Systematics of optimumQvalues in multinucleon transfer reactions induced by heavy ions

The most probable effective $Q$ values, $Q_{\mathrm{eff}}^m$, for multinucleon transfer reactions $A(a,b)B(M_b<M_a)$ have been systematically studied on $\mathrm{fp}$-shell nuclei and Zr-Mo isotopes induced by ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, in the energy range between 60 and 100 MeV. As regards the "quasielastic" part of the bump in the energy spectrum, the dependence of $Q_{\mathrm{eff}}^m$ on the incident and outgoing channel variables, i.e., $A$, $a$, $E_i$, $\theta$, and $n$, the number of transferred nucleons, has been extensively investigated. The present data, together with those obtained at higher energies by the Dubna group, show systematic behaviors of $Q_{\mathrm{eff}}^m$ (i) for a given $A(a,b)B$ and $E_i$, $Q_{\mathrm{eff}}^m$ changes little with ${\theta }_{\mathrm{lab}}$, (ii) at a given $E_i$, $Q_{\mathrm{eff}}^m$ of ($a,b$) is nearly the same for adjacent $A$ and is not sensitive to their individual nuclear structure, and (iii) the linear relation $Q_{\mathrm{eff}}={\alpha }_{\mathrm{eff}}n+{\beta }_{\mathrm{eff}}$ holds for $n\le 4-5$, whereas the linearity breaks down for larger $n$. The relation ${\alpha }_{\mathrm{eff}}=-0.1(E_i-V_c^i)-0.9\mathrm{}$ MeV holds for a wide range of reactions. The ratio of the most probable effective velocity to the incident velocity $\frac{{\nu }_f^m}{{\nu }_i}$ at the transfer region decreases from about unity to 0.4 - 0.5 as $n$ increases. The differences in reaction mechanisms for smaller $n$ and larger $n$ have been discussed.