The threshold anomaly of the phenomenological potential has been known for a long time in nuclear reactions at energies around the Coulomb barrier, where the connection between the real and imaginary potentials is well described by the dispersion relation. However, this connection is not clear yet for some weakly bound nuclear systems, especially for reactions induced by exotic radioactive nuclei. In this study, precise optical potentials of the halo nuclear system ^{6}He+^{209}Bi were extracted via ^{208}Pb(^{7}Li,^{6}He) transfer reactions with energies measured downward to the extremely sub-barrier region. The real potential presents a bell-like shape around the barrier as a normal threshold anomaly in tightly bound nuclear systems. However, the imaginary potential shows an abnormal behavior: it increases first with energy decreasing below the barrier and then falls quickly down to 0. It is the first time the threshold of the imaginary potential has been determined in an exotic nuclear system. Moreover, experimental results show the dispersion relation is not applicable for this system, which may be a common phenomenon for exotic nuclear systems. We discuss possible explanations for such a peculiar behavior, but further study is still desired for the underlying physics.

Is the Dispersion Relation Applicable for Exotic Nuclear Systems? The Abnormal Threshold Anomaly in the ^{6}He+^{209}Bi System.

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.

/pdf/abnormal-behavior-of-the-optical-potential-for-the-halo-38qdp9lrhm.pdf

Abnormal behavior of the optical potential for the halo nuclear system 6 He+ 209 Bi

Elastic scattering for 6Li+51V and systematic study of breakup threshold anomaly

Using different potentials based on phenomenological, semi microscopic, and microscopic models, we investigated the reaction dynamics induced by the weakly bound 6Li ions on a heavy mass target 208Pb at sixteen energy sets ranging from 25 MeV to 210 MeV. The 6Li cluster nature and its dissociation into a core (α-particle) and a valence particle (deuteron) orbiting this core was taken into consideration using the cluster folding model (CFM). The new version of Sao Paulo potential (SPP2) is also used to investigate 6Li+208Pb data. In order to reproduce the experimental data, the strength of real part of potential created using SPP and CFM should be reduced by ~ 49 % and 62 %, respectively. The data could be well reproduced using non-renormalized real cluster folding potential, if an additional dynamical polarization potential (DPP) of repulsive real surface form is introduced. The observed reduction in the strength of the real double folded and cluster folding potentials is due to the break-up effect of 6Li.

Break-up effect of the weakly bound 6Li nuclei scattered by 208Pb target

In the present research, we utilized the single-folding model to develop a systematical optical potential for $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$, employing the nucleon-nucleus global potentials introduced by Koning and Delaroche (KD02). We analyzed the elastic scattering angular distributions of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ on targets with mass numbers ranging from 24 to 209 using the single-folding potential. Incident energies between 5 and 55 MeV/nucleon were considered. The real part of the single-folding model potential was renormalized with one free parameter, while leaving its imaginary part unchanged. The resulting renormalization factors of the single-folding model potentials show consistent systematics. Our approach effectively reproduced the elastic scattering and reaction cross sections of the targets in our current study. In addition, we also compared the prediction abilities of our systematic optical potentials with those of others. 

Systematic single-folding optical potential for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Li</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Li</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> based on …

The angular distributions of elastic scattering for the 6Li +208Pb system have been measured at several energies around the Coulomb barrier. The parameters of optical potential are extracted by means of a phenomenological optical model analysis. It is found that the real and imaginal potentials show a pronounced energy dependence. The behaviour of the potential at the nearly especially sub-barrier energies in the 6Li+208Pb system is quite different from the results of some previous reports observed in other systems, such as 19F+208Pb and 16O+208Pb. This unusual threshold phenomenon indicates that breakup channel is strongly coupled with the elastic channel and has obvious effects on optical potential.

http://iopscience.iop.org/article/10.1088/0256-307X/23/5/023/pdf

Unusual Threshold Anomaly in the 6 Li+ 208 Pb System

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Unusual Threshold Anomaly in the 6 Li+ 208 Pb System