Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei:systematic investigation of the triaxiality effect on the fission barrier

Qing-Zhen Chai; Wei-Juan Zhao; Min-Liang Liu; Hua-Lei Wang

doi:10.1088/1674-1137/42/5/054101

Chinese Physics C> 2018, Vol. 42> Issue(5) : 054101 DOI: 10.1088/1674-1137/42/5/054101

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei:systematic investigation of the triaxiality effect on the fission barrier

1.
School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, China
2.
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Static fission barriers for 95 even-even transuranium nuclei with charge number Z=94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional (β₂, γ, β₄) deformation space. Taking the heavier ²⁵²Cf nucleus (with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β₂ values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei (e.g., the Z=112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications (e.g., the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.
- static fission barriers ,
- potential energy surface approach ,
- triaxiality ,
- Woods-Saxon potential

References

[1]	A. N. Andreyev, K. Nishio, and K-H Schmidt, Rep. Prog. Phys., 81:016301(2018)
[2]	R. Eichler, J. Phys.:Conf. Ser., 420:012003(2013)
[3]	S. Hofmann and G. Mm nzenberg, Rev. Mod. Phys., 72:733(2000)
[4]	Yu. Ts. Oganessian, A. Sobiczewski, and G. M. Ter-Akopian, Phys. Scr., 92:023003(2017)
[5]	F. P. Heberger, Eur. Phys. J. A, 53:75(2017)
[6]	M. Arnould and K. Takahashi, Rep. Prog. Phys., 62:395(1999)
[7]	A. Mamdouh, J. M. Pearson, M. Rayet, and F. Tondeur, Nucl. Phys. A, 679:337(2001)
[8]	N. Bohr and J. A. Wheeler, Phys. Rev., 56:426(1939)
[9]	R. Capote, M. Herman, P. Obložinsk, P. G. Young, S. Goriely, T. Belgya, A. V. Ignatyuk, A. J. Koning, S. Hilaire, V. A. Plujko, M. Avrigeanu, O. Bersillon, M. B. Chadwick, T. Fukahori, Z. Ge, Y. Han, S. Kailas, J. Kopecky, V. M. Maslov, G. Reffo, M. Sin, E. Sh. Soukhovitskii, and P. Talou, Nucl. Data Sheets, 110:3107(2009)
[10]	V. V. Pashkevich, Nucl. Phys. A, 133:400(1969)
[11]	P. Mmller and S. G. Nilsson, Phys. Lett. B, 31:283(1970)
[12]	B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C, 85:011301(R) (2012)
[13]	B. N. Lu, J. Zhao, E. G. Zhao, and S. G. Zhou, Phys. Rev. C, 89:014323(2014)
[14]	P. Mmller, A. J. Sierk, and A. Iwamoto, Phys. Rev. Lett, 92:072501(2004)
[15]	A. Sobiczewski and M. Kowal, Phys. Scr., T125:68(2006)
[16]	A. Dobrowolski, K. Pomorski, and J. Bartel, Phys. Rev. C, 75:024613(2007)
[17]	P. Mmller, A. J. Sierk, T. Ichikawa, A. Iwamoto, R. Bengtsson, H. Uhrenholt, and S. berg, Phys. Rev. C, 79:064304(2009)
[18]	A. Dobrowolski, B. Nerlo-Pomorska, K. Pomorski, and J. Bartel, Acta Phys. Pol. B, 40:705(2009)
[19]	M. Kowal, P. Jachimowicz, and A. Sobiczewski, Phys. Rev. C, 82:014303(2010)
[20]	P. Mmller, A. J. Sierk, T. Ichikawa, A. Iwamoto, and M. Mumpower, Phys. Rev. C, 91:024310(2015)
[21]	A. Staszczak, A. Baran, J. Dobaczewski, and W. Nazarewicz, Phys. Rev. C, 80:014309(2009)
[22]	M. Bender, K. Rutz, P.-G. Reinhard, J. A. Maruhn, and W. Greiner, Phys. Rev. C, 58:2126(1998)
[23]	L. Bonneau, P. Quentin, and D. Samsoen, Eur. Phys. J. A, 21:391(2004)
[24]	A. Staszczak, J. Dobaczewski, and W. Nazarewicz, Acta Phys. Pol. B, 38:1589(2007)
[25]	A. K. Dutta, J. M. Pearson, and F. Tondeur, Phys. Rev. C, 61:054303(2000)
[26]	H. Abusara, A. V. Afanasjev, and P. Ring, Phys. Rev. C, 82:044303(2010)
[27]	Z. P. Li, T. Nikmimć, D. Vretenar, P. Ring, and J. Meng, Phys. Rev. C, 81:064321(2010)
[28]	P. Ring, H. Abusara, A. V. Afanasjev, G. A. Lalazissis, T. Nikm imć, and D. Vretenar, Int. J. Mod. Phys. E, 20:235(2011)
[29]	H. Abusara, A. V. Afanasjev, and P. Ring, Phys. Rev. C, 85:024314(2012)
[30]	S. E. Agbemava, A. V. Afanasjev, D. Ray, and P. Ring, Phys. Rev. C, 95:054324(2017)
[31]	S. W. degrd, G. B. Hagemann, D. R. Jesen, M. Bergstrm, B. Herskind, G. Sletten, S. Trmnen, J. N. Wilson, P. O. Tjm, I. Hamamoto, K. Spohr, H. Hbel, A. Grgen, G. Schnwasser, A. Bracco, S. Leoni, A. Maj, C. M. Petrache, P. Bednarczyk, and D. Curien, Phys. Rev. Lett, 86:5866(2001)
[32]	R. Bengtsson, H. Frisk, F. R. May, and J. A. Pinston, Nucl. Phys. A, 415:189(1984)
[33]	K. Starosta, T. Koike, C. J. Chiara, D. B. Fossan, D. R. LaFosse, A. A. Hecht, C. W. Beausang, M. A. Caprio, J. R. Cooper, R. Krcken, J. R. Novak, N. V. Zamfir, K. E. Zyromski, D. J. Hartley, D. L. Balabanski, J. Y. Zhang, S. Frauendorf, and V. I. Dimitrov, Phys. Rev. Lett, 86:971(2001)
[34]	H. L. Wang, J. Yang, M. L. Liu, and F. R. Xu, Phys. Rev. C, 92:024303(2015)
[35]	Q. Z. Chai, H. L. Wang, Q. Yang, and M. L. Liu, Chin. Phys. C, 39:024101(2015)
[36]	Q. Yang, H. L. Wang, M. L. Liu, and F. R. Xu, Phys. Rev. C, 94:024310(2016)
[37]	H. L. Wang, H. L. Liu, F. R. Xu, and C. F. Jiao, Chin. Sci. Bull., 57:1761(2012)
[38]	M. G. Itkis, Yu. Ts. Oganessian, and V. I. Zagrebaev, Phys. Rev. C, 65:044602(2002)
[39]	Yu. Ts. Oganessian, J. Phys. G:Nucl. Phys., 34:R165(2007)
[40]	K. Rutz, M. Bender, T. Brvenich, T. Schilling, P.-G. Reinhard, J. A. Maruhn, and W. Greiner, Phys. Rev. C, 56:238(1997)
[41]	B. Belgoumne, J. Dudek, and T. Werner, Phys. Lett. B, 267:431(1991)
[42]	J. Dudek, B. Szpak, M. G. Porquet, H. Molique, K. Rybak, and B. Fornal, J. Phys. G:Nucl. Phys., 37:064301(2010)
[43]	J. Dudek, B. Szpak, B. Fornal, and A. Dromard, Phys. Scr., T154:014002(2013)
[44]	F. R. Xu, P. M. Walker, J. A. Sheikh, and R. Wyss, Phys. Lett. B, 435:257(1998)
[45]	J. R. Nix, Annu. Rev. Nucl. Sci., 22:65(1972)
[46]	W. Nazarewicz, R. Wyss, and A. Johnson, Nucl. Phys. A, 503:285(1989)
[47]	V. M. Strutinsky, Nucl. Phys. A, 95:420(1967)
[48]	M. Brack, J. Damgaard, A. S. Jensen, H. C. Pauli, V. M. Strutinsky, and C. Y. Wong, Rev. Mod. Phys 44:320(1972)
[49]	P. H. Regan, F. R. Xu, P. M. Walker, M. Qi, A. K. Rath, and P. D. Stevenson, Phys. Rev. C, 65:037302(2002)
[50]	H. L. Liu, F. R. Xu, P. M. Walker, and C. A. Bertulani, Phys. Rev. C, 83:011303(2011)
[51]	W. Nazarewicz, J. Dudek, R. Bengtsson, T. Bengtsson, and I. Ragnarsson, Nucl. Phys. A, 435:397(1985)
[52]	A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26:1(1952)
[53]	A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. Ⅱ (World Scientific, Singapore, 1998)
[54]	W. D. Myers and W. J. Swiatecki, Nucl. Phys., 81:1(1966)
[55]	P. Mller and J. R. Nix, At. Data and Nucl. Data Tables, 39:213(1988)
[56]	P. Mller, W. D. Myers, W. J. Swiatecki, and J. Treiner, At. Data and Nucl. Data Tables, 39:225(1988)
[57]	K. Pomorski and J. Dudek, Phys. Rev. C, 67:044316(2003)
[58]	S. Ćwiok, J. Dudek, W. Nazarewicz, J. Skalski, and T. Werner, Comp. Phys. Comm., 46:379(1987)
[59]	M. Bolsterli, E. O. Fiset, J. R. Nix, and J. L. Norton, Phys. Rev. C, 5:1050(1972)
[60]	R. Bengtsson, J. Dudek, W. Nazarewicz, and P. Olanders, Phys. Scr., 39:196(1989)
[61]	P. Mmller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables, 59:185(1995)
[62]	J. Dudek, W. Nazarewicz and T. Werner, Nucl. Phys. A, 341:253(1980)
[63]	G. A. Leander, J. Dudek, W. Nazarewicz, J. R. Nix, and Ph. Quentin, Phys. Rev. C, 30:416(1984)
[64]	J. Dudek and T. Werner, J. Phys. G:Nucl. Phys., 4:1543(1978)
[65]	J. Dudek, A. Majhofer, J. Skalski, T. Werner, S. Ćwjok and W. Nazarewicz, J. Phys. G:Nucl. Phys., 5:1359(1979)
[66]	J. Dudek, Z. Szymański and T. Werner, Phys. Rev. C, 23:920(1981)
[67]	R. Nojarov, J. Phys. G:Nucl. Phys., 10:539(1984)
[68]	H. C. Pradhan, Y. Nogami, and J. Law, Nucl. Phys. A, 201:357(1973)
[69]	P. Mmller and J. R. Nix, Nucl. Phys. A, 536:20(1992)
[70]	G. Andersson, S. E. Larsson, G. Leander, P. Mller, S. G. Nilsson, I. Ragnarsson, S. berg, R. Bengtsson, J. Dudek, B. Nerlo-Pomorska, K. Pomorski, and Z. Szymański, Nucl. Phys. A, 268:205(1976)
[71]	K. Rutz, J. A. Maruhn, P.-G. Reinhard, and W. Greiner, Nucl. Phys. A, 590:680(1995)
[72]	S. Ćwiok, J. Dobaczewski, P.-H. Heenen, P. Magierski, and W. Nazarewicz, Nucl. Phys. A, 611:211(1996)
[73]	M. Samyn, S. Goriely, and J. M. Pearson, Phys. Rev. C, 72:044316(2005)
[74]	J.-P. Delaroche, M. Girod, H. Goutte, and J. Libert, Nucl. Phys. A, 771:103(2006)
[75]	G. N. Smirenkin, IAEA Report No. INDC(CCP)-359, Vienna, 1993
[76]	S. Karatzikos, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Lett. B, 689:72(2010)
[77]	J. Zhao, B. N. Lu, T. Nikić, D. Vretenar, and S. G. Zhou, Phys. Rev. C, 93:044315(2016)
[78]	B. Pritychenko, M. Birch, B. Singh, and M. Horoi, At. Data Nucl. Data Tables, 107:1(2016)
[79]	A. Sobiczewski, I. Muntian, and Z. Patyk, Phys. Rev. C, 63:034306(2001)
[80]	P. Mmller, A. J. Sierk, T. Ichikawa, and H. Sagawa, At. Data Nucl. Data Tables, 109-110:1(2016)
[81]	S. Goriely, F. Tondeur, and J. M. Pearson, At. Data Nucl. Data Tables, 77:311(2001)
[82]	Y. Aboussir, J. M. Pearson, A. K. Dutta, and F. Tondeur, At. Data Nucl. Data Tables, 61:127(1995)
[83]	J. Dudek, W. Nazarewicz, and P. Olanders, Nucl. Phys. A, 420:285(1984)
[84]	K. Mazurek, J. Dudek, A. Maj, and D. Rouvel, Phys. Rev. C, 91:034301(2015)
[85]	J. Sadhukhan, W. Nazarewicz, and N. Schunck, Phys. Rev. C, 93:011304(R) (2016)
[86]	N. Wang, M. Liu, X. Z. Wu, and J. Meng, Phys. Lett. B, 734:215(2014)
[87]	Q. Zhi and Z. Ren, Phys. Lett. B, 638:166(2006)
[88]	P. Marmier and E. Sheldon, Physics of Nuclei and Particles (Academic Press, New York, 1971)
[89]	C. L. Wu, M. Guidry, and D. H. Feng, Phys. Lett. B, 387:449(1996)

[1]	Wei Zhang , Jin-Ke Huang , Ting-Ting Sun , Jing Peng , Shuang-Quan Zhang . Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum. Chinese Physics C, 2024, 48(10): 104105. doi: 10.1088/1674-1137/ad62dd
[2]	Lin Gan , Zhi-Hong Li , Hui-Bin Sun , Shi-Peng Hu , Er-Tao Li , Jian Zhong . Systematic study of the Woods-Saxon potential parametersbetween heavy-ions. Chinese Physics C, 2021, 45(5): 054105. doi: 10.1088/1674-1137/abe84f
[3]	Jun-Gang Deng , Jie-Cheng Zhao , Jiu-Long Chen , Xi-Jun Wu , Xiao-Hua Li . α decay properties of ²⁹⁶Og within the two-potential approach. Chinese Physics C, 2018, 42(4): 044102. doi: 10.1088/1674-1137/42/4/044102
[4]	Dong Bai , Zhongzhou Ren . Woods-Saxon-Gaussian potential and alpha-cluster structures ofalpha + closed shell nuclei. Chinese Physics C, 2018, 42(12): 124102. doi: 10.1088/1674-1137/42/12/124102
[5]	Guan-Ying Wang , Ran Han , Xiao-Ping Ouyang , Jin-Cheng He , Jun-Yao Yan . Potential reduction interior point algorithm unfolding of neutron energy spectrum measured by recoil proton method. Chinese Physics C, 2017, 41(5): 056201. doi: 10.1088/1674-1137/41/5/056201
[6]	Jun-Gang Deng , Jun-Hao Cheng , Bo Zheng , Xiao-Hua Li . α decay properties of ²⁹⁷Og within the two-potential approach. Chinese Physics C, 2017, 41(12): 124109. doi: 10.1088/1674-1137/41/12/124109
[7]	U. T. Yakhshiev , Hyun-Chul Kim , B. Turimov , M. M. Musakhanov , Emiko Hiyama . Instanton effects on the heavy-quark static potential. Chinese Physics C, 2017, 41(8): 083102. doi: 10.1088/1674-1137/41/8/083102
[8]	Ming Chen , Yong-Chang Huang . Thermodynamic surface system of static black holes and area law. Chinese Physics C, 2016, 40(11): 113101. doi: 10.1088/1674-1137/40/11/113101
[9]	SHEN Zhen-Yu , XU Xiao-Ming . Relationship between quark-antiquark potential andquark-antiquark free energy in hadronic matter. Chinese Physics C, 2015, 39(7): 074103. doi: 10.1088/1674-1137/39/7/074103
[10]	N. Salehi , H. Hassanabadi , A. A. Rajabi . A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential. Chinese Physics C, 2015, 39(6): 063106. doi: 10.1088/1674-1137/39/6/063106
[11]	CHAI Qing-Zhen , WANG Hua-Lei , YANG Qiong , LIU Min-Liang . Spin-dependent γ softness or triaxiality in even-even ^132-138Nd nuclei. Chinese Physics C, 2015, 39(2): 024101. doi: 10.1088/1674-1137/39/2/024101
[12]	Manjeet Singh Gautam . Static versus energy-dependent nucleus-nucleus} potential for description of sub-barrier fusion dynamics of ₈¹⁶O+₅₀^112,116,120Sn reactions. Chinese Physics C, 2015, 39(11): 114102. doi: 10.1088/1674-1137/39/11/114102
[13]	E. Momtazi , B. H. Yazarloo , H. Hassanabadi . Solutions of the two-body Salpeter equation under the Coulomb and exponential potential for any l state with Laplace approach. Chinese Physics C, 2014, 38(2): 023101. doi: 10.1088/1674-1137/38/2/023101
[14]	E. Maghsoodi , S. Zarrinkamar . Approximate solutions of Dirac equation with a ring-shaped Woods-Saxon potential by Nikiforov-Uvarov method. Chinese Physics C, 2013, 37(11): 113104. doi: 10.1088/1674-1137/37/11/113104
[15]	M. Ghominejad , B. H. Yazarloo , S. Zarrinkamar , H. Hassanabadi . Two-body Spinless Salpeter equation for the Woods-Saxon potential. Chinese Physics C, 2013, 37(8): 083102. doi: 10.1088/1674-1137/37/8/083102
[16]	S. M. Ikhdair , A. A. Rajabi . A semi-relativistic treatment of spinless particles subjectto the nuclear Woods-Saxon potential. Chinese Physics C, 2013, 37(6): 063101. doi: 10.1088/1674-1137/37/6/063101
[17]	WANG Nan , ZHOU Shan-Gui , ZHAO En-Guang . Influence of octupole deformation and orientation on the potential energy surface in the di-nuclear system model. Chinese Physics C, 2010, 34(10): 1615-1621. doi: 10.1088/1674-1137/34/10/012
[18]	XU Qiang , WANG Ruo-Dong , ZHU Sheng-Jiang . Pseudospin symmetry in the relativistic Woods-Saxon. Chinese Physics C, 2006, 30(3): 207-211.
[19]	Feng Dachun , Liu Wenqin , Ma Zhongyu . Analysis of Relativistic Optical Potential for Medium-Energy Protons. Chinese Physics C, 1993, 17(S1): 81-88.
[20]	Dai Guangxi . The Shape and Potential of Hot Nuclei in Symmetric Ternary Fission. Chinese Physics C, 1992, 16(S3): 305-311.

Access

Get Citation

Qing-Zhen Chai, Wei-Juan Zhao, Min-Liang Liu and Hua-Lei Wang. Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei:systematic investigation of the triaxiality effect on the fission barrier[J]. Chinese Physics C, 2018, 42(5): 054101. doi: 10.1088/1674-1137/42/5/054101

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2018-02-06

Fund

Supported by National Natural Science Foundation of China (11675148, 11505157), the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province (2017GGJS008), the Foundation and Advanced Technology Research Program of Henan Province (162300410222), the Outstanding Young Talent Research Fund of Zhengzhou University (1521317002) and the Physics Research and Development Program of Zhengzhou University (32410017)

Article Metric

Article Views(1698)
PDF Downloads(37)
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

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei:systematic investigation of the triaxiality effect on the fission barrier

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei:systematic investigation of the triaxiality effect on the fission barrier

HTML

目录