Covariant density functional theory for excited states in nuclei far from stability*

Abstract

Investigations of nuclei far from stability are presently at the forefront of nuclear science. Density functional theory (DFT) is an important tool for a universal description of medium heavy and heavy systems. Because of the consistent treatment of spin degrees of freedom static and dynamic versions of covariant density functional Theory (CDFT) provide a very successful description of nuclear properties all over the periodic table. Excited states are treated in time dependent density functional theory (TDDFT) which is treated in different approximations:a) On the mean field level the relativistic quasiparticle random phase approximation (RQRPA) is used to investigate the multipole response in spherical and deformed nuclei far from stability, in particular low-lying modes [1], giant resonances [2], spin-isospin modes, scissor modes [3] and new exotic resonances, such as pygmy [4] or toroidal modes.b) Going beyond the mean field approximation, an energy dependent self-energy is constructed by coupling of the single particle motion to low-lying surface modes. This leads to an enhanced level density at the Fermi surface and an induced interaction in the resulting Bethe-Salpeter equation, which is solved in the time blocking approximation (TBA) [5]. No additional parameters are used and double counting is avoided by a proper subtraction method. This method is applied in several isotopic chains of spherical nuclei for the investigation of the width of giant resonances and of the coupling of low-lying dipole excitations to complex configurations [6].c) In transitional nuclei a theory is developed which uses the relativistic generator coordinate method (RGCM) as a basis to perform configuration mixing calculations of angular momentum and particle number projected wave functions [7] and to derive a collective hamiltonian in five quadrupole degrees of freedom [8]. This allows to calculate spectra of transitional nuclei and provides a microscopic interpretation of quantum phase transitions in finite fermion systems [9]. A number of illustrative calculations are presented and they are compared with results obtained in non-relativistic models based on Skyrme and Gogny effective interactions.[1] A. Ansari and P. Ring, Phys. Rev. C74, 054313 (2006).[2] J. Daoutidis and P. Ring, Phys. Rev. C80, 024309 (2009).[3] D. Pe~na Arteaga, E. Khan, and P. Ring, Phys. Rev. C79, 034311 (2009).[4] N. Paar, P. Ring, T. Nik_si_c, and D. Vretenar, Phys. Rev. C67, 034312 (2003).[5] E. Litvinova, P. Ring, and V. I. Tselyaev, Phys. Rev. C78, 014312 (2008).[6] E. Litvinova, P. Ring, V. I. Tselyaev, and K. Langanke, Phys. Rev. C79, 054312(2009).[7] J.-M. Yao, J. Meng, P. Ring, and D. Pe~na Arteaga, Phys. Rev. C79, 044312 (2009).[8] T. Nik_si_c, Z. P. Li, D. Vretenar, L. Pr_ochniak, J. Meng, and P. Ring, Phys. Rev. C79, 034303 (2009).[9] T. Nik_si_c, D. Vretenar, G. A. Lalazissis, and P. Ring, Phys. Rev. Lett. 99, 092502 (2007). * Work was supported in part by the DFG cluster of excellence Origin and Structure of the Universe(www.universe-cluster.de).