Optical model potentials for ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$ from ${}^{63}\mathrm{Cu}({}^7\mathrm{Li},{}^6\mathrm{He}){}^{64}\mathrm{Zn}$ reactions

Angular distributions of the transfer reaction ${}^{63}\mathrm{Cu}\left({}^7\mathrm{Li},{}^6\mathrm{He}\right){}^{64}\mathrm{Zn}$ were measured at $E_{\mathrm{lab}}\left({}^7\mathrm{Li}\right)=12.67$, 15.21, 16.33, 23.30, 27.30, and 30.96 MeV. With the interaction potentials of the entrance channel ${}^7\mathrm{Li}+{}^{63}\mathrm{Cu}$ obtained from elastic scattering data as input, the optical potentials of the halo nuclear system ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$ in the exit channel were extracted by fitting the experimental data with the distorted-wave Born approximation (DWBA) and coupled reaction channels (CRC) methods, respectively. The results show that the threshold anomaly presents in the weakly bound system of ${}^7\mathrm{Li}+{}^{63}\mathrm{Cu}$ and the dispersion relation can be adopted to describe the connection between the real and imaginary potentials, while both the real and imaginary potentials nearly keep constant within the researched energy region for the halo system of ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$. Moreover, calculations by the potentials extracted from the CRC method can reproduce the experimental elastic scattering of the ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$ system rather well, but those by the potentials from the DWBA method cannot, where the couplings between ${}^7\mathrm{Li}$ and ${}^6\mathrm{He}$ are absent. This work verifies the validity of the transfer method in the medium-mass target region and lays a solid foundation for the further study of optical potentials for exotic nuclear systems.

Figure 1

Typical energy spectrum obtained by a single Si(Au) detector at $E_{\mathrm{lab}}\left({}^7\mathrm{Li}\right)=30.96$ MeV and ${\theta }_{\mathrm{lab}}=23.2^{\circ }$. The solid curve presents the results of Gaussian fitting.

Figure 2

Elastic scattering angular distributions of the ${}^7\mathrm{Li}+{}^{63}\mathrm{Cu}$ system. Open circles represent the experimental data. Solid and dashed curves show the fitting results with the coupled reaction channel (CRC) and optical model (OM) calculations, respectively. See text for details.

Figure 3

(a) Typical $\mathrm{\Delta }E\text{−}{E}_{\mathrm{R}}$ spectrum and (b) $\mathrm{\Delta }E$-POS spectrum obtained by the focal plane detector at $E_{\mathrm{lab}}\left({}^7\mathrm{Li}\right)=30.96$ MeV and ${\theta }_{\mathrm{lab}}=16.0^{\circ }$. The two groups of ${}^6\mathrm{He}$ selected by circles correspond to the one-proton transfers from ${}^7\mathrm{Li}$ to the ground state and the first excited state of ${}^{64}\mathrm{Zn}$, respectively.

Figure 4

Angular distributions of transfer reactions ${}^{63}\mathrm{Cu}\left({}^7\mathrm{Li},{}^6\mathrm{He}\right){}^{64}\mathrm{Zn}^{*}$. The energies labeled with an “*” correspond to the one-proton transfers to the first excited state of ${}^{64}\mathrm{Zn}$ $(E^{*}=0.99$ MeV). The solid and dashed curves are the fitting results with CRC and distorted-wave Born approximation (DWBA) methods, respectively. See text for details.

Figure 5

(a) $\mathrm{\Delta }E\text{−}{E}_{\mathrm{R}}$ spectrum obtained by the telescope at $E_{\mathrm{lab}}=15.21$ MeV and ${\theta }_{\mathrm{lab}}={110}^{\circ }$, and (b) the projected energy spectrum of the selected ${}^6\mathrm{He}$ band, where peaks labeled by “g.s.” and “ex. 1” are responsible for the proton transfers to the ground and first excited states of ${}^{64}\mathrm{Zn}$.

Figure 6

Diagrams of couplings of (a) transitions to the excited states of ${}^7\mathrm{Li}$ and ${}^{63}\mathrm{Cu}$, as well as their respective reorientations, and of (b) elastic channels to transfer channels.

Figure 7

Depths of (a) real and (b) imaginary potentials vary with the reaction energy of the ${}^7\mathrm{Li}+{}^{63}\mathrm{Cu}$ system. Solid curves in panel (b) present the segmental linear fitting results with errors as weights. And the curve in panel (a) shows the dispersion relation calculation according to the variation of the imaginary part. The vertical dashed line denotes the position of the Coulomb barrier, which is about 13.05 MeV.

Figure 8

Depths of (a) real and (b) imaginary potentials vary with the reaction energy of the ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$ system. The solid and empty circles represent the results obtained with the CRC and DWBA methods, respectively. Solid and dashed lines are the corresponding linear fitting results with errors as weights.

Figure 9

Elastic scattering of the ${}^6\mathrm{He}+{}^{64}\mathrm{Zn}$ system at (a) $E_{\mathrm{lab}}\left({}^6\mathrm{He}\right)=10.0$ MeV and (b) $E_{\mathrm{lab}}\left({}^6\mathrm{He}\right)=13.6$ MeV. Open circles are the experimental data taken from Ref. [15]. The solid and dashed curves represent the calculation results with the systematic OMPs obtained by the CRC and DWBA methods, respectively.