Abstract
We study the ground state properties, potential energy curves and potential energy surfaces of the superheavy nucleus 270Hs by using the multidimensionally-constrained relativistic mean-field model with the effective interaction PC-PK1. The binding energy, size and shape as well as single particle shell structure corresponding to the ground state of this nucleus are obtained. 270Hs is well deformed and exhibits deformed doubly magic feature in the single neutron and proton level schemes. One-dimensional potential energy curves and two-dimensional potential energy surfaces are calculated for 270Hs with various spatial symmetries imposed. We investigate in detail the effects of the reflection asymmetric and triaxial distortions on the fission barrier and fission path of 270Hs. When the axial symmetry is imposed, the reflection symmetric and reflection asymmetric fission barriers both show a double-hump structure and the former is higher. However, when triaxial shapes are allowed the reflection symmetric barrier is lowered very much and then the reflection symmetric fission path becomes favorable.
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J. H. Hamilton, S. Hofmann, and Y. T. Oganessian, Annu. Rev. Nucl. Part. Sci. 63, 383 (2013).
W. Nazarewicz, Nat. Phys. 14, 537 (2018).
S. A. Giuliani, Z. Matheson, W. Nazarewicz, E. Olsen, P. G. Reinhard, J. Sadhukhan, B. Schuetrumpf, N. Schunck, and P. Schwerdtfeger, Rev. Mod. Phys. 91, 011001 (2019).
W. D. Myers, and W. J. Swiatecki, Nucl. Phys. 81, 1 (1966).
C. Y. Wong, Phys. Lett. 21, 688 (1966).
A. Sobiczewski, F. A. Gareev, and B. N. Kalinkin, Phys. Lett. 22, 500 (1966).
H. Meldner, Ark. Fys. 36, 593 (1967).
U. Mosel, and W. Greiner, Z. Phys. 222, 261 (1969).
S. G. Nilsson, C. F. Tsang, A. Sobiczewski, Z. Szymański, S. Wycech, C. Gustafson, I. L. Lamm, P. Möller, and B. Nilsson, Nucl. Phys. A 131, 1 (1969).
S. Hofmann, and G. Münzenberg, Rev. Mod. Phys. 72, 733 (2000).
K. Morita, Nucl. Phys. A 944, 30 (2015).
Y. T. Oganessian, A. Sobiczewski, and G. M. Ter-Akopian, Phys. Scr. 92, 023003 (2017).
K. Rutz, M. Bender, T. Burvenich, T. Schilling, P. G. Reinhard, J. A. Maruhn, and W. Greiner, Phys. Rev. C 56, 238 (1997).
W. Zhang, J. Meng, S. Q. Zhang, L. S. Geng, and H. Toki, Nucl. Phys. A 753, 106 (2005).
A. Sobiczewski, and K. Pomorski, Prog. Particle Nucl. Phys. 58, 292 (2007).
X.-R. Zhou, C. Qiu, and H. Sagawa, in Effect of Tensor Interaction on the Shell Structure of Superheavy Nuclei: Nuclear Structure in China 2010—Proceedings of the 13th National Conference on Nuclear Structure in China, edited by H.-B. Bai, J. Meng, E.-G. Zhao, and S.-G. Zhou, Chi-Feng, Inner Mongolia, China, 24–30 July 2010, (World Scientific, Singapore, 2011), pp. 259–267.
J. J. Li, W. H. Long, J. Margueron, and N. Van Giai, Phys. Lett. B 732, 169 (2014), arXiv: 1303.2765.
Q. Mo, M. Liu, and N. Wang, Phys. Rev. C 90, 024320 (2014), arXiv: 1408.4872.
A. V. Afanasjev, S. E. Agbemava, and A. Gyawali, Phys. Lett. B 782, 533 (2018), arXiv: 1804.06395.
S. E. Agbemava, A. V. Afanasjev, A. Taninah, and A. Gyawali, Phys. Rev. C 99, 034316 (2019), arXiv: 1902.10108.
P. Moller, S. G. Nilsson, and J. R. Nix, Nucl. Phys. A 229, 292 (1974).
S. Čwiok, V. V. Pashkevich, J. Dudek, and W. Nazarewicz, Nucl. Phys. A 410, 254 (1983).
Z. Patyk, J. Skalski, A. Sobiczewski, and S. Ćwiok, Nucl. Phys. A 502, 591 (1989).
Z. Patyk, and A. Sobiczewski, Nucl. Phys. A 533, 132 (1991).
R. Smolanczuk, J. Skalski, and A. Sobiczewski, Phys. Rev. C 52, 1871 (1995).
J. Dvorak, W. Brüchle, M. Chelnokov, R. Dressler, C. E. Dullmann, K. Eberhardt, V. Gorshkov, E. Jäger, R. Krücken, A. Kuznetsov, Y. Nagame, F. Nebel, Z. Novackova, Z. Qin, M. Schädel, B. Schausten, E. Schimpf, A. Semchenkov, P. Thörle, A. Türler, M. Wegrzecki, B. Wierczinski, A. Yakushev, and A. Yeremin, Phys. Rev. Lett. 97, 242501 (2006).
Y. T. Oganessian, V. K. Utyonkov, F. S. Abdullin, S. N. Dmitriev, R. Graeger, R. A. Henderson, M. G. Itkis, Y. V. Lobanov, A. N. Mezentsev, K. J. Moody, S. L. Nelson, A. N. Polyakov, M. A. Ryabinin, R. N. Sagaidak, D. A. Shaughnessy, I. V. Shirokovsky, M. A. Stoyer, N. J. Stoyer, V. G. Subbotin, K. Subotic, A. M. Sukhov, Y. S. Tsyganov, A. Türler, A. A. Voinov, G. K. Vostokin, P. A. Wilk, and A. Yakushev, Phys. Rev. C 87, 034605 (2013).
V. V. Pashkevich, Nucl. Phys. A 133, 400 (1969).
P. Möller, J. R. Nix, in Calculation of Fission barriers: Proceedings of the Third IAEA Symposium on Physics and Chemistry of Fission, Rochester, New York, 13–17 August 1973, Vol. 1 (International Atomic Energy Agency, Vienna, 1974), pp. 103–140.
K. Rutz, J. A. Maruhn, P. G. Reinhard, and W. Greiner, Nucl. Phys. A 590, 680 (1995).
L. M. Robledo, and M. Warda, Int. J. Mod. Phys. E 17, 204 (2008), arXiv: 0710.4411.
M. Kowal, P. Jachimowicz, and A. Sobiczewski, Phys. Rev. C 82, 014303 (2010).
Z. P. Li, T. Nikšić, D. Vretenar, P. Ring, and J. Meng, Phys. Rev. C 81, 064321 (2010).
H. Abusara, A. V. Afanasjev, and P. Ring, Phys. Rev. C 82, 044303 (2010), arXiv: 1010.1803.
A. Staszczak, A. Baran, and W. Nazarewicz, Int. J. Mod. Phys. E 20, 552 (2011).
G. Royer, M. Jaffré, and D. Moreau, Phys. Rev. C 86, 044326 (2012).
B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 85, 011301 (2012), arXiv: 1110.6769.
M. Warda, and J. L. Egido, Phys. Rev. C 86, 014322 (2012), arXiv: 1204.5867.
B. N. Lu, J. Zhao, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 89, 014323 (2014), arXiv: 1304.2513.
S. G. Zhou, Phys. Scr. 91, 063008 (2016), arXiv: 1605.00956.
J. Zhao, B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 95, 014320 (2017), arXiv: 1606.08994.
B. D. Serot, and J. D. Walecka, Adv. Nucl. Phys. 16, 1 (1986).
P. G. Reinhard, Rep. Prog. Phys. 52, 439 (1989).
P. Ring, Prog. Particle Nucl. Phys. 37, 193 (1996).
M. Bender, P. H. Heenen, and P. G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).
D. Vretenar, A. Afanasjev, G. Lalazissis, and P. Ring, Phys. Rep. 409, 101 (2005).
J. Meng, H. Toki, S. G. Zhou, S. Q. Zhang, W. H. Long, and L. S. Geng, Prog. Particle Nucl. Phys. 57, 470 (2006).
N. Paar, D. Vretenar, E. Khan, and G. Coló, Rep. Prog. Phys. 70, 691 (2007).
T. Nikšić, D. Vretenar, and P. Ring, Prog. Particle Nucl. Phys. 66, 519 (2011), arXiv: 1102.4193.
H. Liang, J. Meng, and S. G. Zhou, Phys. Rep. 570, 1 (2015), arXiv: 1411.6774.
J. Meng, and S. G. Zhou, J. Phys. G-Nucl. Part. Phys. 42, 093101 (2015), arXiv: 1507.01079.
J. Meng, Relativistic Density Functional for Nuclear Structure, Vol. 10 of International Review of Nuclear Physics (World Scientific Pub, Singapore, 2016).
Y. K. Gambhir, P. Ring, and A. Thimet, Ann. Phys. 198, 132 (1990).
P. Ring, Y. K. Gambhir, and G. A. Lalazissis, Comput. Phys. Commun. 105, 77 (1997).
A. V. Afanasjev, P. Ring, and J. König, Nucl. Phys. A 676, 196 (2000).
L. S. Geng, J. Meng, and H. Toki, Chin. Phys. Lett. 24, 1865 (2007), arXiv: 0706.0491.
W. Zhang, Z. P. Li, S. Q. Zhang, and J. Meng, Phys. Rev. C 81, 034302 (2010), arXiv: 1003.2231.
Y. Y. Wang, and Z. X. Ren, Sci. China-Phys. Mech. Astron. 61, 082012 (2018), arXiv: 1711.07799.
B. Qi, H. Jia, C. Liu, and S. Y. Wang, Sci. China-Phys. Mech. Astron. 62, 012012 (2019).
H. J. Xia, X. Y. Wu, H. Mei, and J. M. Yao, Sci. China-Phys. Mech. Astron. 62, 042011 (2019), arXiv: 1811.01486.
M. Warda, J. L. Egido, L. M. Robledo, and K. Pomorski, Phys. Rev. C 66, 014310 (2002).
S. Karatzikos, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Lett. B 689, 72 (2010), arXiv: 0909.1233.
Y. Tian, and Z. Y. Ma, Chin. Phys. Lett. 23, 3226 (2006).
Y. Tian, Z. Y. Ma, and P. Ring, Phys. Lett. B 676, 44 (2009), arXiv: 0908.1844.
Y. Tian, Z. Y. Ma, and P. Ring, Phys. Rev. C 79, 064301 (2009), arXiv: 0908.1845.
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin/Heidelberg/New York, 1980).
J. Zhao, B. N. Lu, D. Vretenar, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 91, 014321 (2015), arXiv: 1404.5466.
J. Zhao, B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 86, 057304 (2012), arXiv: 1209.6567.
C. Liu, S. Y. Wang, R. A. Bark, S. Q. Zhang, J. Meng, B. Qi, P. Jones, S. M. Wyngaardt, J. Zhao, C. Xu, S. G. Zhou, S. Wang, D. P. Sun, L. Liu, Z. Q. Li, N. B. Zhang, H. Jia, X. Q. Li, H. Hua, Q. B. Chen, Z. G. Xiao, H. J. Li, L. H. Zhu, T. D. Bucher, T. Dinoko, J. Easton, K. Juhász, A. Kamblawe, E. Khaleel, N. Khumalo, E. A. Lawrie, J. J. Lawrie, S. N. T. Majola, S. M. Mullins, S. Murray, J. Ndayishimye, D. Negi, S. P. Noncolela, S. S. Ntshangase, B. M. Nyakó, J. N. Orce, P. Papka, J. F. Sharpey-Schafer, O. Shirinda, P. Sithole, M. A. Stankiewicz, and M. Wiedeking, Phys. Rev. Lett. 116, 112501 (2016).
X. C. Chen, J. Zhao, C. Xu, H. Hua, T. M. Shneidman, S. G. Zhou, X. G. Wu, X. Q. Li, S. Q. Zhang, Z. H. Li, W. Y. Liang, J. Meng, F. R. Xu, B. Qi, Y. L. Ye, D. X. Jiang, Y. Y. Cheng, C. He, J. J. Sun, R. Han, C. Y. Niu, C. G. Li, P. J. Li, C. G. Wang, H. Y. Wu, Z. H. Li, H. Zhou, S. P. Hu, H. Q. Zhang, G. S. Li, C. Y. He, Y. Zheng, C. B. Li, H. W. Li, Y. H. Wu, P. W. Luo, and J. Zhong, Phys. Rev. C 94, 021301 (2016).
B. N. Lu, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 84, 014328 (2011), arXiv: 1104.4638.
B. N. Lu, E. Hiyama, H. Sagawa, and S. G. Zhou, Phys. Rev. C 89, 044307 (2014), arXiv: 1403.5866.
J. Zhao, B. N. Lu, T. Niksic, and D. Vretenar, Phys. Rev. C 92, 064315 (2015).
J. Zhao, B. N. Lu, T. Nikšić, D. Vretenar, and S. G. Zhou, Phys. Rev. C 93, 044315 (2016), arXiv: 1603.00992.
J. Zhao, T. Nikšić, D. Vretenar, and S. G. Zhou, Phys. Rev. C 99, 014618 (2019).
J. Zhao, J. Xiang, Z.-P. Li, T. Nikšić, D. Vretenar, and S. G. Zhou, Phys. Rev. C 99, 054613 (2019), arXiv: 1902.09535.
P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C 82, 054319 (2010), arXiv: 1002.1789.
P. W. Zhao, and Z. X. Li, Int. J. Mod. Phys. E 27, 1830007 (2018).
B. H. Sun, P. W. Zhao, and J. Meng, Sci. China-Phys. Mech. Astron. 54, 210 (2011).
P. W. Zhao, L. S. Song, B. Sun, H. Geissel, and J. Meng, Phys. Rev. C 86, 064324 (2012), arXiv: 1210.5010.
K. Q. Lu, Z. X. Li, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C 91, 027304 (2015), arXiv: 1502.06908.
X. W. Xia, Y. Lim, P. W. Zhao, H. Z. Liang, X. Y. Qu, Y. Chen, H. Liu, L. F. Zhang, S. Q. Zhang, Y. Kim, and J. Meng, Atomic Data Nucl. Data Tables 121–122, 1 (2018), arXiv: 1704.08906.
P. W. Zhao, S. Q. Zhang, and J. Meng, Phys. Rev. C 89, 011301 (2014).
D. T. Yordanov, D. L. Balabanski, M. L. Bissell, K. Blaum, I. Budinčević, B. Cheal, K. Flanagan, N. Frömmgen, G. Georgiev, C. Geppert, M. Hammen, M. Kowalska, K. Kreim, A. Krieger, J. Meng, R. Neugart, G. Neyens, W. Nörtershäuser, M. M. Rajabali, J. Papuga, S. Schmidt, and P. W. Zhao, Phys. Rev. Lett. 116, 032501 (2016).
H. Haas, S. P. A. Sauer, L. Hemmingsen, V. Kellö, and P. W. Zhao, Europhys. Lett. 117, 62001 (2017).
S. Quan, Z. P. Li, D. Vretenar, and J. Meng, Phys. Rev. C 97, 031301 (2018), arXiv: 1803.02142.
P. W. Zhao, Phys. Lett. B 773, 1 (2017), arXiv: 1706.06127.
P. W. Zhao, S. Q. Zhang, J. Peng, H. Z. Liang, P. Ring, and J. Meng, Phys. Lett. B 699, 181 (2011), arXiv: 1101.4547.
P. W. Zhao, J. Peng, H. Z. Liang, P. Ring, and J. Meng, Phys. Rev. Lett. 107, 122501 (2011), arXiv: 1105.3622.
J. Meng, J. Peng, S. Q. Zhang, and P. W. Zhao, Front. Phys. 8, 55 (2013), arXiv: 1301.1808.
J. Peng, and P. W. Zhao, Phys. Rev. C 91, 044329 (2015).
J. Meng, and P. W. Zhao, Phys. Scr. 91, 053008 (2016), arXiv: 1604.02213.
W. Zhang, Z. P. Li, and S. Q. Zhang, Phys. Rev. C 88, 054324 (2013).
S. E. Agbemava, A. V. Afanasjev, T. Nakatsukasa, and P. Ring, Phys. Rev. C 92, 054310 (2015), arXiv: 1510.07909.
Z. X. Li, Z. H. Zhang, and P. W. Zhao, Front. Phys. 10, 268 (2015).
Y. Tian, Z. Ma, and P. Ring, Phys. Rev. C 80, 024313 (2009), arXiv: 0908.1848.
G. Audi, F. G. Kondev, M. Wang, W. J. Huang, and S. Naimi, Chin. Phys. C 41, 030001 (2017).
W. J. Huang, G. Audi, M. Wang, F. G. Kondev, S. Naimi, and X. Xu, Chin. Phys. C 41, 030002 (2017).
M. Wang, G. Audi, F. G. Kondev, W. J. Huang, S. Naimi, and X. Xu, Chin. Phys. C 41, 030003 (2017).
Z. Ren, Phys. Rev. C 65, 051304 (2002).
Z. Ren, F. Tai, and D. H. Chen, Phys. Rev. C 66, 064306 (2002).
L. Geng, H. Toki, and J. Meng, Prog. Theor. Phys. 113, 785 (2005).
L. Geng, Ground State Properties of Finite Nuclei in the Relativistic Mean Field Model, Dissertation for Doctoral Degree (Osaka University, Osaka, 2006).
S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. C 88, 024308 (2013).
H. F. Zhang, Y. Gao, N. Wang, J. Q. Li, E. G. Zhao, and G. Royer, Phys. Rev. C 85, 014325 (2012).
N. Wang, M. Liu, X. Wu, and J. Meng, Phys. Lett. B 734, 215 (2014), arXiv: 1405.2616.
P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, Atomic Data Nucl. Data Tables 109–110, 1 (2016), arXiv: 1508.06294.
M. Shi, Z. M. Niu, and H. Z. Liang, Chin. Phys. C 43, 074104 (2019).
N. Wang, M. Liu, and X. Wu, Phys. Rev. C 81, 044322 (2010), arXiv: 1001.1493.
N. Wang, Z. Liang, M. Liu, and X. Wu, Phys. Rev. C 82, 044304 (2010), arXiv: 1008.2115.
M. Liu, N. Wang, Y. Deng, and X. Wu, Phys. Rev. C 84, 014333 (2011), arXiv: 1104.0066.
J. Meng, and P. Ring, Phys. Rev. Lett. 77, 3963 (1996).
J. Meng, and P. Ring, Phys. Rev. Lett. 80, 460 (1998).
J. Meng, Nucl. Phys. A 635, 3 (1998).
X. Y. Qu, Y. Chen, S. Q. Zhang, P. W. Zhao, I. J. Shin, Y. Lim, Y. Kim, and J. Meng, Sci. China-Phys. Mech. Astron. 56, 2031 (2013), arXiv: 1309.3987.
M. D. Buhmann, Radial Basis Functions (Cambridge University Press, Cambridge, 2006).
N. Wang, and M. Liu, Phys. Rev. C 84, 051303 (2011), arXiv: 1111.0354.
J. S. Zheng, N. Y. Wang, Z. Y. Wang, Z. M. Niu, Y. F. Niu, and B. Sun, Phys. Rev. C 90, 014303 (2014).
Z. M. Niu, B. H. Sun, H. Z. Liang, Y. F. Niu, and J. Y. Guo, Phys. Rev. C 94, 054315 (2016), arXiv: 1607.02075.
S. G. Zhou, J. Meng, P. Ring, and E. G. Zhao, Phys. Rev. C 82, 011301 (2010), arXiv: 0909.1600.
L. Li, J. Meng, P. Ring, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 85, 024312 (2012), arXiv: 1202.0070.
L. L. Li, J. Meng, P. Ring, E. G. Zhao, and S. G. Zhou, Chin. Phys. Lett. 29, 042101 (2012), arXiv: 1203.1363.
X. X. Sun, J. Zhao, and S. G. Zhou, Phys. Lett. B 785, 530 (2018), arXiv: 1807.04991.
Q. Z. Chai, W. J. Zhao, M. L. Liu, and H. L. Wang, Chin. Phys. C 42, 054101 (2018), arXiv: 1803.04616.
P. Möller, A. J. Sierk, T. Ichikawa, A. Iwamoto, R. Bengtsson, H. Uhrenholt, and S. Åberg, Phys. Rev. C 79, 064304 (2009).
N. Dubray, and D. Regnier, Comput. Phys. Commun. 183, 2035 (2012), arXiv: 1112.4196.
Z. Matheson, S. A. Giuliani, W. Nazarewicz, J. Sadhukhan, and N. Schunck, Phys. Rev. C 99, 041304 (2019), arXiv: 1812.06490.
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Meng, X., Lu, B. & Zhou, S. Ground state properties and potential energy surfaces of 270Hs from multidimensionally-constrained relativistic mean field model. Sci. China Phys. Mech. Astron. 63, 212011 (2020). https://doi.org/10.1007/s11433-019-9422-1
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DOI: https://doi.org/10.1007/s11433-019-9422-1