Probing the isovector transition strength of the low-lying nuclear excitations induced by inverse kinematics proton scattering

A compact approach based on the folding model is suggested for the determination of the isoscalar and isovector transition strengths of the low-lying ($\Delta S=\Delta T=0$) excitations induced by inelastic proton scattering measured with exotic beams. Our analysis of the recently measured inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon has given for the first time an accurate estimate of the isoscalar $\beta_0$ and isovector $\beta_1$ deformation parameters (which cannot be determined from the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited states in $^{18,20}$O. Quite strong isovector mixing was found in the 2$^+_1$ inelastic $^{20}$O+p scattering channel, where the strength of the isovector form factor $F_1$ (prototype of the Lane potential) corresponds to a $\beta_1$ value almost 3 times larger than $\beta_0$ and a ratio of nuclear transition matrix elements $M_n/M_p\simeq 4.2$.