Electric and magnetic dipole strength in ${}_{58}\mathrm{Ni}$ from forward-angle proton scattering

Background: Electric and magnetic dipole strengths in nuclei at excitation energies well below the giant resonance region are of interest for a variety of nuclear structure problems including a possible electric dipole toroidal mode or the quenching of spin-isospin flip modes.

Purpose: The aim of the present work is a state-by-state analysis of possible $E1$ and $M1$ transitions in ${}_{58}\mathrm{Ni}$ with a high-resolution $(p,p^{\prime })$ experiment at 295 MeV and very forward angles including $0^{\circ }$ and a comparison to results from studies of the dipole strength with the $(\gamma ,{\gamma }^{\prime })$ and $(e,e^{\prime })$ reactions.

Methods: The $E1$ and $M1$ cross sections of individual peaks in the spectra are deduced with a multipole decomposition analysis (MDA). They are converted to reduced $E1$ and spin $M1$ transition strengths using the virtual photon method of relativistic Coulomb excitation and the unit cross-section method, respectively. The experimental $M1$ strength distribution is compared to large-scale shell-model calculations with the effective GXPF1A and KB3G interactions.

Results: In total, 11 $E1$ and 26 $M1$ transitions could be uniquely identified in the excitation energy region $6–13$ MeV. In addition, 22 dipole transitions with preference for either $E1$ or $M1$ multipolarity and 57 transitions with uncertain multipolarity were found. Despite the high level density good agreement is obtained for the deduced excitation energies of $J=1$ states in the three types of experiments indicating that the same states are excited. The $B\left(E1\right)$ and $B\left(M1\right)$ strengths deduced in the $(\gamma ,{\gamma }^{\prime })$ experiments are systematically smaller than in the present work because of the lack of information on branching ratios to lower-lying excited states and the competition of particle emission. Fair agreement with the $B\left(M1\right)$ strengths extracted from the $(e,e^{\prime })$ data is obtained after removal of $E1$ transitions uniquely assigned in the present work belonging to a low-energy toroidal mode with unusual properties mimicking $M1$ excitations in electron scattering. The shell-model calculations provide a good description of the isospin splitting and the running sum of the $M1$ strength. A quenching factor 0.74 for the spin-isospin part of the $M1$ operator is needed to attain quantitative agreement with the data.

Conclusions: High-resolution forward-angle inelastic proton scattering experiments at beam energies of about 300 MeV are a highly selective tool for an extraction of resolved $E1$ and $M1$ strength distributions in medium-mass nuclei. Fair agreement with results from electron scattering experiments is obtained indicating a dominance of spin contributions to the $M1$ strength. Shell-model calculations are in good agreement with gross properties of the $M1$ strength distribution when a quenching factor for the spin-isospin part comparable to the one needed for a description of Gamow-Teller (GT) strength is included.