Possibilities of producing superheavy nuclei in multinucleon transfer reactions based on radioactive
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Long Zhu , Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China Received Date:2019-08-02 Available Online:2019-12-01 Abstract:The multinucleon transfer (MNT) process has been proposed as a promising approach to produce neutron-rich superheavy nuclei (SHN). MNT reactions based on the radioactive targets 249Cf, 254Es, and 257Fm are investigated within the framework of the improved version of a dinuclear system (DNS-sysu) model. The MNT reaction 238U + 238U was studied extensively as a promising candidate for producing SHN. However, based on the calculated cross-sections, it was found that there is little possibility to produce SHN in the reaction 238U + 238U. In turn, the production of SHN in reactions with radioactive targets is likely.
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2.Description of the modelIn Ref. [25], detailed descriptions on the DNS-sysu model were presented. Here, the brief introductions regarding the model are presented. The master equation in the DNS-sysu model can be written as [25, 27].
Here, $ P(Z_{1},N_{1},\beta_{2},t) $ is the probability distribution function for the fragment 1 with proton number $ Z_{1} $ and neutron number $ N_{1} $ at time t. $ \beta_{2} $ is the dynamical deformation parameter of the DNS. $ W_{Z_{1},N_{1},\beta_{2};Z_{1}^{'},N_{1},\beta_{2}} $, $ W_{Z_{1},N_{1},\beta_{2};Z_{1},N_{1}^{'},\beta_{2}} $, and $ W_{Z_{1},N_{1},\beta_{2};Z_{1},N_{1},\beta_{2}^{'}} $ denote the mean transition probabilities from the channels ($ Z_{1} $, $ N_{1} $, $ \beta_{2} $) to ($ Z_{1}^{'} $, $ N_{1} $, $ \beta_{2} $), ($ Z_{1} $, $ N_{1} $, $ \beta_{2} $) to ($ Z_{1} $, $ N_{1}^{'} $, $ \beta_{2} $), and ($ Z_{1} $, $ N_{1} $, $ \beta_{2} $) to ($ Z_{1} $, $ N_{1} $, $ \beta_{2}^{'} $), respectively. $ d_{Z_{1},N_{1},\beta_{2}} $ is the microscopic dimension (the number of channels) corresponding to the macroscopic state ($ Z_{1} $, $ N_{1} $, $ \beta_{2} $) [28]. For the degrees of freedom of the charge and neutron number, the sum is taken over all possible proton and neutron numbers that fragment 1 may take, however only one nucleon transfer is considered in the model ($ Z_{1}^{'} = Z_{1}\pm1 $; $ N_{1}^{'} = N_{1}\pm1 $). For $ \beta_{2} $, we assume the range –$ 0.5 \sim 0.5 $. The evolution step length is 0.01. The transition probability is related to the local excitation energy [27, 29]. The PES is defined as
where $ \Delta(Z_{i}, N_{i}) $ ($ i = 1 $, 2) is mass excess of the fragment i. $ V_{ \rm{cont}}(Z_{1}, N_{1},\beta_{2}, R_{ \rm{cont}}) $ is the effective nucleus-nucleus interaction potential. The last two terms in the right side of the equation are deformation energies. The detailed description of each term is provided in Ref. [25] and the references therein. The cross-sections of the primary products can be calculated as
Clear signatures were observed for the formation of DNS in heavy collision systems, such as 238U + 238U [30]. For heavy systems without a potential pocket, there is no capture. I consider that the DNS is formed when incident energy is higher than the interaction potential at the contact position. The contact positions are near the relatively flat parts of interaction potential curves [23]. From the diffusion point of view, the strength of diffusion strongly depends on the interaction time, which is reflected from the probability distribution function $ P(Z_{1},N_{1},\beta_{2},E_{ \rm{c.m.}}) $. Therefore, it is reasonable to consider $ T_{ \rm{cap}} $ as 1. In the DNS-sysu model, with consideration of the deformation evolution, the excitation energy of primary products can be calculated with following equation [25].
Here, $ E^{*}_{\rm DNS} $ is the local excitation energy of the system [25]. The total kinetic energy loss (TKEL) for the configuration (Z1, N1, β2) calculated in the DNS-sysu model as shown in Ref. [27] can be written as
Here, Zp and Np are the charge number and neutron number of the projectile, which denotes the configuration in the entrance channel. The detailed description of Ediss can be seen in Ref. [25]. In the cooling process, the statistical model is applied with the Monte Carlo method [25]. In the ith de-excitation step, the probability of the s event can be written as
where, $ {\rm s} = $ n, p, $ \alpha $, $ \gamma $, and fission. $ E_{i}^{*} $ is the excitation energy before ith decay step, which can be calculated from the equation $ E^{*}_{i+1} = E^{*}_{i}-B_{i} $. $ B_{i} $ is the separation energy of particle or energy assumed by the $ \gamma $ ray in the ith step. $ \Gamma_{\rm tot} = \Gamma_{\rm n}+\Gamma_{\rm f}+\Gamma_{\rm p}+\Gamma_{\alpha}+\Gamma_{\gamma} $. Detailed descriptions of the decay width in each decay channel are provided in Ref. [25] and the references therein. Here, I would like to emphasize that the parameters in the DNS-sysu model are usually fixed.