Nuclear charge-exchange excitations play very important roles in understanding many important topics in nuclear physics, astrophysics, and particle physics. The fully self-consistent descriptions of these excitations in covariant density functional theory (DFT) were achieved only recently with the random phase approximation (RPA) based on the relativistic Hartree-Fock (RHF) theory [1], where the delicate balance between the sigma- and omega-meson fields via the exchange terms are found to play the crucial roles [1-3]. According to this special feature, we proposed a new kind of RHF equivalent but local functional [4]. In such a way, the advantages of existing local covariant density functionals used in the past a couple of decades can be maintained, while their common problems in the isovector channel can be solved.

In order to extend this approach to the deformed systems, one of the ongoing projects is the self- consistent relativistic RPA with the finite amplitude method (FAM) proposed in Ref. [5]. The FAM provides an efficient way to find the RPA equation solutions, in particular, when the dimension of the matrix is huge as in the deformed cases. The feasibility of the FAM in covariant DFT has been demonstrated [6]. Meanwhile, it is shown that the effects of Dirac sea can be taken into account implicitly in the r-space representation and the rearrangement terms due to the density-dependent couplings can be treated practically without extra computational costs.

[1] H. Liang, N. Van Giai, and J. Meng, Phys. Rev. Lett. 101, 122502 (2008);

[2] H. Liang, N. Van Giai, and J. Meng, Phys. Rev. C 79, 064316 (2009);

[3] H. Liang, P.W. Zhao, and J. Meng, Phys. Rev. C 85, 064302 (2012);

[4] H. Liang, P.W. Zhao, P. Ring, X. Roca-maza, and J. Meng, Phys. Rev. C 86, 021302(R) (2012);

[5] T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007);

[6] H. Liang, T. Nakatsukasa, Z.M. Niu, and J. Meng, in preparation.