Effects of anharmonic vibration on large-angle quasi-elastic scattering of ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$

We study the effects of double octupole and quadrupole phonon excitations in the ${}^{144}\mathrm{Sm}$ nucleus on quasi-elastic ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ scattering at backward angles. To this end, we use the coupled-channels framework, taking into account explicitly the anharmonicities of the vibrations. We use the same coupling scheme as that previously employed to explain the experimental data of sub-barrier fusion cross sections for the same system. We show that the experimental data for the quasi-elastic cross sections are well reproduced in this way, although the quasi-elastic barrier distribution has a distinct high energy peak which is somewhat smeared in the experimental barrier distribution. We also discuss the effects of proton transfer on the quasi-elastic barrier distribution. Our study indicates that the fusion and quasi-elastic barrier distributions for this system cannot be accounted for simultaneously with the standard coupled-channels approach.

Figure 1

Comparison between the experimental fusion (the filled circles) and quasi-elastic (the open squares) barrier distributions for the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction. They are normalized to unit area in the energy interval between $E_{\mathrm{c}.\mathrm{m}.}=$ 56 and 70 MeV. The experimental data are taken from Refs. [9] and [11].

Figure 2

Comparison of the experimental data with the coupled-channels calculations for ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction for (a) the ratio of quasi-elastic to the Rutherford cross sections and for (b) quasi-elastic barrier distribution. The dotted and dashed lines are obtained by including up to the single and the double phonon excitations in the harmonic limit, respectively. The solid line is the result of the coupled-channels calculations with the double anharmonic phonon excitations. The experimental data are taken from Ref. [11].

Figure 3

(a) Comparison of the measured pure elastic (the open squares), the $Z=8\hspace{1em}(-\hspace{1em}\mathrm{el})$ (the open circles) and the residual (the filled circles) components of $d{\sigma }_{\mathrm{qel}}/d{\sigma }_R$ with the coupled-channels calculations for ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction. The $Z=8\hspace{1em}(-\hspace{1em}\mathrm{el})$ component is defined as the $Z=8$ yields subtracted the elastic component, while the residual component the sum of $Z=6$ and 7 yields. The dashed line is the result of elastic scattering, while the dotted line shows the inelastic cross sections for the single $2^{+}$ and $3^{-}$ phonon states. The solid line is the result of the sum of inelastic cross sections for the double phonon states in ${}^{144}\mathrm{Sm}$. (b) The same as (a) but for the pure elastic and the total inelastic cross sections. The experimental data are taken from Ref. [11].

Figure 4

Same as Fig. 3, but for the fraction of cross section for each channel in the quasi-elastic cross sections.

Figure 5

Effect of proton transfers on the quasi-elastic scattering cross sections (the upper panel) and on the quasi-elastic barrier distribution (the lower panel) for ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ reaction. The solid line is the result of the coupled-channels calculations including the effect of double anharmonic vibrations only. The dashed line is obtained by including, in addition, the couplings to the proton transfer channels. The experimental data are taken from Ref. [11].

Figure 6

Contribution of quasi-elastic cross sections from several channels. The solid and dashed line are the results of the coupled-channels calculations for the proton transfer and the elastic cross sections, respectively. The dotted line denotes the sum of total inelastic and proton transfer cross sections. The corresponding experimental data are shown by the filled circles, the open squares, and the open triangles, respectively, which are taken from Ref. [11].

Figure 7

Same as Fig. 6, but for the fraction in the quasi-elastic cross sections.

Figure 8

Comparison of the theoretical fusion barrier distribution (dashed line) with the quasi-elastic barrier distribution (solid line) obtained with different coupling schemes for ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ system. Both functions are normalized to unit area in energy interval between 54 and 70 MeV. (a) The results of the coupling to one phonon state of quadrupole and octupole excitations of ${}^{144}\mathrm{Sm}$ in the harmonic oscillator limit. (b) The same as (a) but for the coupling up to double phonon states. (c) The result when the coupling to anharmonic vibration of double quadrupole and octupole excitations in ${}^{144}\mathrm{Sm}$ is taken into account.