QRPA calculations for M1 transitions with the noniterative finite amplitude method and the application to neutron radiative capture cross sections

We derive the equations of quasiparticle random-phase approximation (QRPA) based on the finite amplitude method (FAM) with the Hartree-Fock+BCS (HF+BCS) single-particle states, and calculate the magnetic dipole (M1) transition for deformed gadolinium isotopes. Our QRPA calculation shows both large spin-flip transitions in the 5 to 10 MeV excitation energy and the low energy orbital transition that would correspond to the M1 scissors mode observed in nuclear experiments. Then, we calculate neutron capture reactions based on the statistical Hauser-Feshbach theory with the photoabsorption cross sections given by QRPA. We find that the capture cross section is enhanced due to the contribution from the low energy M1 transition although the calculated capture cross section still underestimates the experimental data. This issue in the calculated capture cross section could be improved by uncertainties of low energy E1 transition neglected in our QRPA calculation.