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The synthesis of superheavy nuclei (SHN) is a leading research frontier in nuclear physics today. In the experiments for synthesizing SHN via fusion-evaporation reactions, the appropriate choice of projectile-target combination and determination of the optimal incident energy are crucial. The number of SHN that can be synthesized with stable projectiles is very small. The fusion-evaporation reaction with radioactive projectile is one of the promising ways for SHN synthesis and it is of great significance to investigate this kind of reactions deeply. In this work a systematic study has been carried out on the fusion-evaporation reactions with radioactive projectiles. The capture cross section is calculated with the empirical coupled channel model, the fusion probability is computed by the dinuclear system model with a dynamical potential energy surface (DNS-DyPES model) and the survival probability is determined through the statistical model. In the systematic study, 11 actinide isotopes with $Z=90$–100 are used as targets which are $^{232}{\rm{Th}}$, $^{231}{\rm{Pa}}$, $^{238}{\rm{U}}$, $^{237}{\rm{Np}}$, $^{244}{\rm{Pu}}$, $^{243}{\rm{Am}}$, $^{248}{\rm{Cm}}$, $^{249}{\rm{Bk}}$, $^{251}{\rm{Cf}}$, $^{254}{\rm{Es}}$ and $^{257}{\rm{Fm}}$. Projectiles are isotopes between proton and neutron drip lines for elements $Z=4$–32 and most of these projectiles are radioactive. By combining these projectiles and targets, 4969 reaction systems are proposed for synthesizing isotopes of superheavy elements $Z=104$–122. Through large-scale calculations, the excitation functions for $2n$–$5n$ evaporation channels of each reaction system are obtained. With the results of these reaction systems, we establish a synthesis cross section dataset for superheavy nuclei. For each reaction system, the dataset includes the identities of the synthesized SHN, the optimal incident energies and the maximal evaporation residue cross sections in $2n$–$5n$ evaporation channels. This dataset may serve as a theoretical support for synthesizing new superheavy nuclides and elements. Additionally, taking the reactions with $^{232}{\rm{Th}}$ target as examples, we discuss systematic trends in the results and explore the underlying SHN synthesis mechanism. The synthesis cross sections of these reactions, shown in Fig. 1 , are in vastly differences. We find that inner fusion barrier of the compound system formed after the projectile touches the target and fission barrier of the compound nucleus are key factors that influence the synthesis cross section. Qualitatively, the projectile-target combinations with relatively large synthesis cross sections are featured by a lower inner fusion barrier in the compound system formed upon contact which favors fusion and a higher fission barrier in the compound nucleus which enhances survival probability. These conclusions may provide valuable references for the theoretical research related to superheavy nuclei synthesis. The dataset presented in this paper are available at the Science Data Bank athttp://www.doi.org/10.57760/sciencedb.27854 .
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Keywords:
- superheavy nuclei /
- heavy-ion fusion-evaporation reactions /
- radioactive beams /
- dinuclear system models
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图 1 反应体系$ ^{48} {\rm{Ca}}$+$ ^{238} {\rm{U}}$的(a)俘获截面$ \sigma_{\mathrm{capture}} $、(b)熔合概率$ P_{\mathrm{CN}} $、(c)存活概率$ W_{\mathrm{sur, }\; xn} $和(d)蒸发剩余截面$ \sigma_{\mathrm{ER}} $随质心系入射能$ E_{\mathrm{c.m.}} $的函数关系. 子图(a)中实验数据取自文献[99]. 子图(d)中实验数据取自文献[100]
Figure 1. (a) Capture cross section $ \sigma_{\mathrm{capture}} $, (b) fusion probability $ P_{\mathrm{CN}} $, (c) survival probability $ W_{\mathrm{sur, }\; xn} $ and (d) evaporation residue cross section $ \sigma_{\mathrm{ER}} $ as functions of the incident energy in the center-of-mass frame $ E_{\mathrm{c.m.}} $ for the reaction $ ^{48} {\rm{Ca}}$+$ ^{238} {\rm{U}}$. The experimental data in subfigure (a) are taken from Ref. [99]. The experimental data in subfigure (d) are taken from Ref. [100].
图 2 合成108号超重元素同位素的最大蒸发剩余截面$ \sigma_{\mathrm{ER}} $和最佳反应道. 横坐标为超重核的质量数$ A_{\mathrm{SHN}} $. 纵坐标靶核电荷数$ Z_\mathrm{T} = 90{—}100 $对应的靶核分别为$ ^{232} {\rm{Th}}$、$ ^{231} {\rm{Pa}}$、$ ^{238} {\rm{U}}$、$ ^{237} {\rm{Np}}$、$ ^{244} {\rm{Pu}}$、$ ^{243} {\rm{Am}}$、$ ^{248} {\rm{Cm}}$、$ ^{249} {\rm{Bk}}$、$ ^{251} {\rm{Cf}}$、$ ^{254} {\rm{Es}}$和$ ^{257} {\rm{Fm}}$. 最佳反应道由数据点的形状给出: 叉形为$ 2 n $道; 正方形为$ 3 n $道; 圆形为$ 4 n $道; 三角形为$ 5 n $道
Figure 2. Maximal evaporation residue cross section $ \sigma_{\mathrm{ER}} $ and optimal reaction channel for synthesizing isotopes of superheavy element $ Z = 108 $. The horizontal coordinate represents the mass number of superheavy nuclei $ A_{\mathrm{SHN}} $. The vertical coordinate represents the charge number of target nucleus, the range $ Z_\mathrm{T} = 90{-}100 $ corresponds to target nuclei $ ^{232} {\rm{Th}}$, $ ^{231} {\rm{Pa}}$, $ ^{238} {\rm{U}}$, $ ^{237} {\rm{Np}}$, $ ^{244} {\rm{Pu}}$, $ ^{243} {\rm{Am}}$, $ ^{248} {\rm{Cm}}$, $ ^{249} {\rm{Bk}}$, $ ^{251} {\rm{Cf}}$, $ ^{254} {\rm{Es}}$ and $ ^{257} {\rm{Fm}}$, respectively. Optimal reaction channels are indicated by various symbols: cross for $ 2 n $ channel; square for $ 3 n $ channel; circle for $ 4 n $ channel; triangle for $ 5 n $ channel.
图 3 合成119号超重元素同位素的最大蒸发剩余截面$ \sigma_{\mathrm{ER}} $和最佳反应道. 横坐标为超重核的质量数$ A_{\mathrm{SHN}} $. 纵坐标靶核电荷数$ Z_\mathrm{T} = 90{—}100 $对应的靶核分别为$ ^{232} {\rm{Th}}$、$ ^{231} {\rm{Pa}}$、$ ^{238} {\rm{U}}$、$ ^{237} {\rm{Np}}$、$ ^{244} {\rm{Pu}}$、$ ^{243} {\rm{Am}}$、$ ^{248} {\rm{Cm}}$、$ ^{249} {\rm{Bk}}$、$ ^{251} {\rm{Cf}}$、$ ^{254} {\rm{Es}}$和$ ^{257} {\rm{Fm}}$. 最佳反应道由数据点的形状给出: 叉形为$ 2 n $道; 正方形为$ 3 n $道; 圆形为$ 4 n $道; 三角形为$ 5 n $道
Figure 3. Maximal evaporation residue cross section $ \sigma_{\mathrm{ER}} $ and optimal reaction channel for synthesizing isotopes of superheavy element $ Z = 119 $. The horizontal coordinate represents the mass number of superheavy nuclei $ A_{\mathrm{SHN}} $. The vertical coordinate represents the charge number of target nucleus, the range $ Z_\mathrm{T} = 90{-}100 $ corresponds to target nuclei $ ^{232} {\rm{Th}}$, $ ^{231} {\rm{Pa}}$, $ ^{238} {\rm{U}}$, $ ^{237} {\rm{Np}}$, $ ^{244} {\rm{Pu}}$, $ ^{243} {\rm{Am}}$, $ ^{248} {\rm{Cm}}$, $ ^{249} {\rm{Bk}}$, $ ^{251} {\rm{Cf}}$, $ ^{254} {\rm{Es}}$ and $ ^{257} {\rm{Fm}}$, respectively. Optimal reaction channels are indicated by various symbols: cross for $ 2 n $ channel; square for $ 3 n $ channel; circle for $ 4 n $ channel; triangle for $ 5 n $ channel.
图 4 $ ^{232} {\rm{Th}}$作为靶核, 不同放射性核素作为弹核的熔合蒸发反应合成104—122号超重元素同位素的最大蒸发剩余截面$ \sigma_{\mathrm{ER}} $. 横、纵坐标分别为超重核的中子数$ N_{\mathrm{SHN}} $和质子数$ Z_{\mathrm{SHN}} $. 根据截面大小可将这一核素图划分为4个区域, 这些区域的位置被标出
Figure 4. Maximal evaporation residue cross section $ \sigma_{\mathrm{ER}} $ for synthesizing isotopes of superheavy elements $ Z = 104 $–122 via fusion-evaporation reactions with $ ^{232} {\rm{Th}}$ as target and different radioactive nuclides as projectiles. The horizontal and vertical coordinates represent the neutron number $ N_{\mathrm{SHN}} $ and the proton number $ Z_{\mathrm{SHN}} $ of superheavy nuclei, respectively. This chart of nuclides is devided into four regions according to the magnitudes of the cross sections and their locations are indicated.
图 7 (a) 图4中最大蒸发剩余截面对应的存活概率$ W_{\mathrm{sur, }\; xn} $和 (b) 超重核的裂变位垒高度$ B_\mathrm{f} $[93]
Figure 7. (a) Survival probability $ W_{\mathrm{sur, }\; xn} $ corresponding to the maximal evaporation residue cross section in Fig. 4 and (b) fission barrier height $ B_\mathrm{f} $ of the superheavy nuclei[93].
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