Nonquenched Isoscalar Spin-$M1$ Excitations in $sd$-Shell Nuclei

Differential cross sections of isoscalar and isovector spin-$M1$ ($0^{+}\to 1^{+}$) transitions are measured using high-energy-resolution proton inelastic scattering at $E_p=295\mathrm{MeV}$ on ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{32}\mathrm{S}$, and ${}^{36}\mathrm{Ar}$ at 0°–14°. The squared spin-$M1$ nuclear transition matrix elements are deduced from the measured differential cross sections by applying empirically determined unit cross sections based on the assumption of isospin symmetry. The ratios of the squared nuclear matrix elements accumulated up to $E_x=16\mathrm{MeV}$ compared to a shell-model prediction are 1.01(9) for isoscalar and 0.61(6) for isovector spin-$M1$ transitions, respectively. Thus, no quenching is observed for isoscalar spin-$M1$ transitions, while the matrix elements for isovector spin-$M1$ transitions are quenched by an amount comparable with the analogous Gamow-Teller transitions on those target nuclei.

Figure 1

(a) Excitation energy spectrum of the ${}^{28}\mathrm{Si}(p,p^{\prime })$ reaction at $E_p=295\mathrm{MeV}$ and ${\theta }_{\text{lab}}=0°–0.5°$. The arrows in the figure indicate states which are assigned definitely as $1^{+}$. Angular distributions of (b) an IS and (c) an IV spin-$M1$ transition marked by red and blue arrows in (a), respectively, in comparison with theoretical angular distributions for several multipolarities.

Figure 2

Observed distributions of IS and IV-spin-$M1$ SNME [open (filled) bars represent IS (IV) transitions]. The bars $\text{labeled}+\text{indicate}$ states with a less confident spin assignment.

Figure 3

Mass dependences of the UCS for (a) IS and (b) IV transitions.

Figure 4

Accumulated sums of the spin-$M1$ SNMEs for (a) IS and (b) IV transitions up to $E_x=16\mathrm{MeV}$. The error bars and gray bands indicate the total experimental uncertainties and the partial uncertainties from the spin assignment, respectively. The solid lines and dotted lines are the predictions of shell-model calculations using the USD with bare and effective $g$ factors, respectively.

Figure 5

Experimental ${\mathrm{\Delta }}_{\text{spin}}(E_x)$ and theoretical $⟨{\overrightarrow{S}}_p·{\overrightarrow{S}}_n⟩$ values explained in the text for (a) ${}^4\mathrm{He}$, (b) ${}^{12}\mathrm{C}$, and (c) $sd$-shell nuclei. The experimental results in (c) are summed up to $E_x=16\mathrm{MeV}$ with the same definition of the error bars as in Fig. 4. The arrows of the NCSM results in (c) indicate that the results are considered to represent a lower limit.