Abnormal behavior of the optical potential for the halo nuclear system ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$

In a recent transfer reaction measurement of ${}^{208}\mathrm{Pb}$(${}^7\mathrm{Li},{}^6\mathrm{He}$)${}^{209}\mathrm{Bi}$ at energies around and below the Coulomb barrier, the optical model potentials of the halo nuclear system ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ were extracted by fitting the experimental data with the theoretical frameworks of the distorted-wave Born approximation and coupled reaction channels, respectively. With the high-precision result, a complete picture of the behavior of the optical potential for this halo system is clearly derived for the first time. The real potential presents a bell-like shape around the barrier as a normal threshold anomaly. However, for the imaginary part, it first increases with the energy decreasing below the barrier and then falls quickly to 0, hence the threshold energy can be determined by fitting the variation trend. Moreover, the result also provides some evidence that the dispersion relation does not hold for this halo nuclear system, which calls for further investigation of the underlying physics.

Figure 1

Schematic of the experimental setup.

Figure 2

Typical energy spectrum obtained by a single PIN detector at $E_{\mathrm{lab}}$(${}^7\mathrm{Li})=21.20$ MeV and ${\theta }_{\mathrm{lab}}=27.0^{\circ }$.

Figure 3

Angular distributions of elastic scattering of the ${}^7\mathrm{Li}+{}^{208}\mathrm{Pb}$ system. Open circles represent experimental data. Solid and dashed curves show fitting results from the CRC and OM calculations, respectively.

Figure 4

(a) $\mathrm{\Delta }E\text{−}{E}_R$ spectrum obtained by the telescope at $E_{\mathrm{lab}}=24.30$ MeV with ${\theta }_{\mathrm{lab}}={144}^{\circ }$–${171}^{\circ }$ and (b) projected energy spectrum of the selected ${}^6\mathrm{He}$ band, where the peaks are labeled corresponding to the excitation energies of ${}^{209}\mathrm{Bi}$ (in MeV).

Figure 5

Angular distributions of ${}^{208}\mathrm{Pb}$(${}^7\mathrm{Li},{}^6\mathrm{He}$) reactions for protons transferred to different states of ${}^{209}\mathrm{Bi}$ at $E_{\mathrm{lab}}=28.55$ MeV. Experimental results are labeled according to the excitation energy of ${}^{209}\mathrm{Bi}$. Solid and dashed curves represent the CRC and DWBA fitting results, respectively.

Figure 6

Same as Fig. 5, but for the incident energy of $E_{\mathrm{lab}}=25.67$ MeV.

Figure 7

Same as Fig. 5, but for the incident energies of (a) $E_{\mathrm{lab}}=24.30$ MeV and (b) $E_{\mathrm{lab}}=21.20$ MeV.

Figure 8

Variations of angular distributions of ${}^{208}\mathrm{Pb}$(${}^7\mathrm{Li},{}^6\mathrm{He}$)${}^{209}\mathrm{Bi}$ with (a) $V$ and (b) $W$ of ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ in the exit channel at $E_{\mathrm{lab}}{(}^7\mathrm{Li})=21.20$ MeV. (c, d) Corresponding results for elastic scattering of ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ at the responsible energy $E_{\mathrm{c}.\mathrm{m}.}{(}^6\mathrm{He})=14.34$ MeV.

Figure 9

Energy dependence of the (a) real and (b) imaginary potentials at the sensitivity radius of 13.5 fm for the ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ system. Filled circles and open squares represent CRC and DWBA results from the present work; filled and open stars denote CRC and DWBA results taken from Ref. [18]. Solid and dashed curves in (b) represent the linear segment fitting for the imaginary potential derived by the CRC and DWBA approaches. The predictions of the dispersion relation according to the variations of the imaginary potentials are presented in (a) by the corresponding curves for the CRC and DWBA results. Inset in (a): Fine structure of the real potential.

Figure 10

Elastic scattering angular distributions of the ${}^6\mathrm{He}+{}^{209}\mathrm{Bi}$ system. Open circles represent experimental data taken from Refs. [38] and [39]. Solid and dashed curves are calculation results with OMP parameters extracted through the CRC and DWBA methods, respectively.