Global optical potential for ${}^7\mathrm{Be}$ on various targets at sub- and near-barrier energies

A global phenomenological energy dependent optical potential for the radioactive nucleus ${}^7\mathrm{Be}$ on various targets is developed. This optical potential is based on Woods-Saxon form factors with a smooth mass dependent potential depth for above-barrier energies and an energy and mass dependent depth below barrier. The potential is validated with elastic scattering and fusion calculations which are compared with experimental data and are found to be in very good agreement. The present potential is compared with the energy dependent Cook potential, developed for ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$.

Figure 1

Previous angular distribution data for ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$, at (a) 37.6 MeV, (b) 40.5 MeV, (c) 42 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [36].

Figure 2

Previous angular distribution data for ${}^7\mathrm{Be}+{}^{90}\mathrm{Zr}$, at (a) 19.7 MeV, (b) 21.3 MeV, (c) 27.1 MeV, (d) 27.5 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines respectively. The data are from Ref. [23]. Note that the data at 26.6 MeV now appear as data at 27.1 MeV due to a recalibration of the beam energies.

Figure 3

Previous angular distribution data for ${}^7\mathrm{Be}+{}^{58}\mathrm{Ni}$, at (a) 15.1 MeV, (b) 17.1 MeV, (c) 19.9 MeV, (d) 21.5 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data designated with the stars are from Ref. [37] for all energies, while for the highest energy data of Ref. [38] also appear and are designated with the filled circles.

Figure 4

Previous angular distribution data for ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$, at (a) 12.9 MeV, (b) 16.7 MeV, (c) 19.5 MeV, (d) 21.7 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed-green and dotted-dashed blue lines, respectively. The data are from Ref. [24].

Figure 5

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{208}\mathrm{Pb}$, at (a) 31 MeV, (b) 35 MeV, (c) 39 MeV, (d) 44 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [39].

Figure 6

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{144}\mathrm{Sm}$, at (a) 22.6 MeV, (b) 25 MeV, (c) 27 MeV, (d) 32 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [40].

Figure 7

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{138}\mathrm{Ba}$, at (a) 22. MeV, (b) 24 MeV, (c) 26 MeV, (d) 30 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [41].

Figure 8

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{64}\mathrm{Zn}$, at (a) 23.8 MeV, (b) 15.02 MeV, (c) 18.15 MeV, (d) 20.12 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [42].

Figure 9

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{58}\mathrm{Ni}$, at (a) 14.22 MeV, (b) 16.25 MeV, (c) 18.28 MeV, (d) 20.31 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are showm with the dashed-green and dotted-dashed blue lines, respectively. The data are from Ref. [43].

Figure 10

Previous angular distribution data for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$, at (a) 7.8 MeV, (b) 9.82 MeV, (c) 12.84 MeV, (d) 14.85 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed- green and dotted-dashed blue lines, respectively. The data are from Ref. [44].

Figure 11

Elastic scattering data at 52 MeV for (a) ${}^7\mathrm{Li}+{}^{208}\mathrm{Pb}$ [45], (b) ${}^7\mathrm{Li}+{}^{144}\mathrm{Sm}$ [46], and (c) ${}^7\mathrm{Li}+{}^{138}\mathrm{Ba}$ [47], are compared with calculations adopting the present potential, solid red line, and the ${}^{6,7}\mathrm{Li}$ modified Cook potential, designated with the dotted dashed and dashed blue and green lines. The rainbow structure is clearly seen and it is reproduced very well with the present potential.

Figure 12

Previous angular distribution data for ${}^6\mathrm{Li}+{}^{90}\mathrm{Zr}$, at (a) 14.89 MeV, (b) 16.9 MeV, (c) 18.9 MeV, (d) 24.92 MeV, are compared with OMP calculations. Calculations with the present potential are designated with the solid red line, while those with the Cook potential for ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ are shown with the dashed green and dotted-dashed blue lines, respectively. The data are from Ref. [48].

Figure 13

Previous fusion data for ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ and ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ [54] are compared with BPM calculations taking into account a dispersion corrected potential [22], the present potential, the modified Cook potential for ${}^{6,7}\mathrm{Li}$, and the Wong prediction (UFF).

Figure 14

Barrier penetration fusion calculations, appropriately reduced, are presented for ${}^6\mathrm{Li}+{}^{90}\mathrm{Zr}$ with the present potential and the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ Cook ones. The calculations are compared with total fusion data [55, 56] for ${}^{59}\mathrm{Co}$ and ${}^{120}\mathrm{Sn}$ due to lack of data on ${}^{90}\mathrm{Zr}$.

Figure 15

Barrier penetration fusion calculations, appropriately reduced, are presented for light, medium, and heavy mass targets with the present potential as well as with the modified Cook potential for ${}^{6,7}\mathrm{Li}$, for ${}^7\mathrm{Be}$ on various targets as shown in the inset.

Figure 16

The present optical potential is compared with the modified Cook potential for ${}^{6,7}\mathrm{Li}$ and a BDM3Y1 interaction for the system ${}^7\mathrm{Be}+{}^{90}\mathrm{Zr}$ at projectile energy of 27 MeV.