Effects of weakly coupled channels on quasielastic barrier distributions

Heavy-ion collisions often produce fusion barrier distributions with structures displaying a fingerprint of couplings to highly collective excitations. Similar distributions can be obtained from large-angle quasielastic scattering, although in this case, the role of the many weak direct-reaction channels is unclear. For ${}^{20}\mathrm{Ne}+{}^{90}\mathrm{Zr}$, we have observed the barrier structures expected for the highly deformed neon projectile; however, for ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$, we find significant extra absorption into a large number of noncollective inelastic channels. This leads to smearing of the barrier distribution and a consequent reduction in the “resolving power” of the quasielastic method.

Figure 1

Comparison of the excitation functions for backscattering of ${}^{20}\mathrm{Ne}$ on ${}^{90,92}\mathrm{Zr}$ isotopes.

Figure 2

Barrier distributions for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems [panels (a) and (b), respectively]. Different symbols refer to different laboratory detector angles. The scaling to $E_{\mathrm{eff}}$ (see text) can be seen to be very good. The dashed line in the upper panel shows the CC prediction [folded with the experimental resolution of 1.2 MeV (FWHM)]. The solid line in the lower panel shows the result of transforming the ${}^{20}\mathrm{Ne}+{}^{90}\mathrm{Zr}$ experimental data as described in the text (see Sec. 3). This transformation reproduces extremely well the ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$ data, without any input from the CC calculations.

Figure 3

Schematic view of the measurement setup (see detailed description in the text).

Figure 4

Comparison of differential transfer cross sections measured for the ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ systems at $E_{\mathrm{eff}}=50$ MeV and a CM angle around ${156}^{°}$. Different bars represent different transfer channels.

Figure 5

Inelastic (nontransfer) $Q$-value spectra for ${}^{20}\mathrm{Ne}+{}^{90,92}\mathrm{Zr}$ (open and filled circles, respectively), taken from scattering of the ${}^{20}\mathrm{Ne}$ projectile at ${156}^{°}$. The circles show the number of counts in a 0.44-MeV $Q$-value bin. Lines represent CC calculations after folding with the experimental resolution (see text). The solid line treats the zirconium targets as inert (i.e., it ignores their excitations), whereas the dashed line for ${}^{90}\mathrm{Zr}$ and the dot-dashed curve for ${}^{92}\mathrm{Zr}$ take into account the single and mutual excitations of the target quadrupole- and octupole-phonon states. All distributions are normalized to have the same value as the ${}^{20}\mathrm{Ne}+{}^{90}\mathrm{Zr}$ data at the elastic peak.

Figure 6

Squares show the difference between the ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$ inelastic data (filled circles) and those for ${}^{20}\mathrm{Ne}+{}^{90}\mathrm{Zr}$ (open circles). In the region between the energies of the $2^{+}$ and $4^{+}$ states in ${}^{20}\mathrm{Ne}$, the difference shows none of the structure due to the coupling to those states that is seen in the individual curves. This implies that their contributions are the same in both reactions. The cumulative sum of the difference (dashed line) shows that 75% of the extra cross section in the ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$ reaction comes from the region $-Q<5$ MeV.

Figure 7

Known levels in ${}^{90}\mathrm{Zr}$ and ${}^{92}\mathrm{Zr}$ up to 5.3 MeV [20]. The level density is significantly higher for the heavier isotope owing to the two valence neutrons outside the $N=50$ closed shell. The dashed lines indicate the energies of the most collective states in these two nuclides; quadrupole ($2^{+}$) and octupole ($3^{-}$) vibrational states. Even these collective states individually contribute little to the $Q$-value spectra (see Fig. 5). It is clear, however, that the large number of noncollective (n-particle-n-hole) states generates a broad background to the $Q$-value spectrum for ${}^{20}\mathrm{Ne}+{}^{92}\mathrm{Zr}$. Arrows indicate the energies of the $2^{+}$ and $4^{+}$ rotational states in ${}^{20}\mathrm{Ne}$. Note that 75% of the noncollective background comes from states below 5 MeV excitation energy.

Figure 8

Test function for the one-channel calculation (${}^{16}\mathrm{O}+{}^{92}\mathrm{Zr}$) with the optical-model potential of Takagui et al. (solid line), the same with the imaginary potential confined to the nuclear interior (dotted line), and the result of transforming the latter $f_{\mathrm{QE}}$ to the wider one (dashed line). See text.