Abstract
Shape transitions in the isotopes of transitional nuclei W, Os, and Pt are studied by using the energy density functional framework rooted in the effective nucleon-nucleon interactions. The UNEDF1 parametrization of the Skyrme energy density functionals along with the Lipkin-Nogami corrections are employed to obtain the potential energy surfaces of the even-even isotopes of these nuclei around the \(N=126\) neutron shell closure. Further, to get more insight into the shape changes, we extract the nucleonic localization functions for selected isotopes. For all three isotopic chains, we observed shape transitions from triaxial deformation to oblate, then spherical ground state for shell-closed isotopes, and finally prolate deformation for highly neutron-rich isotopes. Moreover, we calculate other observables like pairing gaps, two-neutron separation energies, and reduced transition probabilities in support of our predictions based on the potential energy surfaces.
Similar content being viewed by others
Data Availability
This manuscript has no associated data or the data will not be deposited [Authors’ comment: This study is based on the theoretical model. Hence, no experimental data has been listed].
References
R.F. Casten, Nat. Phys. 2, 811 (2006)
P. Cejnar, J. Jolie, R.F. Casten, Rev. Mod. Phys. 82, 2155 (2010)
F. Iachello, N.V. Zamfir, Phys. Rev. Lett. 92, 212501 (2004)
R.F. Casten, Prog. Part. Nucl. Phys. 62(1), 183 (2009)
K. Nomura, N. Shimizu, T. Otsuka, Phys. Rev. Lett. 101, 142501 (2008)
N. Alkhomashi, P.H. Regan, Z. Podolyák et al., Phys. Rev. C 80, 064308 (2009)
Z. Podolyák, P. Regan, M. Pfützner et al., Phys. Lett. B 491(3), 225 (2000)
A. Rohilla, C.K. Gupta, R.P. Singh, S. Muralithar et al., Eur. Phys. J. A 53(4), 64 (2017)
P.R. John, V. Modamio, J.J. Valiente-Dobón et al., Phys. Rev. C 90, 021301 (2014)
S.K. Chamoli, A. Rohilla, C.K. Gupta, R.P. Singh, S. Muralithar, S. Chakraborty, H.P. Sharma, A. Kumar, I.M. Govil, D.C. Biswas, Acta Phys. Pol. B 48, 337 (2017)
P.R. John, J.J. Valiente-Dobón, D. Mengoni et al., Phys. Rev. C 95, 064321 (2017)
M. Khalil, A.M. Khalaf, M. Kotb, M.D. Okasha, Nucl. Phys. A 991, 121610 (2019)
K. Nomura, T. Nikšić, D. Vretenar, Phys. Rev. C 94, 064310 (2016)
K. Nomura, T. Otsuka, R. Rodríguez-Guzmán et al., Phys. Rev. C 83, 054303 (2011)
K. Nomura, T. Otsuka, R. Rodríguez-Guzmán et al., Phys. Rev. C 84, 054316 (2011)
K. Nomura, T. Otsuka, R. Rodríguez-Guzmán, L.M. Robledo, P. Sarriguren, Phys. Rev. C 83, 014309 (2011)
I.O. Morales, A. Frank, C.E. Vargas, P.V. Isacker, Phys. Rev. C 78, 024303 (2008)
K. Nomura, T. Nikšić, D. Vretenar, Phys. Rev. C 96, 014304 (2017)
K. Nomura, T. Nikšić, D. Vretenar, Phys. Rev. C 102, 034315 (2020)
R.F. Casten, E.A. McCutchan, J. Phys. G 34(7), R285 (2007)
L.M. Robledo, R.R. Rodríguez-Guzmán, P. Sarriguren, Phys. Rev. C 78, 034314 (2008)
T.R. Rodríguez, J. Luis Egido, Phys. Lett. B 663(1), 49 (2008)
J. Jolie, A. Linnemann, Phys. Rev. C 68, 031301 (2003)
Y. Zhang, F. Pan, Y.X. Liu, Y.A. Luo, J.P. Draayer, Phys. Rev. C 85, 064312 (2012)
D. Bonatsos, I.E. Assimakis, Minkov, et al., Phys. Rev. C 95, 064326 (2017)
A. Martinou, D. Bonatsos, K.E. Karakatsanis et al., Eur. Phys. J. A 57(3), 83 (2021)
A. Ansari, Phys. Rev. C 33, 321 (1986)
P. Sarriguren, R. Rodríguez-Guzmán, L.M. Robledo, Phys. Rev. C 77, 064322 (2008)
L.M. Robledo, R. Rodríguez-Guzmán, P. Sarriguren, J. Phys. G 36(11), 115104 (2009)
R. Rodríguez-Guzmán, P. Sarriguren, L.M. Robledo, J.E. García-Ramos, Phys. Rev. C 81, 024310 (2010)
M. Bender, P.H. Heenen, P.G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)
M. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Borycki, Int. J. Mass Spectrom. 251(2), 243 (2006)
S.S. Nayak, G. Mukherjee, Nucl. Phys. A 1023, 122449 (2022)
T. Nikšić, D. Vretenar, G.A. Lalazissis, P. Ring, Phys. Rev. Lett. 99, 092502 (2007)
Z. Shi, Z.P. Li, Phys. Rev. C 97, 034329 (2018)
Y. Fu, H. Tong, X.F. Wang et al., Phys. Rev. C 97, 014311 (2018)
J. Xiang, Z.P. Li, W.H. Long et al., Phys. Rev. C 98, 054308 (2018)
S. Nandi, G. Mukherjee, A. Dhal, R. Banik, S. Bhattacharya, S. Basu, S. Dar, S. Bhattacharyya, C. Bhattacharya, S. Kundu, D. Paul, S. Rajbanshi, S. Chatterjee, S. Das, S. Samanta, R. Raut, S.S. Ghugre, H. Pai, S. Ali, S. Biswas, A. Goswami, Phys. Rev. C 105, 034336 (2022)
N. Ashok, A. Joseph, Int. J. Mod. Phys. E 28(10), 1950093 (2019)
M. Kortelainen, J. McDonnell, W. Nazarewicz, P.G. Reinhard, J. Sarich, N. Schunck, M.V. Stoitsov, S.M. Wild, Phys. Rev. C 85, 024304 (2012)
P.G. Reinhard, J.A. Maruhn, A.S. Umar, V.E. Oberacker, Phys. Rev. C 83, 034312 (2011)
C.L. Zhang, B. Schuetrumpf, W. Nazarewicz, Phys. Rev. C 94, 064323 (2016)
J. Sadhukhan, C. Zhang, W. Nazarewicz, N. Schunck, Phys. Rev. C 96, 061301 (2017)
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, 1980)
J. Dobaczewski, P. Olbratowski, Comput. Phys. Commun. 158(3), 158 (2004)
J. Sadhukhan, J. Dobaczewski, W. Nazarewicz, J.A. Sheikh, A. Baran, Phys. Rev. C 90, 061304 (2014)
M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz et al., Phys. Rev. C 68, 054312 (2003)
N. López Vaquero, T.R. Rodriguez, J.L. Egido, Phys. Lett. B 704(5), 520 (2011)
N.L. Vaquero, J.L. Egido, T.R. Rodríguez, Phys. Rev. C 88, 064311 (2013)
J. Dobaczewski, W. Nazarewicz, M.V. Stoitsov, Eur. Phys. J. A 15, 21 (2002)
J. Terasaki, H. Flocard, P.H. Heenen, P. Bonche, Nucl. Phys. A 621(3), 706 (1997)
N. Schunck, J.D. McDonnell, J. Sarich, S.M. Wild, D. Higdon, Jour. Phys. G 42(3), 034024 (2015)
M. Kortelainen, J. McDonnell, W. Nazarewicz et al., Phys. Rev. C 85, 024304 (2012)
N. Schunck, J. Dobaczewski, W. Satuła et al., Comp. Phys. Comm. 216, 145 (2017)
S. Mizutori, J. Dobaczewski, G.A. Lalazissis et al., Phys. Rev. C 61, 044326 (2000)
L. Lühmann, M. Debray, K.P. Lieb, W. Nazarewicz, B. Wörmann, J. Eberth, T. Heck, Phys. Rev. C 31, 828 (1985)
G. Mukherjee, P. Joshi, R. Bhowmik, S. Roy, S. Dutta, S. Muralithar, R. Singh, Nucl. Phys. A 829(3), 137 (2009)
T. Nikšić, D. Vretenar, P. Ring, Progress Particle Nucl. Phys. 66(3), 519 (2011)
X.Q. Yang, L.J. Wang, J. Xiang, X.Y. Wu, Z.P. Li, Phys. Rev. C 103, 054321 (2021)
M. Wang, G. Audi, F.G. Kondev et al., Chin. Phys. C 41(20170303), 030003 (2017)
M. Birk, A.E. Blaugrund, G. Goldring, E.Z. Skurnik, J.S. Sokolowski, Phys. Rev. 126, 726 (1962)
E. Bashandy, M. El-nesr, Nucl. Phys. 34(2), 483 (1962)
C.Y. Wu, D. Cline, A.B. Hayes, M.W. Simon, R. Krücken, J.R. Cooper, C.J. Barton, C.W. Beausang, C. Bialik, M.A. Caprio, R.F. Casten, A.A. Hecht, H. Newman, J. Novak, N. Pietralla, K. Zyromski, N.V. Zamfir, Phys. Rev. C 64, 014307 (2001)
R. Chopra, P. Tandon, S. Devare, H. Devare, Nucl. Phys. A 209(3), 461 (1973)
T. Daniel, S. Kisyov, P.H. Regan, N. Marginean, Z. Podolyák, R. Marginean, K. Nomura, M. Rudigier, R. Mihai, V. Werner, R.J. Carroll, L.A. Gurgi, A. Oprea, T. Berry, A. Serban, C.R. Nita, C. Sotty, R. Suvaila, A. Turturica, C. Costache, L. Stan, A. Olacel, M. Boromiza, S. Toma, Phys. Rev. C 95, 024328 (2017)
N.R. Johnson, P.P. Hubert, E. Eichler, D.G. Sarantites, J. Urbon, S.W. Yates, T. Lindblad, Phys. Rev. C 15, 1325 (1977)
Acknowledgements
The authors acknowledge the Computer Division of Variable Energy Cyclotron Centre, Kolkata for providing the necessary computational resources.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Takashi Nakatsukasa
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kannan, M.T.S., Ashok, N., Nayak, S.S. et al. Shape evolution of sub-lead neutron-rich nuclei around the neutron shell closure. Eur. Phys. J. A 59, 220 (2023). https://doi.org/10.1140/epja/s10050-023-01127-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/s10050-023-01127-z