Implementation of a finite-amplitude method in a relativistic meson-exchange model

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Figure 1

The elimination of a spurious state relating to particle number symmetry breaking in the $K^{\pi }=0^{+}$ channel. The figure shows the giant monopole resonance of ${}^{22}\mathrm{O}$; the dashed line represents the result corresponding to the RMF-FAM-RPA calculation, while the solid line for the self-consistent RMF-FAM-QRPA. The dotted-dashed line shows the mixing of the spurious state with physical ones when dynamic pairing is not included, namely, omitting the pairing interaction in the excitation calculations; see text for details.

Figure 2

The giant monopole resonance of Cd isotopes. The solid line represents the self-consistent FAM-QRPA calculation with the separable pairing (SP) force, while the dashed line represents the pairing-absent case. The experimental results are denoted by error bars.

Figure 3

ISGMR of ${}^{208}\mathrm{Pb}$; the “‘dashed-dotted” and “dashed” lines represent results produced by Skyrme interactions SLy5 and SkM*, respectively. The “solid” line represents our calculation result with relativistic meson-exchange interaction DD-ME2. The response strength is smeared with $\mathrm{\Gamma }=1\mathrm{MeV}$.

Figure 4

The electric dipole resonance of ${}^{60}\mathrm{Ni}$. Strength distribution belonging to $K^{\pi }=0^{-}$ and $K^{\pi }=1^{-}$ are represented by the dashed line and dotted-dashed line, respectively.