Quasi-elastic scattering in the ${}^{20}$Ne+${}^{90,92}$Zr reactions: Role of noncollective excitations

Conventional coupled-channels analyses, that take account of only the collective excitations of the colliding nuclei, have failed to reproduce the different behavior of the experimental quasi-elastic barrier distributions for the ${}^{20}$Ne+${}^{90,92}$Zr systems. To clarify the origins of this difference, we investigate the effect of noncollective excitations of the Zr isotopes. Describing these excitations in a random-matrix model, we explicitly take them into account in our coupled-channels calculations. The noncollective excitations are capable of reproducing the observed smearing of the peak structure in the barrier distribution for ${}^{20}$Ne+${}^{92}$Zr, while not significantly altering the structure observed in the ${}^{20}$Ne+${}^{90}$Zr system. The difference is essentially related to the closed neutron shell in ${}^{90}$Zr.

Figure 1

Upper panel: the number of levels of ${}^{90}$Zr up to excitation energy $\epsilon$ as a function of $\epsilon$. The histogram represents the experimental data [22], while the dashed line shows its fit with a sixth-order polynomial. Lower panel: the continuous level density obtained as the first derivative of the fitting function of the upper panel.

Figure 2

The same as Fig. 1 but for ${}^{92}$Zr.

Figure 3

The quasi-elastic cross section (upper panel) and the quasi-elastic barrier distribution (lower panel) for the ${}^{20}$Ne+${}^{90}$Zr system at the scattering angle ${\theta }_{\mathrm{lab}}={150}^{\circ }$. Dots represent the experimental data, taken from Ref. [21]. Dashed lines show the results obtained by including only collective excitations, while solid lines show the results including the noncollective excitations. The solid lines are shifted in energy by the amount shown in the figure in order to compensate for the trivial change of Coulomb barrier height due to the noncollective couplings.

Figure 4

The same as Fig. 3 but for the ${}^{20}$Ne+${}^{92}$Zr system.

Figure 5

The $Q$-value distributions for the ${}^{20}$Ne+${}^{90}$Zr system at a scattering angle ${\theta }_{\mathrm{c}.\mathrm{m}.}={156}^{\circ }$ and incident center-of-mass energy $E_{\mathrm{c}.\mathrm{m}.}=51.85$ MeV. Experimental data are taken from Ref. [21]. The calculated results are smeared with a Gaussian function with a width of $\eta =0.5$ MeV, and then normalized to the experimental elastic peak at $E^{*}=0$.

Figure 6

The same as Fig. 5, but for the ${}^{20}$Ne+${}^{92}$Zr system. Experimental data are from Refs. [21, 44].

Figure 7

Comparison of the $Q$-value distributions for the ${}^{20}$Ne+${}^{90}$Zr and ${}^{20}$Ne+${}^{92}$Zr systems. The circles and the dashed line show, respectively,the experimental data and the calculated result for the ${}^{20}$Ne+${}^{90}$Zr system, while the squares and the solid line represent the ${}^{20}$Ne+${}^{92}$Zr system.

Figure 8

The energy dependence of the $Q$-value distribution for the ${}^{20}$Ne+${}^{90}$Zr system. The dashed and the solid peaks show the contributions from the collective and the non-collective excitations, respectively. The solid lines are obtained by smearing the spectra with a Gaussian function of width 0.2 MeV.

Figure 9

Same as Fig. 8, but for ${}^{20}$Ne+${}^{92}$Zr.