  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.
