Analysis of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ elastic and inelastic scattering using the optical model and the coupled-channels mechanism

Inelastic ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ scattering at $E_{\mathrm{lab}}=250,350,704,\mathrm{and}1120\mathrm{MeV}$ for the transitions to the lowest $2^{+}$ and $3^{-}$ states in the ${}^{16}\mathrm{O}$ nucleus have been analyzed within the coupled-channels mechanism by using the semimicroscopic optical potential and inelastic form factor given by the phenomenological squared Woods-Saxon potential, the full cluster potential, and the M3Y $NN$ effective interaction without density dependence. The obtained real potentials, in conjunction with the phenomenological squared Woods-Saxon imaginary potential, provide a satisfactory agreement with the experimental data for the elastic- and inelastic-scattering angular distributions. The deformation length and the intrinsic quadrupole $\left(Q_{20}\right)$ and octupole $\left(Q_{30}\right)$ moment values were extracted and were compared with the electromagnetic measurement values and those obtained from previous studies.

Figure 1

A comparison between the measured ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ elastic and inelastic differential cross sections that lead to $0^{+},2^{+}$ (6.92-MeV), and $3^{-}$ (6.13-MeV) states in the ${}^{16}\mathrm{O}$ target and the theoretical predictions obtained by using the WS2, M3Y, and DFC1 potentials at $E_{\mathrm{lab}}=250\mathrm{MeV}$. Data are taken from Ref. [15].

Figure 2

The same as Fig. 1 but at $E_{\mathrm{lab}}=350\mathrm{MeV}$. Data are taken from Ref. [15].

Figure 3

The same as Fig. 1 but at $E_{\mathrm{lab}}=704\mathrm{MeV}$. Data are taken from Ref. [15].

Figure 4

The same as Fig. 1 but at $E_{\mathrm{lab}}=1120\mathrm{MeV}$. Data are taken from Ref. [15].

Figure 5

Energy dependence of the deformation length ${\delta }_{\lambda }$was obtained from the corresponding ${\beta }_{\lambda }$and electromagnetic measurement $B\left(E\lambda \right)\uparrow$ as in Eqs. (4) and (7), where ${\delta }_{\lambda }=1.2{\beta }_{\lambda }{A}_T^{1/3}$ was deduced from the analysis of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ inelastic scattering by using the CC analysis by WS2, M3Y, and DFC1 potentials. Lines are drawn to guide the eyes.

Figure 6

Energy dependence of the intrinsic electric moment $Q_{\lambda 0}$ was obtained from the corresponding ${\beta }_{\lambda }$and electromagnetic measurement $B\left(E\lambda \right)\uparrow$ as in Eqs. (4) and (7), where ${\delta }_{\lambda }=1.2{\beta }_{\lambda }{A}_T^{1/3}$ was deduced from the analysis of the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ inelastic scattering by using the CC analysis by WS2, M3Y, and DFC1 potentials. Lines are drawn to guide the eyes.