Diffusion as a possible mechanism controlling the production of superheavy nuclei in cold fusion reactions

The fusion probability for the production of superheavy nuclei in cold fusion reactions was investigated and compared with recent experimental results for ${}^{48}\mathrm{Ca}, {}^{50}\mathrm{Ti}$, and ${}^{54}\mathrm{Cr}$ incident on a ${}^{208}\mathrm{Pb}$ target. Calculations were performed within the fusion-by-diffusion model (FbD) using the new nuclear data tables by Jachimowicz et al. [At. Data Nucl. Data Tables 138, 101393 (2021)]. It is shown that the experimental data could be well explained within the framework of the FbD model. The saturation of the fusion probability at bombarding energies above the interaction barrier is reproduced. It emerges naturally from the physical effect of the suppression of contributions of higher partial waves in fusion reactions. The role of the difference in values of the rotational energies in the fusion saddle point and contact (sticking) configuration of the projectile-target system is discussed.

Figure 1

The injection point systematics obtained for the set of $1n$ cold fusion reactions [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36] using new nuclear data tables [4]. If not indicated otherwise, the targets were ${}^{208}\mathrm{Pb}$ or ${}^{209}\mathrm{Bi}$. The color of the points indicates the laboratory where the reaction was studied: LBNL (red), GSI (black), RIKEN (blue). See text for details.

Figure 2

Fusion probability $P_{\mathrm{fus}}\left(l\right)$ as a function of temperature $T$ and the barrier height opposing fusion $H\left(l\right)$. Lines correspond to selected angular momenta $l=0\hslash , 20\hslash , 40\hslash$, and $60\hslash$. Calculations for ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ (green lines), ${}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$ (blue lines), and ${}^{54}\mathrm{Cr}+{}^{208}\mathrm{Pb}$ (red lines) fusion reactions. The color of the surface marks the temperature gradient of the synthesized system. The labels “outside” and “inside” refer to the injection point position relative to the saddle [see Eq. (3) and its discussion].

Figure 3

Capture cross section ${\sigma }_{\mathrm{cap}}$ (top panels) and averaged fusion probability $P_{\mathrm{fus}}$ (bottom panels) for the reactions (a), (b) ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, (c), (d) ${}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$, (e), (f) ${}^{54}\mathrm{Cr}+{}^{208}\mathrm{Pb}$. Solid lines show the FbD model calculations of ${\sigma }_{\mathrm{cap}}$ and $P_{\mathrm{fus}}$. Dashed lines in the top panels show calculated ${\sigma }_{\mathrm{cap}}$ scaled by the indicated suppression factors. The arrows indicate the value of the mean entrance channel barrier $B_0$ for each reaction. The error corridors resulting from the $s_{\mathrm{inj}}$ systematics uncertainty are shown as shaded areas in the bottom panels. Points represent relevant experimental data taken from Refs. [6, 37, 38, 39, 40, 41]. If not shown, error bars are smaller than the symbol sizes.

Figure 4

Calculated compound nucleus formation cross sections ${\sigma }_{\mathrm{fus}}$ for ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}, {}^{50}\mathrm{Ti}+{}^{208}\mathrm{Pb}$, and ${}^{54}\mathrm{Cr}+{}^{208}\mathrm{Pb}$ fusion reactions. Points are derived from the experimental data presented in Ref. [6]. Dashed lines show calculations for two extreme orientations of spherical target and ${}^{54}\mathrm{Cr}$ projectile in the entrance channel. The arrows indicate the value of the mean entrance channel barrier $B_0$ for each reaction. See text for details.