Quenching of Isovector and Isoscalar Spin-M1 Excitation Strengths in N = Z Nuclei

Spin- (Formula presented.) excitations of nuclei are important for describing neutrino reactions in supernovae or in neutrino detectors since they are allowed transitions mediated by neutral current neutrino interactions. The spin- (Formula presented.) excitation strength distributions in self-conjugate (Formula presented.) nuclei were studied by proton inelastic scattering at forward angles for each of isovector and isoscalar excitations as reported in H. Matsubara et al., Phys. Rev. Lett. 115, 102501 (2015). The experiment was carried out at the Research Center for Nuclear Physics, Osaka University, employing a proton beam at 295 MeV and the high-resolution spectrometer Grand Raiden. The measured cross-section of each excited state was converted to the squared nuclear matrix elements of spin- (Formula presented.) transitions by applying a unit cross-section method. Comparison with predictions by a shell-model has revealed that isoscalar spin- (Formula presented.) strengths are not quenched from the prediction although isovector spin- (Formula presented.) strengths are quenched similarly with Gamow-Teller strengths in charged-current reactions. This finding hints at an important origin of the quenching of the strength relevant to neutrino scattering, that is, the proton-neutron spin-spin correlation in the ground state of the target nucleus. In this manuscript we present the details of the unit cross-section method used in the data analysis and discuss the consistency between the quenching of the isoscalar magnetic moments and that of the isoscalar spin-M1 strengths.