the recent experiment performed at GSI, Darm- stadt [1], the distribution of electric dipole strength in the unstable nuclei 130,132 Sn was measured. Together with some theoretical results [2–6], obtained within different theoretical approaches, it gives a hint for the existence of a low-lying dipole mode commonly referred as “pygmy” dipole resonance (PDR). These excited states are known to be slightly collective; i.e., they exhaust a few percent of the energy-weighted sum rule (EWSR), and the collectivity increases with enlargement of the neutron excess. The tin isotopic chain includes 18 even–even nuclei in the domain between the neutron magic numbers 50 and 82, and it is quite suitable to study the dependence of the PDR on neutron excess. We have calculated the distribution of E1 strength along the chain 100 Sn− 132 Sn. The structure of ex- cited states was calculated by means of the quasi- particle random phase approximation (QRPA). The residual particle–hole (ph) interaction is of the Skyrme type. A method known as the finite rank approximation for RPA calculations with Skyrme interaction is used [7–9]. The approximation is based on a Landau–Migdal representation of the Skyrme ∗ The text was submitted by the authors in English. 1) Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria. 2) Institut de Physique Nucl ´ eaire, Orsay Cedex, France. 3) Bogolyubov Laboratory of Theoretical Physics, Joint Insti- tute for Nuclear Research, Dubna, Russia. ** E-mail: tarpanov@inrne.bas.bg *** E-mail: stoyanov@inrne.bas.bg interaction [10]. The method was proven to be useful in a large configuration space, where the problem with the diagonalization of the model Hamiltonian Table 1. Summed B(E1) values and the contribution to EWSR of the QRPA 1 - states in the excitation energy range below 10.5 MeV (calculations are performed with SkM * , SLy4, and SIII parametrizations) Nuc- leus SkM * SLy4 SIII B(E1), EWSR, B(E1), EWSR, B(E1), EWSR, e 2 fm 2 % e 2 fm 2 % e 2 fm 2 % 100 Sn 0.93 0.62 0.21 0.21 1.44 0.96 102 Sn 1.17 0.76 0.24 0.24 0.19 0.13 104 Sn 1.00 0.66 0.01 0.06 0.23 0.15 106 Sn 0.92 0.62 0.31 0.31 0.26 0.17 108 Sn 0.92 0.64 0.32 0.32 0.27 0.17 110 Sn 1.03 0.72 0.43 0.43 0.25 0.16 112 Sn 1.02 0.72 0.24 0.24 0.24 0.16 114 Sn 1.00 0.70 0.31 0.31 0.40 0.27 116 Sn 1.50 1.01 0.62 0.62 0.30 0.20 118 Sn 2.42 1.59 0.78 0.78 1.17 0.77 120 Sn 6.25 4.19 1.87 1.87 3.28 2.13 122 Sn 10.6 7.33 2.24 2.24 3.65 2.37 124 Sn 11.0 7.59 2.41 2.41 3.62 2.33 126 Sn 12.7 8.88 2.56 2.56 3.29 2.19 128 Sn 16.5 12.0 2.22 2.22 2.47 1.60 130 Sn 17.8 13.1 2.44 2.44 1.84 1.20 132 Sn 13.8 10.2 2.09 2.09 1.42 0.91 1402