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在ImQMD模型中[42-45],每个核子由相干态的高斯波包描述,波包中心的演化遵循正则方程:
$$ \dot{{\boldsymbol{r}}}_{i} = \frac{\partial H}{\partial {\boldsymbol{p}}_{i}},~~~ \dot{ {\boldsymbol{p}}}_{i} = -\frac{\partial H}{\partial {\boldsymbol{r}}_{i}}{\text{。}} $$ (1) 体系的哈密顿量由势能和动能
$ T = \sum\limits_{i} \frac{{\boldsymbol{p}}_{i}^{2}}{2m} $ 两部分组成:$$ H = T+U_{\rm{Coul}}+U_{\rm{loc}}{\text{。}} $$ (2) 其中,库仑能
$ U_{\rm{Coul}} $ 为直接项和交换项之和:$$\begin{split} U_{\rm{Coul}} =& \frac{1}{2}\mathop{{\displaystyle\iint}}{\rho_{\rm p}({\boldsymbol{r}})} \frac{e^{2}}{|{\boldsymbol{r}}-{\boldsymbol{r}}'|}{\rho_{\rm p}({\boldsymbol{r}}')}{\rm d}{\boldsymbol{r}}{\rm d}{\boldsymbol{r}}'- \\& e^{2}\frac{3}{4}\Big(\frac{3}{\pi}\Big)^{1/3}\int \rho_{\rm p}^{4/3}{\rm d}{\boldsymbol{r}}, \end{split}$$ (3) $ \rho_{\rm p} $ 是质子的密度。核相互作用势能由Skyrme能量密度泛函给出:$$ U_{{{\rm loc}}} = \int V_{ {\rm loc}}({\boldsymbol{r}}){\rm d}{\boldsymbol{r}}{\text{。}} $$ (4) 核相互作用势可以表示为
$$ \begin{split} V_{{\rm{loc}}} = &\frac{\alpha}{2}\frac{\rho ^{2}}{\rho _{0}}+\frac{\beta }{\gamma +1} \frac{\rho ^{\gamma +1}}{\rho _{0}^{\gamma }}+\frac{{g}_{\rm sur}}{2\rho _{0}} (\nabla \rho )^{2}+\\ &\ \frac{C_{\rm s}}{2\rho _{0}}\big[\rho ^{2}-\kappa _{\rm s}(\nabla \rho )^{2}\big]\delta ^{2} + g_{\tau}\frac{\rho ^{\eta +1}}{\rho_{0}^{\eta }}, \end{split} $$ (5) 式中,
$ \rho = \rho_{\rm n}+\rho_{\rm p} $ 是核子的密度。$ \delta = (\rho_{\rm n}-\rho_{\rm p})/ (\rho_{\rm n}+\rho_{\rm p}) $ 为同位旋不对称度。核相互作用势参数选用IQ2,见表1,其不可压缩系数$ K_{\infty} = 195 $ MeV。IQ2参数组被广泛应用于多核子转移反应研究,在描述58Ni+$ ^{208} {\rm{Pb}}$ 、$ ^{136} {\rm{Xe}}$ +$ ^{208} {\rm{Pb}}$ 、$ ^{136} {\rm{Xe}}$ +$ ^{198} {\rm{Pt}}$ 和204Hg+$ ^{198} {\rm{Pt}}$ 等反应的产物截面上取得了很大的成功[13-14, 22, 29, 46]。表 1 IQ2参数组
参数 数值 $\alpha$/MeV –356 $\beta$/MeV 303 $\gamma$ 7/6 ${g}_{\rm sur}$/(MeV·fm2) 7.0 $g_{\tau}$/MeV 12.5 $\eta$ 2/3 $C_{\rm s}$/MeV 32.0 $\kappa_{\rm s}$/fm2 0.08 $\rho_{0}$/fm–3 0.165 在计算中,弹靶的初始距离设定为30 fm,反应演化时间为2 000 fm/c,时间步长为1 fm/c,碰撞参数
$ b = 0\sim 13 $ fm,总共模拟了3 120 000个事件。初始产物的退激过程采用统计模型GEMINI处理[47]。
Study on Production Mechanism of the Neutron-rich Nuclei in Multinucleon Transfer Reactions via Reaction Time Analysis
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摘要: 在改进的量子分子动力学(ImQMD)模型框架下,研究了
$^{136}{\rm{Xe}}$ +$^{198}{\rm{Pt}}$ 体系的多核子转移反应过程。给出了不同弹靶接触时间下二分裂碎片的总动能-质量分布,发现准弹性碰撞、深度非弹性碰撞和准裂变反应事件可以采用弹靶接触时间进行粗略的划分。分析了不同弹靶接触时间下类靶碎片的双微分截面分布以及Ba同位素的产生截面分布,结果表明丰中子核素产生于深度非弹性碰撞。另外研究发现,对于$^{136}{\rm{Xe}}$ +$^{198}{\rm{Pt}}$ 体系,出射角在0°附近的类靶碎片产生于中心碰撞。Abstract: The multinucleon transfer reaction processes of$^{136}{\rm{Xe}}$ +$^{198}{\rm{Pt}}$ are investigated by using the ImQMD model. The TKE-Mass distributions of binary fragments at different contact time scales are analysed. It is found that the quasielastic collisions, the deep-inelastic collisions and the quasifission reactions can be roughly distinguished by the contact time. By analysing the double differential cross sections of the TLFs and the isotopic cross sections of Ba nuclei under the different contact time, we find that the neutron-rich nuclei are produced in the deep-inelastic collisions. In addition, the TLFs with emission angle around 0° are produced in central collisions for the reactions of$^{136}{\rm{Xe}}$ +$^{198}{\rm{Pt}}$ . -
图 1 (在线彩图)
$^{136}{\rm{Xe}}$ +$^{198}{\rm{Pt}}$ 在入射能量为7.98 MeV/nucleon下与束流方向夹角为30°时类弹碎片的计数和截面分布(a)为实验数据,取自文献[48];(b)和(c)分别为ImQMD和ImQMD+GEMINI模型的计算结果。
图 6 (在线彩图) 类弹产物Ba( Z=56 )的同位素产生截面分布
(a)为ImQMD+GEMINI模型计算的不同弹靶接触时间下的同位素产生截面;(b)为实验测量的不同总动能损失下的同位素产生截面,测量角度为30°,实验数据取自文献[50]。
表 1 IQ2参数组
参数 数值 $\alpha$/MeV –356 $\beta$/MeV 303 $\gamma$ 7/6 ${g}_{\rm sur}$/(MeV·fm2) 7.0 $g_{\tau}$/MeV 12.5 $\eta$ 2/3 $C_{\rm s}$/MeV 32.0 $\kappa_{\rm s}$/fm2 0.08 $\rho_{0}$/fm–3 0.165 -
[1] THOENNESSEN M. The Discovery of Isotopes, A Complete Compilation[M]. New York: Springer International Publishing, 2016. [2] THOENNESSEN M, SHERRILL B. Nature, 2011, 473: 25. doi: 10.1038/473025a [3] Discovery of Nuclides Project [EB/OL].[2020-07-10].https://people.nscl.msu.edu/thoennes/isotopes/. [4] WANG N, LIU M, WU X Z, et al. Phys Lett B, 2014, 734: 215. doi: 10.1016/j.physletb.2014.05.049 [5] MÖLLER P, NIX J R, MYERS W D, et al. At Data Nucl Data Tables, 1995, 59: 185. doi: 10.1006/adnd.1995.1002 [6] ERLER J, BIRGE N, KORTELAINEN M, et al. Nature (London), 2012, 486: 509. doi: 10.1038/nature11188 [7] KURCEWICZ J, FARINON F, GEISSEL H, et al. Phys Lett B, 2012, 717: 371. doi: 10.1016/j.physletb.2012.09.021 [8] FUKUDA N, KUBO T, KAMEDA D, et al. J Phys Soc Jpn, 2018, 87: 014202. doi: 10.7566/JPSJ.87.014202 [9] SHIMIZU Y, KUBO T, FUKUDA N, et al. J Phys Soc Jpn, 2018, 87: 014203. doi: 10.7566/JPSJ.87.014203 [10] ZAGREBAEV V I, GREINER W. Phys Rev Lett, 2008, 101: 122701. doi: 10.1103/PhysRevLett.101.122701 [11] ZHANG F S, LI C, ZHU L, et al. Front Phys, 2018, 13: 132113. doi: 10.1007/s11467-018-0843-6 [12] ZHU L, LI C, GUO C C, et al. Int J Mod Phys E, 2020, 29: 2030004. doi: 10.1142/S0218301320300040 [13] LI C, XU X X, LI J J, et al. Phys Rev C, 2019, 99: 024602. doi: 10.1103/PhysRevC.99.024602 [14] LI C, SOKHNA C A T, XU X X, et al. Phys Rev C, 2019, 99: 034619. doi: 10.1103/PhysRevC.99.034619 [15] BAO X J, GUO S Q, LI J Q, et al. Phys Lett B, 2018, 785: 221. doi: 10.1016/j.physletb.2018.08.049 [16] ZHU L. Chin Phys C, 2017, 41: 124102. doi: 10.1088/1674-1137/41/12/124102 [17] ZHU L. Chin Phys C, 2019, 43: 124103. doi: 10.1088/1674-1137/43/12/124103 [18] CHEN P H, NIU F, ZUO W, et al. Phys Rev C, 2020, 101: 024610. doi: 10.1103/PhysRevC.101.024610 [19] GUO S Q, BAO X J, ZHANG H F, et al. Phys Rev C, 2019, 100: 054616. doi: 10.1103/PhysRevC.100.054616 [20] JIANG X, WANG N. Phys Rev C, 2020, 101: 014604. doi: 10.1103/PhysRevC.101.014604 [21] MUN M H, ADAMIAN G G, ANTONENKO N V, et al. Phys Rev C, 2015, 91: 054610. doi: 10.1103/PhysRevC.91.054610 [22] LI C, WEN P W, LI J J, et al. Phys Lett B, 2018, 776: 278. doi: 10.1016/j.physletb.2017.11.060 [23] WANG N, GUO L. Phys Lett B, 2016, 760: 236. doi: 10.1016/j.physletb.2016.06.073 [24] ZHAO K, LIU Z, ZHANG F S, et al. Phys Lett B, 2021, 815: 136101. doi: 10.1016/j.physletb.2021.136101 [25] ZHU L. Phys Lett B, 2021, 816: 136226. doi: 10.1016/j.physletb.2021.136226 [26] LI C, TIAN J L, ZHANG F S. Phys Lett B, 2020, 809: 135697. doi: 10.1016/j.physletb.2020.135697 [27] 赵凯, 夏政通, 段济正. 原子核物理评论, 2020, 37: 160. doi: 10.11804/NuclPhysRev.37.2020022 ZHAO K, XIA Z T, DUAN J Z. Nuclear Physics Review, 2020, 37: 160. (in Chinese) doi: 10.11804/NuclPhysRev.37.2020022 [28] 蒋翔, 王楠. 原子核物理评论, 2021, 38: 17. doi: 10.11804/NuclPhysRev.38.2020076 JIANG X, WANG N. Nuclear Physics Review, 2021, 38: 17. (in Chinese) doi: 10.11804/NuclPhysRev.38.2020076 [29] WELSH T, LOVELAND W, YANEZ R, et al. Phys Lett B, 2017, 771: 119. doi: 10.1016/j.physletb.2017.05.044 [30] BARRETT J S, LOVELAND W, YANEZ R, et al. Phys Rev C, 2015, 91: 064615. doi: 10.1103/PhysRevC.91.064615 [31] WATANABE Y X, KIM Y H, JEONG S C, et al. Phys Rev Lett, 2015, 115: 172503. doi: 10.1103/PhysRevLett.115.172503 [32] BELIUSKINA O, HEINZ S, ZAGREBAEV V I, et al. Eur Phys J A, 2014, 50: 161. doi: 10.1140/epja/i2014-14161-3 [33] MIJATOVIć T, SZILNER S, CORRADI L, et al. , Phys Rev C, 2016, 94: 064616. doi: 10.1103/PhysRevC.94.064616 [34] CORRADI L, POLLAROLO G, SZILNER S. J Phys G Nucl Part Phys, 2009, 36: 113101. doi: 10.1088/0954-3899/36/11/113101 [35] VOGT A, BIRKENBACH B, REITER P, et al. Phys Rev C, 2015, 92: 024619. doi: 10.1103/PhysRevC.92.024619 [36] DESAI V V, LOVELAND W, MCCALEB K, et al. Phys Rev C, 2019, 99: 044604. doi: 10.1103/PhysRevC.99.044604 [37] DESAI V V, LOVELAND W, YANEZ R, et al. Eur Phys J A, 2020, 56: 150. doi: 10.1140/epja/s10050-020-00154-4 [38] REJMUND M, LECORNU B, NAVIN A, et al. Nucl Instr and Meth A, 2011, 646: 184. doi: 10.1016/j.nima.2011.05.007 [39] KOZULIN E M, KNYAZHEVA G N, DMITRIEV S N, et al. Phys Rev C, 2014, 89: 014614. doi: 10.1103/PhysRevC.89.014614 [40] ITKIS I M, KOZULIN E M, ITKIS M G, et al. Phys Rev C, 2011, 83: 064613. doi: 10.1103/PhysRevC.83.064613 [41] KOZULIN E M, VARDACI E, KNYAZHEVA G N, et al. Phys Rev C, 2012, 86: 044611. doi: 10.1103/PhysRevC.86.044611 [42] AICHELIN J. Phys. Rep., 1991, 202: 233. doi: 10.1016/0370-1573(91)90094-3 [43] WANG N, LI Z X, WU X Z. Phys Rev C, 2002, 65: 064608. doi: 10.1103/PhysRevC.65.064608 [44] WANG N, LI Z X, WU X Z, et al. Phys Rev C, 2004, 69: 034608. doi: 10.1103/PhysRevC.69.034608 [45] ZHANG Y X, WANG N, LI Q F, et al. Front Phys, 2020, 15: 54301. doi: 10.1007/s11467-020-0961-9 [46] LI C, ZHANG F, LI J J, et al. Phys Rev C, 2016, 93: 014618. doi: 10.1103/PhysRevC.93.014618 [47] CHARITY R J. Phys Rev C, 2010, 82: 014610. doi: 10.1103/PhysRevC.82.014610 [48] WATANABE Y X, HIRAYAMA Y, IMAI N, et al. Nucl Instr and Meth B, 2013, 317: 752. doi: 10.1016/j.nimb.2013.04.036 [49] YAO H, WANG N. Phys Rev C, 2017, 95: 014607. doi: 10.1103/PhysRevC.95.014607 [50] KIM Y H, WATANABE Y X, HIRAYAMA Y, et al. EPJ Web of Conf, 2014, 66: 3044. doi: 10.1051/epjconf/20146603044