The process of the synthesis of superheavy elements (SHEs) is not yet understood completely. In the presented work we make an attempt to describe the cold fusion reactions of the type $X+(\mathrm{P}\mathrm{b},\mathrm{B}\mathrm{i})\to \mathrm{SHE}+1n$ at subbarrier energies. The process of the formation of SHEs is subdivided into three steps. (1) The capture of two spherical nuclei and the formation of a common shape of the two touching nuclei. Low-energy surface vibrations and transfer of few nucleons are taken into account in the first step of the reaction. (2) The formation of a spherical or near spherical compound nucleus. (3) The survival of the excited compound nucleus due to evaporation of neutrons and $\gamma$-ray emission in competition with fission. A lowering of the fission barrier was taken into account, which arises from a reduction of shell effects at increasing excitation energy of the compound nucleus. The following reactions were analyzed in detail: ${(}^{58}\mathrm{Fe},$ ${}^{64}\mathrm{Ni},$ ${}^{70}\mathrm{Zn},$ ${}^{78}\mathrm{Ge}{)+}^{207}\mathrm{Pb},$ ${(}^{50}\mathrm{Ti},$ ${}^{54}\mathrm{Cr},$ ${}^{58}\mathrm{Fe},$ ${}^{59}\mathrm{Co},$ ${}^{62,64}\mathrm{Ni},$ ${}^{65}\mathrm{Cu},$ ${}^{66,68,70}\mathrm{Zn},$ ${}^{71}\mathrm{Ga},$ ${}^{74,76,78}\mathrm{Ge},$ ${}^{75}\mathrm{As},$ ${}^{80,82}\mathrm{Se}{)+}^{208}\mathrm{Pb},$ ${(}^{58}\mathrm{Fe},$ ${}^{64}\mathrm{Ni},$ ${}^{70}\mathrm{Zn},$ ${}^{78}\mathrm{Ge}{)+}^{210}\mathrm{Pb},$ and ${(}^{50}\mathrm{Ti},$ ${}^{54}\mathrm{Cr},$ ${}^{58}\mathrm{Fe},$ ${}^{64}\mathrm{Ni},$ ${}^{70}\mathrm{Zn},$ ${}^{78}\mathrm{Ge}{)+}^{209}\mathrm{Bi}.$ The presented model describes well the available experimental cross-section data and allows for predicting cross-section values for the synthesis of so-far unknown heavier elements.

• Received 10 February 1999

DOI:https://doi.org/10.1103/PhysRevC.61.034606