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Elastic and inelastic cross sections of the $p+{}^6\textrm{He}$,$p+{}^8\textrm{He}$, and $\alpha+{}^8\textrm{He}$ reactions were investigatedusing the Melbourne $g$-matrix folding approach with the theoretical densitiesof ${}^6\textrm{He}$ and ${}^8\textrm{He}$ obtained by a microscopic structuremodel of antisymmetrized molecular dynamics (AMD). Microscopic coupled-channel(MCC) calculations of the $p+{}^6\textrm{He}$ and $p+{}^8\textrm{He}$ reactionswere performed to investigate transition properties of the${}^6\textrm{He}(2^+_1)$ and ${}^8\textrm{He}(2^+_1)$ states. The MCC+AMDcalculations reproduced elastic cross sections of the $p+{}^6\textrm{He}$reaction at $E=40.9$ MeV/A and of the $p+{}^8\textrm{He}$ reaction at $E=32.5$and 72 MeV/A, which have both been measured by inverse kinematics experiments.For $p+{}^6\textrm{He}$ inelastic scattering to the $2^+_1$ state, thecalculated result was in reasonable agreement with the $(p,p')$ data at$E=24.5$ and 40.9 MeV/A and supported the AMD prediction of the neutrontransition matrix element $M_n=7.9$ fm$^2$. For the $p+{}^8\textrm{He}$inelastic scattering to ${}^8\textrm{He}(2^+_1)$, the MCC+AMD calculationovershot the $(p,p')$ cross sections at $E=72$ MeV/A by a factor of three.According to a phenomenological model analysis, $M_n$ values in the range of4--6 fm$^2$ were favored to reproduce the ${}^8\textrm{He}(2^+_1)$ crosssections of the $p+{}^8\textrm{He}$ reaction at $E=72$ MeV/A. For the$\alpha+{}^8\textrm{He}$ reaction, the MCC+AMD calculation reproduced theelastic cross sections at $E=26$ MeV/A. Theoretical predictions of the ($p,p'$)and ($\alpha,\alpha'$) cross sections to the ${}^8\textrm{He}(0^+_2)$,${}^8\textrm{He}(1^-_1)$, ${}^8\textrm{He}(2^+_3)$ and ${}^8\textrm{He}(3^-_1)$states are also given.

Microscopic calculation of proton and alpha-particle inelastic scattering to study the excited states of $^{6}$He and $^{8}$He