Modified fusion probability by reflection boundary

HAN Jie; BAO Jing-Dong

doi:10.1088/1674-1137/39/5/054104

Chinese Physics C> 2015, Vol. 39> Issue(5) : 054104 DOI: 10.1088/1674-1137/39/5/054104

Modified fusion probability by reflection boundary

HAN Jie ^, ,
BAO Jing-Dong ^,

Abstract
HTML
Reference
Related

PDF

Abstract：
We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.

References

[1]

Kramers H A. Physica (Utrecht), 1940, 7: 284[2] WU Xi-Zhen, ZHUO Yi-Zhong. Chin. Phys. C, 1980, 4(1): 113[3] WU Xi-Zhen, LI Zhu-Xia, ZHUO Yi-Zhong. Chin. Phys. C, 1990, 14(4): 345[4] Abe Y. Physique J de., 1986, 47(8): C4-329[5] Hanggi P, Talkner P, Borkovec M. Rev. Mod. Phys., 1990, 62: 251[6] Frobrich P, Gontchar I I. Phys. Rep., 1998, 292: 131[7] YE W, WANG N, TIAN J. Phys. Rev. C, 2014, 90: 041604(R)[8] Aritomo Y, Wada T, Ohta M, Abe Y. Phys. Rev. C, 1997, 55: R1011[9] Abe Y, Aritomo Y, Wada T, Ohta M. J. Phys. G: Nucl. Part. Phys., 1997, 23: 1275[10] Abe Y, Boilley D, Kosenko G, BAO J D, SHEN C W, Giraud B, Wada T. Prog. Theor. Phys. Suppl., 2002, 146: 104[11] SHEN C W, Kosenko G, Abe Y. Phys. Rev. C, 2002, 66: 061602(R)[12] Światecki W J, Siwek-Wilczyńska K, Wilczyński J. Acta Phys. Pol. B, 2003, 34: 2049[13] Światecki W J, Siwek-Wilczyńska K, Wilczyński J. Phys. Rev. C,2005, 71: 014602[14] LIU Z H, BAO J D. Phys. Rev. C, 2006, 74: 057602[15] LIU Z H, BAO J D. Phys. Rev. C, 2007, 76: 037604[16] LIU Z H, BAO J D. Phys. Rev. C, 2013, 87: 034616[17] Hofmann H, Samhammer R. Z. Phys. A, 1985, 322: 157[18] Abe Y, Boilley D, Giraud B G, Wada T. Phys. Rev. E, 2000, 61: 1125[19] BAO J D, Boilley D. Nucl. Phys. A, 2002, 707: 47[20] Boilley D, Abe Y, BAO J D. Eur. Phys. J. A, 2003, 18: 627[21] BAO J D, ZHUO Y Z. Phys. Rev. C, 2003, 67: 064606[22] MAO J W, Shen C W. Phys. Rev. E, 2011, 83: 041108[23] Abe Y, SHEN C W, Kosenko G, Boilley D, Giraud B G. Int. J. Mod. Phys. E, 2008, 17: 2214[24] Boilley D, Lallouet Y. J. Stat. Phys., 2006, 125: 2[25] Yilmaz B, Ayik S, Abe Y, Boilley D. Phys. Rev. E, 2008, 77: 011121[26] Gitterman M, Weiss G H, Stat J. Phys., 1993, 70: 107[27] Talkner P, Braun H, Chem J. Phys., 1988, 88: 7537[28] Grote R F, Hynes J T. J. Chem. Phys., 1980, 73: 2715[29] Mel'nikov V I, Meshkov S V. J. Chem. Phys., 2006, 85: 1018[30] Boilley D, Marchix A, Jurado B, Schmidt K H. Eur. Phys. J. A, 2007, 33: 47[31] Talkner P. Chem. Phys., 1994, 180: 199[32] Kim S K. J. Chem. Phys., 1985, 28: 1057[33] Hofmann H, Ivanyuk F A. Phys. Rev. Lett., 2003, 90: 132701[34] Hofmann H, Magner A G. Phys. Rev. C, 2003, 68: 014606[35] BAO J D, JIA Y. Phys. Rev. C, 2004, 69: 027602[36] Boilley D, Jurado B, Schmitt C. Phys. Rev. E, 2004, 70: 056129[37] Risken H. The Fokker-Planck Equation. Berlin: Springer, 1989; Gardiner C W. Handbook of Stochastic Methods. Berlin: Springer, 2002

[1]	Yi Ling;Meng-He Wu;Yikang Xiao . Entanglement in simple spin networks with a boundary. Chinese Physics C, 2019, df87c41e-622f-49a7-b081-5c584df157aa(11): 13106-.
[2]	F. Koyuncu , A. Soylu . Screening effects on ¹²C+¹²C fusion reaction. Chinese Physics C, 2018, 42(5): 054106. doi: 10.1088/1674-1137/42/5/054106
[3]	Xiao-Dong Sun , Xi-Jun Wu , Bo Zheng , Dong Xiang , Ping Guo , Xiao-Hua Li . Systematic study of α preformation probability of nuclear isomeric and ground states. Chinese Physics C, 2017, 41(1): 014102. doi: 10.1088/1674-1137/41/1/014102
[4]	Zhi-zhong Xing , Jing-yu Zhu . Neutrino mass ordering and μ-τ reflection symmetry breaking. Chinese Physics C, 2017, 41(12): 123103. doi: 10.1088/1674-1137/41/12/123103
[5]	Long Zhu , Jun Su , Ching-Yuan Huang , Feng-Shou Zhang . Effects of entrance channel on fusion probability in hot fusion reactions. Chinese Physics C, 2016, 40(12): 124105. doi: 10.1088/1674-1137/40/12/124105
[6]	LIU Zhi-Feng . A modified explanation of cold nuclear matter effects on J/ψ production in p+A collisions. Chinese Physics C, 2015, 39(8): 084104. doi: 10.1088/1674-1137/39/8/084104
[7]	LIU Xing-Xing , ZHANG Gao-Long , ZHANG Huan-Qiao . Study of fusion Q-value rule in sub-barrier fusion of heavy ions. Chinese Physics C, 2015, 39(7): 074101. doi: 10.1088/1674-1137/39/7/074101
[8]	HU Ling-Fei , GAO Li-Dan , LI Zhen-Jie , WANG Shan-Feng , SHENG Wei-Fan , LIU Peng , XU Wei . Monochromatic X-ray-induced thermal effect on four-reflection. Chinese Physics C, 2015, 39(9): 096004. doi: 10.1088/1674-1137/39/9/096004
[9]	HUANG Xiao-Long , JIANG Li-Yang , CHEN Xiong-Jun , CHEN Guo-Chang . Evaluation of the 1077 keV γ-ray emission probability from ⁶⁸Ga decay. Chinese Physics C, 2014, 38(4): 044001. doi: 10.1088/1674-1137/38/4/044001
[10]	H. Eslamizadeh , M. Pirpour . Study of pre-scission particle emissions and fission probability of the ¹⁷⁸W produced in fusion reactions. Chinese Physics C, 2014, 38(6): 064101. doi: 10.1088/1674-1137/38/6/064101
[11]	ZHANG Wei , LI Zhi-Pan , ZHANG Shuang-Quan . Octupole deformation for Ba isotopes in a reflection-asymmetric relativistic mean-field approach. Chinese Physics C, 2010, 34(8): 1094-1099. doi: 10.1088/1674-1137/34/8/011
[12]	ZHANG Chen-Jun . On two-point boundary correlations of the gl(1\|1) supersymmetric vertex model. Chinese Physics C, 2010, 34(8): 1069-1075. doi: 10.1088/1674-1137/34/8/006
[13]	ZHANG Huan-Qiao , LIN Cheng-Jian , YANG Feng , JIA Hui-Ming , ZHOU Ping , AN Guang-Peng , ZHANG Chun-Lei , XU Xin-Xing . An electrostatic deflector for a fusion reaction. Chinese Physics C, 2010, 34(10): 1628-1631. doi: 10.1088/1674-1137/34/10/014
[14]	LIN Xu-Ling , ZHANG Jian-Bing , LUO Feng , BEI Hua , LU Shan-Liang , YU Tie-Min , DAI Zhi-Min . Preliminary result of bunch length measurement using a modified Michelson interferometer. Chinese Physics C, 2009, 33(10): 901-904. doi: 10.1088/1674-1137/33/10/015
[15]	MA Zhong-Jian , WANG Qing-Bin , WU Qing-Biao . Simulation of a modified neutron detector applied in CSNS. Chinese Physics C, 2009, 33(1): 54-57. doi: 10.1088/1674-1137/33/1/012
[16]	Medina Ablikim , Edward Corrigan . Boundary Reflection Factor of the Supersymmetric Sinh-Gordon Model. Chinese Physics C, 2002, 26(S1): 47-53.
[17]	Liu Guoxing , Chen Keliang , Yu Xian , Dai Guangxi . Fission Angular Distributions for the Incomplete Fusion Reactions. Chinese Physics C, 1997, 21(S3): 35-42.
[18]	Chen Min , Hou Boyu , Shi Kangjie . Reflection Matrix of Z_n Belavin Model. Chinese Physics C, 1996, 20(S4): 325-331.
[19]	Zhong Yunxiao , Hu Jimin . Fission Probability Calculation by Solving Fokker-PIank Equation with Variation Method. Chinese Physics C, 1994, 18(Z1): 79-86.
[20]	Yan Jun , Hu Shike . Compact Baby Universe Model in 10 Dimensions and Probability Function of Quantum Gravity. Chinese Physics C, 1991, 15(S4): 353-360.

Access

Get Citation

HAN Jie and BAO Jing-Dong. Modified fusion probability by reflection boundary[J]. Chinese Physics C, 2015, 39(5): 054104. doi: 10.1088/1674-1137/39/5/054104

HAN Jie and BAO Jing-Dong. Modified fusion probability by reflection boundary[J]. Chinese Physics C, 2015, 39(5): 054104. doi: 10.1088/1674-1137/39/5/054104 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2014-10-10
Revised: 1900-01-01

Article Metric

Article Views(1939)
PDF Downloads(187)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Modified fusion probability by reflection boundary

Corresponding author: HAN Jie,

Corresponding author: BAO Jing-Dong,

Received Date: 2014-10-10

Accepted Date: 1900-01-01

Available Online: 2015-05-05

Abstract: We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.

HTML

Reference (1)

Modified fusion probability by reflection boundary

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article