The fission width of nucleus with the fission barrier dependent on excitation energy and the ratio of the fission and neutron emission widths

 

V. Yu. Denisov¹

 

¹ Institute for nuclear research of NAS of Ukraine, Kyiv, Ukraine

 

Nowadays it is well-known that the fission barrier depends on the temperature or on the thermal excitation energy. For example, the fission barrier evaluated in the framework of the Strutinsky shell correction prescription consists of the liquid-drop and shell-correction contributions. The liquid-drop part of the fission barrier weakly depends on temperature at T<2.5 MeV and strongly decreases at T>2.5 MeV. The temperature dependence of the Strutinsky shell correction contribution into the fission barrier is induced by both the disappearance of the pair gap at critical temperature T~0.5 MeV and exponential drops of the shell correction energy with the thermal excitation energy. The shell correction energy is close to zero at T~2.5 MeV.

According to the Bohr-Wheeler transition state approach the fission width of nucleus relates to the number of states located over the fission barrier. Therefore, the reduced value of the fission barrier in hot nucleus leads to the increasing of the number of states located over the fission barrier in comparison the number of states located over the fission barrier obtained with the same value of the fission barrier as the one in the cold nucleus. As a result, the fission width calculated for the fission barrier dependent on excitation energy is larger than the one evaluated for the fission barrier independent on excitation energy. The detailed consideration of the temperature dependence of the fission barrier height and of the fission width of nuclei with the such fission barrier is presented. The influence of the energy-dependent barrier on the fission width is very important for superheavy nuclei and heavy nuclei, which have large shell-correction contribution into the fission barrier height.

The ratio of the fission and neutron emission widths Γ_f(E)/Γ_n(E) is calculated using different expressions for the fission width, which take into account and ignore the dependence of the fission barrier on the excitation energy. A strong influence of the energy-dependent fission barrier on the ratio Γ_f(E)/Γ_n(E) is shown. The dependence of the synthesis of superheavy nuclei on the ratio Γ_n(E)/Γ_f (E) is discussed. The experimental values of the ratio Γ_f (E)/Γ_n(E) in ¹⁸⁸Os and ^210,212Po are well described using the fission width with a barrier dependent on the excitation energy. The values of the fission barrier height for these nuclei are estimated. The influence of the energy-dependent barrier on the ratio Γ_f(E)/Γ_n(E) is stronger for nuclei with large shell contribution into the fission barrier. It is shown that this influence is very crucial for the superheavy nuclei.