Abstract
The phenomena of shape evolution and shape coexistence in even–even \(^{88-114}\)Zr and \(^{90-116}\)Mo isotopes are studied by employing covariant density functional theory (CDFT) with density-dependent point-coupling parameter set, DD-PCX, and with separable pairing interaction. The results for the rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate–prolate shape coexistence in \(^{96-110}\)Zr isotopes, the correlations between shape transition and discontinuity in the observables are also examined. A smooth trend of charge radii in Mo isotopes is found to be due to the manifestation of triaxiality softness. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi level of neutron and proton, respectively. The rapid shape transition in Zr isotopes near N \(\approx \) 60 is identified to be caused by the evolution of the shell structure associated with massive proton excitations to 1\(\pi g_{9/2}\) orbit. The present calculations also predict a deformed semi-bubble structure in the \(^{100}\)Zr isotope.
Similar content being viewed by others
Data Availability Statement
This manuscript has associated data in a data repository. [Authors’ comment: Some of the data are given in the Tables of this article. However, all the data are available upon request by contacting the corresponding author.]
References
P. Cejnar, J. Jolie, R.F. Casten, Rev. Mod. Phys. 82, 3 (2010)
U. Hager et al., Phys. Rev. Lett. 96, 042504 (2006)
F. Buchinger et al., Phys. Rev. C 41, 2883 (1990)
P. Campbell et al., Phys. Rev. Lett. 89, 082501 (2002)
S. Raman, C.W. Nestor Jr., P. Tikkanen, At. Data Nucl. Data Tables 78, 1–128 (2001)
F.C. Charlwood et al., Phys. Lett. B 674, 23 (2009)
J.L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, P. Van Duppen, Phys. Rep. 215, 101 (1992)
K. Heyde, J.L. Wood, Rev. Mod. Phys. 83, 1467 (2011)
J. Eberth, R.A. Meyer, K. Sistemich, Nuclear structure of the zirconium region (Springer, Berlin, 1988)
A. Chakraborty et al., Phys. Rev. Lett. 110, 022504 (2013)
P. Singh et al., Phys. Rev. Lett. 121, 192501 (2018)
C.Y. Wu et al., Phys. Rev. C 70, 064312 (2004)
C.Y. Wu, H. Hua, D. Cline, Phys. Rev. C 68, 034322 (2003)
M. Zielinska et al., Acta Phys. Pol. B 36, 1289 (2005)
K. Wrzosek-Lipska et al., Int. J. Mod. Phys. E 20, 443 (2011)
K. Wrzosek-Lipska et al., Phys. Rev. C 86, 064305 (2012)
J. Ha et al., Phys. Rev. C 101, 044311 (2020)
K. Nomura, N. Shimizu, D. Vretenar, T. Niksic, T. Otsuka, Phys. Rev. Lett. 108, 132501 (2012)
R. Rodriguez-Guzman, P. Sarriguren, L.M. Robledo, S. Perez-Martin, Phys. Lett. B 691, 202 (2010)
A. Petrovici, Phys. Rev. C 85, 034337 (2012)
J. Xiang, Z.P. Li, Z.X. Li, J.M. Yao, J. Meng, Nucl. Phys. A 873, 1 (2012)
Bao-Mei Yao, Jian-You Guo, Mod. Phys. Lett. A 25, 1177 (2010)
M. Bhuyan, Phys. Rev. C 92, 034323 (2015)
H. Abusara and Shakeb Ahmad, Phys. Rev. C 96, 064303 (2017)
H. Abusara, A. Shakeb, S. Othman, Phys. Rev. C 95, 054302 (2017)
K. Nomura, R. Rodriguez-Guzman, L.M. Robledo, Phys. Rev. C 94, 044314 (2016)
J.E. Garcia-Ramos, K. Heyde, Phys. Rev. C 100, 044315 (2019)
M. Bender, G.F. Bertsch, P.-H. Heenen, Phys. Rev. C 73, 034322 (2006)
M. Bender, G.F. Bertsch, P.-H. Heenen, Phys. Rev. C 78, 054312 (2008)
Y. El Bassem, M. Oulne, Nucl. Phys. A 957, 22 (2017)
H. Mei, J. Xiang, J.M. Yao, Z.P. Li, J. Meng, Phys. Rev. C 85, 034321 (2012)
J. Meng, S.-G. Zhou, I. Tanihata, Phys. Lett. B 532, 209–214 (2002)
J. Meng, H. Toki, J.Y. Zeng, S.Q. Zhang, S.-G. Zhou, Phys. Rev. C 65, 041302 (2002)
Smriti Thakur, Shashi K. Dhiman, Mod. Phys. Lett. A 34, 1950014 (2019)
Virender Thakur, Nucl. Phys. A 992, 121623 (2019)
Virender Thakur, Pankaj Kumar, Suman Thakur, Smriti Thakur, Vikesh Kumar, Shashi K. Dhiman, Nucl. Phys. A 1002, 121981 (2020)
P. Kumar, S.K. Dhiman, Nucl. Phys. A 1001, 121935 (2020)
P.W. Zhao, Z.P. Li, J.M. Yao, J. Meng, Phys. Rev. C 82, 054319 (2010)
T. Niksic, D. Vretenar, P. Ring, Phys. Rev. C 78, 034318 (2008)
E. Yuksel, T. Marketin, N. Paar, Phys. Rev. C 99, 034318 (2019)
T. Niksic, N. Paar, D. Vretenar, P. Ring, Comput. Phys. Commun. 185, 1808 (2014)
Y. Tian, Z.Y. Ma, P. Ring, Phys. Lett. B 676, 44–50 (2009)
Y. Tian, Z.Y. Ma, P. Ring, Phys. Rev. C 80, 024313 (2009)
T. Niksic, P. Ring, D. Vretenar, Y. Tian, Z.Y. Ma, Phys. Rev. C 81, 054318 (2010)
T. Niksic, D. Vretenar, P. Ring, Prog. Part. Nucl. Phys. 66, 519–548 (2011)
X.W. Xia et al., At. Data Nucl. Data Tables 121, 64 (2018)
M. Wang, G. Audi, F.G. Kondev, W.J. Huang, S. Naimi, X. Xu, Chin. Phys. C 41, 030003 (2017)
M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)
J.-P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Peru, N. Pillet, G.F. Bertsch, Phys. Rev. C 81, 014303 (2010)
N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A.C. Vutha, E.A. Hessels, Science 365, 1007–1012 (2019)
T. Togashi, Y. Tsunoda, T. Otsuka, N. Shimizu, Phys. Rev. Lett. 117, 172502 (2016)
P.-G. Reinhard, E.W. Otten, Nucl. Phys. A 420, 173–192 (1984)
G. Saxena, M. Kumawat, M. Kaushik, S.K. Jain, and Mamta Aggarwal, Phys. Lett. B 788, 1–6 (2019)
E. Khan, M. Grasso, J. Margueron, N. Van Giai, Nucl. Phys. A 800, 37 (2008)
J. Decharge, J.-F. Berger, M. Girod, K. Dietrich, Nucl. Phys. A 716, 55 (2003)
J.M. Yao, S. Baroni, M. Bender, P.-H. Heenen, Phys. Rev. C 86, 014310 (2012)
Acknowledgements
The authors would like to thank Himachal Pradesh University for providing computational facilities. One of the authors, Mr. Pankaj Kumar, also thank Council of Scientific and Industrial Research (CSIR), New Delhi for providing financial assistance Senior Research Fellowship vide reference no. 09/237(0165)/2018-EMR-I.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Michael Bender
Rights and permissions
About this article
Cite this article
Kumar, P., Thakur, V., Thakur, S. et al. Nuclear shape evolution and shape coexistence in Zr and Mo isotopes. Eur. Phys. J. A 57, 36 (2021). https://doi.org/10.1140/epja/s10050-021-00346-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/s10050-021-00346-6