Relativistic quasiparticle random phase approximation in deformed nuclei

Abstract

Covariant density functional theory is used to analyse the response to the E1 and M1 electromagnetic transition operators in superfluid deformed nuclei in the framework of self-consistent Hartree-Bogoliubov theory and relativistic quasiparticle random phase (RQRPA) approximation. The fully self-consistent RHB+RQRPA equations are posed for the case of axial symmetry and for three different kinds of energy functionals, and solved with the help of a new parallel code. Special care is taken in order to validate the proper decoupling of spurious modes. Results of the first multipole magnetic operator (M1) response in light and heavy deformed nuclei are presented and analysed; in particular, the scissors mode and spin excitations. Qualitative agreement with experiment is obtained for the position of the scissors mode, and its structure as a rotation of the deformed neutron density against the deformed proton density reproduced. In addition to the scissors mode, a soft M1 mode with strong orbital character is found in heavy nuclei at relatively low energies. From the analysis of the proton and neutron transition densities in the intrinsic frame, and from the structure of the RQRPA amplitudes, it is concluded that this mode corresponds to a collective rotation of the deformed neutron skin against the deformed proton-neutron core. The response in light and heavy nuclei to the electric dipole operator (E1) is also given consideration. The position of the Giant Dipole Resonance is well reproduced within the RHB+RQRPA framework in axial symmetry. The effects of superfluidity and deformation on the Pygmy Dipole Resonance are closely examined. Excellent agreement with recent experimental results is found. v vi AcknowledgementsFirst and foremost I would like to thank my supervisor, Prof. Dr. Peter Ring, not only for stimulating discussions and timely advice, but also for his support throughout the various phases of the work presented in this document. His understanding and experience in many areas has made a pleasure working with him. I am particularly grateful for his optimism and overall confidence in the project, always trying to point me on the right direction but giving me enough leeway to learn from my own mistakes.Many thanks go to Roger Hilton, who was always a source of good humour and interesting conversations while at the TUM. He patiently read the first drafts and helped me polish all the rough edges, both in the contents and in the use of the English language.It is a pleasure for me to thank all my colleagues at the TUM Theory Department and at the TUM campus in Garching, who have provided support and company during my time in Munich, with a special mention to

Low-energy dipole excitations in neon isotopes andN=16isotones within the quasiparticle random-phase approximation and the Gogny force

“…While the low-energy peak is expected in 24 O, one can observe in Fig. 2 that an equivalent structure appears at ω n 12 MeV also for 28 Mg and 30 Si in spite of their small neutron-proton asymmetry. As expected and as shown in Fig.…”

“…Turning to the microscopic analysis of Table I, one can observe that the structure of the first peak in 24 O is quite similar to the one of 26 Ne except for the absence in 24 O of the ν 1d 3/2 → 2p 3/2 contribution, as expected for a particle-particle configuration in a closed-shell nucleus. This particle-particle transition turns out to be very important in 28 Mg, being of the same order of magnitude as the main particle-hole transition ν 2s 1/2 → 2p 3/2 . Finally, in 30 Si the contribution of proton excitations becomes appreciable, being of the order of 30%.…”

“…The low-energy dipole excitations of this nucleus have been experimentally studied [9]. Several theoretical calculations on this nucleus have been already done [27][28][29][30][31]. In Table I, we present a detailed analysis of the microscopic structure of the low-lying dipole modes in 26 Ne (and in N = 16 isotones) considering the first-low energy state.…”

“…Main particle-hole (and particle-particle) configurations contributing to the first low-energy dipole excitations of N = 16 isotones.Total neutron and proton contributions are also given for the low-energy peak, for the main one corresponding to the GDR, and from the sum of all the states with 15 MeV ω n 30 MeV and B(E1) 0.5 e 2 fm 2 . 24 Concerning the N = 16 isotones, the other nuclei we consider here are 24 O, 28 Mg, and 30 Si. While the low-energy peak is expected in 24 O, one can observe in Fig.…”

“…Transition densities of the low-lying dipole states in 26 Ne can be found in [30] and in [28], while results for 24 O are presented in [32] and [24] where a phenomenological RPA is used. In [32], the isoscalar character of the excitation inside the nucleus clearly appears while the isovector behavior of the analyzed low-energy excitation (however, not the lowest one) in [24] is interpreted as the tail part of the GDR.…”