Isovector and isoscalar spin-flip M1 strengths in $^{11}$B
The $^{11}$B($^3$He$, t$), $^{11}$B($d, d'$), and $^{11}$B($p, p'$) reactions were measured at forward scattering angles including $0^\circ$ to study the isovector and isoscalar spin-flip M1 strengths in $^{11}$B. The measured $^{11}$B($^3$He$, t$) cross sections were compared with the results of the distorted-wave impulse-approximation (DWIA) calculation, and the Gamow-Teller (GT) strengths for low-lying states in $^{11}$C were determined. The GT strengths were converted to the isovector spin-flip M1 strengths using the isobaric analog relations under the assumption of the isospin symmetry. The isoscalar spin-flip M1 strengths were obtained from the ($d, d'$) analysis by assuming that the shape of the collective transition form factor with the same $ΔJ^π$ is similar in the $^{11}$B($d, d'$) and $^{12}$C($d, d'$) reactions. The obtained isovector and isoscalar strengths were used in the DWIA calculations for the $^{11}$B($p, p'$) reaction. The DWIA calculation reasonably well explains the present $^{11}$B($p, p'$) result. However, the calculated cross section for the 8.92-MeV 3/2$^-_2$ state was significantly smaller than the experimental values. The transition strengths obtained in the shell-model calculations were found to be 20-50% larger than the experimental strengths. The transition strengths for the neutrino induced reactions were estimated by using the isovector and isoscalar spin-flip M1 strengths. The present results are quantitatively in agreement with the theoretical estimation discussing the axial isoscalar coupling in the neutrino scattering process, and are useful in the measurement of the stellar neutrinos using the neutral- and charged-current reactions on $^{11}$B.