Investigation of the threshold anomaly for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system

Elastic-scattering angular distributions were measured for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system at various energies; namely, 24, 26, 28, 30, 35, 40, and 44 MeV. The optical-model analysis was performed to investigate the energy dependence of real and imaginary potentials, employing a Woods–Saxon form of potential. The dispersion-relation analysis were also carried out to check the consistency of real and imaginary parts of the potentials. The energy dependence of real and imaginary potentials does not follow the trend of conventional threshold anomaly but rather represents unusual behavior of the increase of imaginary part of the potential and corresponding decrease in real part of the potential near the Coulomb barrier energy. The effect of breakup coupling on elastic-scattering angular distributions was studied by a continuum-discretized coupled-channels (CDCC) calculation. The behavior of dynamic polarization potentials obtained due to the breakup coupling is discussed. The total reaction cross sections for the present and various other systems are also compared involving ${}^7\mathrm{Li}$ projectile on different target nuclei in the mass range $A=16$ to 232.

Figure 1

A typical biparametric $\mathrm{\Delta }E\text{−}E$ spectrum for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system at $E_{\mathrm{lab}}=40$ MeV and $\theta ={40}^{\circ }$.

Figure 2

Experimental elastic-scattering cross sections normalized to the Rutherford cross sections as a function of ${\theta }_{\mathrm{c}.\mathrm{m}.}$ and its best fit from optical-model analysis for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system. The curves corresponding to best fit are obtained by using the Woods–Saxon potential (WSP).

Figure 3

Sensitivity radii based on the crossing of the (a) real and (b) imaginary parts of the WSP potential at $E_{\mathrm{lab}}=40$ MeV. The real and imaginary diffuseness, $a_r$ and $a_i$, are varied in steps of 0.02 fm between 0.66 and 0.74 fm.

Figure 4

Energy dependence of the (a) real and (b) imaginary parts of the optical potential obtained for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system at an average radius $R_s=11.5$ fm. The energy $V_b$ of the Coulomb barrier is $\sim 26.6$ MeV in the center-of-mass frame calculated using the Bass formula.

Figure 5

Experimental elastic-scattering cross sections normalized to the Rutherford cross sections as a function of ${\theta }_{\mathrm{c}.\mathrm{m}.}$ for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system. The results of the CDCC calculation with and without including breakup couplings are shown by continuous and dashed lines, respectively.

Figure 6

(a) Real and (b) imaginary parts of the dynamic polarization potentials (DPP) extracted from the CDCC calculation for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system as a function of radius $R$.

Figure 7

(a) Real and (b) imaginary parts of the potential at an average radius $R_s=11.5$ fm as a function of energy for the ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ system. The solid circles show dynamic polarization potentials (DPPs) extracted from the CDCC calculations and the open circles are the bare potentials which do not include any coupling.

Figure 8

Comparison of reduced reaction cross sections for the reactions that involve ${}^7\mathrm{Li}$ projectile and different target nuclei [4, 12, 15, 16, 23, 24, 25, 26, 27, 28].