Magnetic dipole transitions in ${}^{32}\mathrm{S}$ from electron scattering at 180°

Magnetic dipole transitions in the self-conjugate nucleus ${}^{32}\mathrm{S}$ up to an excitation energy of 12 MeV have been investigated in inelastic electron scattering at ${\Theta }_e=180\mathrm{}°$ at the superconducting Darmstadt electron linear accelerator (S-DALINAC). Transition strengths have been determined from a plane-wave Born approximation analysis including Coulomb distortion. For the two strongest $M1\mathrm{}$ transitions, where a discrepancy of a factor of about 2 was observed in previous ${(e,e}^{\prime })$ experiments, values intermediate between the two extremes are deduced from the present work. The resulting strength distribution is well described by shell-model calculations using the unified $\mathrm{sd}$-shell interaction and an effective $M1\mathrm{}$ operator. The shell-model wave functions also provide a reasonable description of the form factors. A quasiparticle random phase approximation calculation is less successful. The present results allow for the first time studies of the form factor of extremely weak l-forbidden and isoscalar $M1\mathrm{}$ excitations in ${}^{32}\mathrm{S}.$ The l-forbidden transition allows a sensitive test of tensor corrections to the $M1\mathrm{}$ operator. A combined analysis with the isospin-analog Gamow-Teller (GT) transitions in the $A=32\mathrm{}$ triplet reveals a situation similar to previous studies in $A=39\mathrm{}$ nuclei: microscopic calculations reasonably account for the GT strengths, but fail in the case of $M1\mathrm{}$ strengths. A possible explanation may be found in the nonrelativistic treatment of the latter. Some examples of the role of relativistic corrections are discussed. A consistent description of the reduced transition strength and the form factor of the isoscalar $M1\mathrm{}$ excitation requires isospin mixing with the close-lying isovector transitions. The extracted Coulomb matrix elements are roughly within the limits set by the approximate constancy of the spreading width derived from the analysis of compound-nucleus reactions.