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

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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)

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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

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Received: 2018-02-06

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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)

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

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