Reaction mechanism in odd-even staggering of reaction cross sections

It was recently suggested that the odd-even staggering of reaction cross sections is evidence of the pairing anti-halo effect on projectile radii. We define the dimensionless staggering parameters ${\Gamma }_{\mathrm{rds}}$ and ${\Gamma }_{\mathrm{R}}$ for projectile radii and reaction cross sections, respectively, and analyze the relation between ${\Gamma }_{\mathrm{rds}}$ and ${\Gamma }_{\mathrm{R}}$ for the scattering of ${}^{14,15,16}$C from a ${}^{12}$C target at 83 MeV/nucleon by taking account of projectile-breakup and nuclear-medium effects with the microscopic version of the continuum discretized coupled-channels method. The value of ${\Gamma }_{\mathrm{R}}$ deviates from that of ${\Gamma }_{\mathrm{rds}}$ by the projectile-breakup effect, the nuclear-medium effect, and an effect resulting from the fact that the scattering is not exactly black-sphere scattering (BSS). The projectile-breakup and nuclear medium effects nearly cancel for ${\Gamma }_{\mathrm{R}}$ at low incident energies. The remaining non-BSS effect becomes small as the incident energy decreases, indicating that nucleus-nucleus scattering at lower incident energies can be a good probe for evaluating ${\Gamma }_{\mathrm{rds}}$ from measured reaction cross sections.

Figure 1

Reaction cross sections ${\sigma }_{\mathrm{R}}$ for ${}^{14,15,16}$C + ${}^{12}$C scattering at 83 MeV/nucleon. Triangle, circle, and square symbols stand for results of Models I, II, and III, respectively. The experimental data are taken from Ref. [11].

Figure 2

$L$ dependence of (a) the absorption probability $P\left(L\right)$ and (b) the partial reaction cross section for ${}^{14,15,16}$C + ${}^{12}$C scattering at 83 MeV/nucleon. Model I is taken.

Figure 3

$E_{\mathrm{in}}$ dependence of ${\Gamma }_{\mathrm{R}}$. Triangle, circle, and square symbols stand for the results of Models I, II, and III, respectively. The solid straight line denotes ${\Gamma }_{\mathrm{rds}}$.