Charge density influence on cold fusion barriers

Cold fusion barriers are studied with respect to the change of the charge density within the overlapping region. Charge evolution from separated target and projectile up to the compound nucleus is taken into account by means of a deduced transition formula which depends on geometric parameter variation defining the shape. Macroscopic, shell correction and total deformation energy for fusionlike configurations are calculated for different charge density paths. Minimization along this coordinate produces variations of about $4\text{MeV}$ for light nuclei and up to $8\text{MeV}$ for superheavy synthesis, for the deformation energy in the last part of the process.

Figure 1

Typical fusionlike shape of ellipsoidally deformed target and projectile in the overlapping region.

Figure 2

Intermediary hypothetic atomic number $Z_{2x}$ (upper plot), real intermediary atomic number $Z_{2i}$ (middle plot), and charge density variation of the target nucleus in the synthesis of ${}^{292}116$.

Figure 3

Coulomb $E_C$ (upper plot), nuclear Yukawa-plus-exponential $E_Y$ (middle plot), and their sum $E_{\mathit{macro}}$ for four configuration paths corresponding to four different charge density variations for ${}^{102}\mathrm{Ru}$ synthesis.

Figure 4

Shell correction $E_{\mathit{shell}}$ (upper plot), and fusion barrier $E_b$ variation within the same four configuration paths as in Fig. 3, in ${}^{102}\mathrm{Ru}$ synthesis.

Figure 5

The corresponding sequences of shapes for ${}^{102}\mathrm{Ru}$; each column represents the path along each of the fusion barriers in Fig. 4.

Figure 6

Coulomb $E_C$ (upper plot), nuclear Yukawa-plus-exponential $E_Y$ (middle plot), and total macroscopic energy $E_{\mathit{macro}}$ for four configuration paths with projectile semiaxis ending at the values indicated in the box, for the synthesis of ${}^{152}\mathrm{Dy}$.

Figure 7

Shell correction $E_{\mathit{shell}}$ (upper plot) and fusion barrier $E_b$ for the paths from Fig. 6, for the synthesis of ${}^{152}\mathrm{Dy}$.

Figure 8

Coulomb $E_C$ (upper plot), nuclear Yukawa-plus-exponential $E_Y$ (middle plot), and macroscopic $E_{\mathit{macro}}$ for four different transition configuration paths (the final values of $b_2$ are indicated in boxes), in the synthesis of the superheavy nucleus ${}^{292}116$.

Figure 9

Shell correction $E_{\mathit{shell}}$ (upper plot) and fusion barrier $E_b$ for the four paths indicated in Fig. 8, in the synthesis of ${}^{292}116$.