Skip to main content
SpringerLink
Log in

Triaxial projected shell model study of \(\gamma \)-bands in atomic nuclei

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

A systematic study of \(\gamma \)-bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the \(\gamma \)-band for most of the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of \(\gamma \)-softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, \(^{76}\)Ge, \(^{112}\)Ru, \(^{170}\)Er and \(^{232}\)Th depict staggering phase with odd-I-below-even-I, which is regarded as an indication of the static \(\gamma \)-deformation in the collective model picture. The inclusion of the quasiparticle excitations in the framework of configuration mixing is shown to reverse the staggering phase from odd-I-down to the even-I-down for all the studied nuclei, except for the aforementioned four nuclei. Furthermore, by fitting a collective Bohr Hamiltonian to the TPSM energies, the differences between the two models are delineated through a comparison of the transition probabilities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: These are theoretical calculations and the whole data is given (plotted) in the manuscript.]

References

  1. S. Frauendorf, Rev. Mod. Phys. 73, 463 (2001)

    Article  ADS  Google Scholar 

  2. S.G. Nilsson, Dan. Mat. Fys. Medd. 29, 16 (1955)

    Google Scholar 

  3. A. Bohr, B.R. Mottelson, Nuclear Structure, vol. II (Benjamin Inc., New York, 1975)

    MATH  Google Scholar 

  4. N.V. Zamfir, R.F. Casten, Phys. Lett. B 3, 260 (1991)

    Google Scholar 

  5. A. S. Davydov, in: Proc. Intern. Conf. on Nuclear structure (Kingston, Canada), eds. D. A. Bromley and E. W. Vogt (University of Toronto Press, Toronto, 1960) p. 801

  6. K. Kumar, Phys. Rev. C 1, 369 (1970)

    Article  ADS  Google Scholar 

  7. C. Baktash, J.X. Saladin, J.J. ÓBrien, J.G. Alassi, Phys. Rev. C 18, 131 (1978)

    Article  ADS  Google Scholar 

  8. C. Baktash, J.X. Saladin, J.J. ÓBrien, J.G. Alassi, Phys. Rev. C 22, 2383 (1980)

    Article  ADS  Google Scholar 

  9. M. Caprio, Phys. Rev. C 83, 064309 (2011)

    Article  ADS  Google Scholar 

  10. A.S. Davydov, G.P. Filippov, Nucl. Phys. 8, 237 (1958)

    Article  Google Scholar 

  11. L. Wilets, M. Jean, Phys. Rev. 102, 788 (1956)

    Article  ADS  Google Scholar 

  12. S. Frauendorf, Int. J. Mod. Phys. E 38, 1541001 (2015)

    Article  Google Scholar 

  13. T. Niks̆ić, Z.P. Li, D. Vretenar, L. Próchniak, J. Meng, P. Ring, Phys. Rev. C 79, 034303 (2009)

    Article  ADS  Google Scholar 

  14. C.L. Zhang, G.H. Bhat, W. Nazarewicz, J.A. Sheikh, Y. Shi, Phys. Rev. C 92, 034307 (2015)

    Article  ADS  Google Scholar 

  15. X.Q. Yang, L.J. Wang, J. Xiang, X.Y. Wu, Z.P. Li, Phys. Rev. C 103, 054321 (2021)

    Article  ADS  Google Scholar 

  16. F.-Q. Chen, J.L. Egido, Phys. Rev. C 95, 024307 (2017)

    Article  ADS  Google Scholar 

  17. E.A. McCutchan, D. Bonatsos, N.V. Zamfir, R.F. Casten, Phys. Rev. C 76, 024306 (2007)

    Article  ADS  Google Scholar 

  18. I. Stefanescu, A. Gelberg, J. Jolie, P. Van Isacker, P. von Brentano, Y.X. Luod, S.J. Zhu, J.O. Rasmussen, J.H. Hamilton, A.V. Ramayya, X.L. Che, Nucl. Phys. A 789, 125 (2007)

    Article  ADS  Google Scholar 

  19. J.A. Sheikh, K. Hara, Phys. Rev. Lett. 82, 3968 (1999)

    Article  ADS  Google Scholar 

  20. G.H. Bhat, W.A. Dar, J.A. Sheikh, Y. Sun, Phys. Rev. C 89, 014328 (2014)

    Article  ADS  Google Scholar 

  21. C.L. Zhang, G.H. Bhat, W. Nazarewicz, J.A. Sheikh, Y. Shi, Phys. Rev. C 92, 034307 (2015)

    Article  ADS  Google Scholar 

  22. J.A. Sheikh, G.H. Bhat, Y. Sun, G.B. Vakil, R. Palit, Phys. Rev. C 77, 034313 (2008)

    Article  ADS  Google Scholar 

  23. P. Ring, P. Schuck, The Nuclear Many Body Problem (Springer-Verlag, New York, 1980)

    Book  Google Scholar 

  24. K. Hara, Y. Sun, Int. J. Mod. Phys. E 4, 637 (1995)

    Article  ADS  Google Scholar 

  25. Y. Sun, K. Hara, J.A. Sheikh, J.G. Hirsch, V. Velazquez, M. Guidry, Phys. Rev. C 61, 064323 (2000)

    Article  ADS  Google Scholar 

  26. S.G. Nilsson, C.F. Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, I. Lamm, P. Moller, B. Nilsson, Nucl. Phys. A 131, 1 (1969)

    Article  ADS  Google Scholar 

  27. Y. Sun, J.L. Egido, Nucl. Phys. A 580, 1 (1994)

    Article  ADS  Google Scholar 

  28. J.A. Sheikh, G.H. Bhat, Y.-X. Liu, F.-Q. Chen, Y. Sun, Phys. Rev. C 84, 054314 (2011)

    Article  ADS  Google Scholar 

  29. G.H. Bhat, J.A. Sheikh, Y. Sun, U. Garg, Phys. Rev. C 86, 047307 (2012)

    Article  ADS  Google Scholar 

  30. G.H. Bhat, J.A. Sheikh, R. Palit, Phys. Lett. B 707, 250 (2012)

    Article  ADS  Google Scholar 

  31. S. Jehangir, G.H. Bhat, J.A. Sheikh, S. Frauendorf, S.N.T. Majola, P.A. Ganai, J.F. Sharpey-Schafer, Phys. Rev. C 97, 014310 (2018)

    Article  ADS  Google Scholar 

  32. J.A. Sheikh, G.H. Bhat, W.A. Dar, S. Jehangir, P.A. Ganai, Phys. Scr. 91, 063015 (2016)

    Article  ADS  Google Scholar 

  33. S. Frauendorf, Y. Gu, J. Sun, Int. J. Mod. Phys. E 20, 465 (2011)

    Article  ADS  Google Scholar 

  34. Y. Toh, C.J. Chiara, E.A. McCutchan, W.B. Walters, R.V.F. Janssens, M.P. Carpenter, S. Zhu, R. Broda, B. Fornal, B.P. Kay, F.G. Kondev, W. Krölas, T. Lauritsen, C.J. Lister, T. Pawlat, D. Seweryniak, I. Stefanescu, N.J. Stone, J. Wrzesin̈ski, K. Higashiyama, N. Yoshinaga, Phys. Rev. C 87, 041304(R) (2013)

  35. A.D. Ayangeakaa, R.V.F. Janssens, S. Zhu, D. Little, J. Henderson, C.Y. Wu, D.J. Hartley, M. Albers, K. Auranen, B. Bucher, M.P. Carpenter, P. Chowdhury, D. Cline, H.L. Crawford, P. Fallon, A.M. Forney, A. Gade, A.B. Hayes, F.G. Kondev, Krishichayan, T. Lauritsen, J. Li, A.O. Macchiavelli, D. Rhodes, D. Seweryniak, S.M. Stolze, W.B. Walters, J. Wu, Phys. Rev. Lett. 123, 102501 (2019)

    Article  ADS  Google Scholar 

  36. J.A. Sheikh, G.H. Bhat, Y. Sun, R. Palit, Phys. Lett. B 688, 305 (2010)

    Article  ADS  Google Scholar 

  37. N. Sensharma, U. Garg, S. Zhu, A.D. Ayangeaka, S. Frauendorf, W. Li, G.H. Bhat, J.A. Sheikh, M.P. Carpenter, Q.B. Chen, J.L. Cozzi, S.S. Ghugre, Y.K. Gupta, D.J. Hartley, K.B. Howard, R.V.F. Janssens, F.G. Kondev, T.C. McMaken, R. Palit, J. Sethi, D. Seweryniak, R.P. Singh, Phys. Lett. B 792, 170 (2019)

    Article  ADS  Google Scholar 

  38. G. H. Bhat et al. (to be published)

  39. M.A. Caprio, D.J. Rowe, T.A. Welsh, Comput. Phys. Commun. 180, 1150 (2009)

    Article  ADS  Google Scholar 

  40. D.T. Dohertya, J.M. Allmond, R.V.F. Janssens, W. Korten, S. Zhu, M. Zielińska, D.C. Radford, A.D. Ayangeakaa, B. Bucherd, J.C. Batchelder, C.W. Beausang, C. Campbell, M.P. Carpenter, D. Cline, H.L. Crawford, H.M. David, J.P. Delaroche, C. Dickerson, P. Fallon, A. Galindo-Uribarri, F.G. Kondev, J.L. Harker, A.B. Hayes, M. Hendricks, P. Humby, M. Girod, C.J. Gross, M. Klintefjord, K. Kolos, G.J. Lane, T. Lauritsen, J. Libert, A.O. Macchiavelli, P.J. Napiorkowski, E. Padilla-Rodal, R.C. Pardo, W. Reviol, D.G. Sarantites, G. Savard, D. Seweryniak, J. Srebrny, R. Varner, R. Vondrasek, A. Wiens, E. Wilson, J.L. Wood, C.Y. Wu, Phys. Let. B 766, 334 (2017)

    Article  ADS  Google Scholar 

  41. M.A. Lee, Nucl. Data Sheets 31, 381 (1980)

    Article  ADS  Google Scholar 

  42. H. Emling, E. Grosse, D. Schwalm, R.S. Simon, H.J. Wollersheim, D. Husar, D. Pelte, Phys. Lett. B 98, 169 (1981)

    Article  ADS  Google Scholar 

  43. S. Raman, C.H. Malarkey, W.T. Milner, C.W. Nestor Jr., P.H. Stelson, Atom. Data Nucl. Data Tables 36, 1 (1987)

    Article  ADS  Google Scholar 

  44. C.Y. Wu, D. Cline, M.W. Simon, R. Teng, K. Vetter, M.P. Carpenter, R.V.F. Janssens, I. Wiedenhover, Phys. Rev. C 61, 021305 (2000)

    Article  ADS  Google Scholar 

  45. C. Fahlander, A. Axelsson, M. Heinebrodt, T. Härtlein, D. Schwalm, Phys. Lett. B 388, 475 (1996)

    Article  ADS  Google Scholar 

  46. S.N. Majola, D.J. Hartley, L.L. Riedinger, J.F. Sharpey-Schafer, J.M. Allmond, C. Beausang, M.P. Carpenter, C.J. Chiara, N. Cooper, D. Curien, B.J.P. Gall, P.E. Garrett, R.V.F. Janssens, F.G. Kondev, W.D. Kulp, T. Lauritsen, E.A. McCutchan, D. Miller, J. Piot, N. Redon, M.A. Riley, J. Simpson, I. Stefanescu, V. Werner, X. Wang, J.L. Wood, C.H. Yu, S. Zhu, Phys. Rev. C 91, 034330 (2015)

  47. J. Simpson, P.A. Butler, P.D. Forsyth, J.F. Sharpey-Schafer, J.D. Garrett, G.B. Hagemannl, B. Herskind, L.P. Ekstromg, J. Phys. G: Nucl. Phys. 10, 383 (1984)

    Article  ADS  Google Scholar 

  48. A. Jungclaus, B. Binder, A. Dietrich, T. Har̈tlein, H. Bauer, Ch. Gund, D. Pansegrau, D. Schwalmet, Phys. Rev. C 66, 014312 (2002)

    Article  ADS  Google Scholar 

  49. C.Y. Wu, D. Cline, M.W. Simon, G.A. Davis, R. Teng, A.O. Macchiavelli, K. Vetter, Phys. Rev. C 64, 064317 (2001)

    Article  ADS  Google Scholar 

  50. A. Aprahamian, X. Wu, S.R. Lesher, D.D. Warnerm, W. Gelletly, H.G. Börner, F. Hoyler, K. Schreckenbach, R.F. Castene, Z.R. Shi, D. Kusnezov, M. Ibrahim, A.O. Macchiavelli, M.A. Brinkman, J.A. Becker, Nucl. Phys. A 764, 42 (2006)

    Article  ADS  Google Scholar 

  51. National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY, USA. https://www.nndc.bnl.gov/

  52. T. Härtlein, M. Heinebrodt, D. Schwalm, C. Fahlander, Eur. Phys. J. A 2, 253 (1998)

    Article  ADS  Google Scholar 

  53. G.D. Dracoulis, G.J. Lane, F.G. Kondev, H. Watanabe, D. Seweryniak, S. Zhu, M.P. Carpenter, C.J. Chiara, R.V.F. Janssens, T. Lauritsen, C.J. Lister, E.A. McCutchan, I. Stefanescu, Phys. Rev. C 81, 054313 (2010)

    Article  ADS  Google Scholar 

  54. E. Ngijoi-Yogo, S.K. Tandel, G. Mukherjee, I. Shestakova, P. Chowdhury, C.Y. Wu, D. Cline, A.B. Hayes, R. Teng, R.M. Clark, P. Fallon, A.O. Macchiavelli, K. Vetter, F.G. Kondev, S. Langdown, P.M. Walker, C. Wheldon, D.M. Cullen, Phys. Rev. C 75, 034305 (2007)

    Article  ADS  Google Scholar 

  55. S.-C. Wu, H. Niu, Nucl. Data Sheets 100, 483 (2003)

    Article  ADS  Google Scholar 

  56. Nucl. Data Sheets, through Vol. 106 109–222, (2005)

  57. D. Ward, H.R. Andrews, G.C. Ball, A. Galindo-Uribarri, V.P. Janzen, T. Nakatsukasa, D.C. Radford, T.E. Drake, J. DeGraaf, S. Pilotte, Y.R. Shimizu, Nucl. Phys. A 600, 88 (1996)

    Article  ADS  Google Scholar 

  58. A. Guessous, N. Schulz, M. Bentale, E. Lubkiewicz, J.L. Durell, C.J. Pearson, W.R. Phillips, J.A. Shannon, W. Urban, B.J. Varley, I. Ahmad, C.J. Lister, L.R. Morss, K.L. Nash, C.W. Williams, S. Khazrouni, Phys. Rev. C 53, 1191 (1996)

    Article  ADS  Google Scholar 

  59. H. Hua, C.Y. Wu, D. Cline, A.B. Hayes, R. Teng, R.M. Clark, P. Fallon, A. Goergen, A.O. Macchiavelli, K. Vetter, Phys. Rev. C 69, 014317 (2004)

    Article  ADS  Google Scholar 

  60. L.M. Yang, S.-J. Zhu, K. Li, J.H. Hamilton, A.V. Ramayya, J.K. Hwang, X.Q. Zhang, L.Y. Zhu, C.-Y. Gan, M. Sakhaee, G.-L. Long, R.-Q. Xu, Z. Zhang, Z. Jiang, J. Myong-Gil, W.C. Ma, B.R.S. Babu, J. Komicki, E.F. Jones, J.D. Cole, R. Aryaeinejad, M.W. Drigert, I.Y. Lee, J.O. Rasmussen, M.A. Stoyer, G.M. Ter-Akopian, A.V. Daniel, Chin. Phys. Lett. 18, 24 (2001)

    Article  ADS  Google Scholar 

  61. X.L. Che, S.J. Zhu, J.H. Hamilton, A.V. Ramayya, J.K. Hwang, U. Yong-Nam, M.L. Li, R.C. Zheng, I.Y. Lee, J.O. Rasmussen, Y.X. Luo, W.C. Ma, Chin. Phys. Lett. 21, 1904 (2004)

    Article  ADS  Google Scholar 

  62. E.F. Jones, P.M. Gore, S.J. Zhu, J.H. Hamilton, A.V. Ramayya, J.K. Hwang, R.Q. Xu, L.M. Yang, K. Li, Z. Jiang, Z. Zhang, S.D. Xiao, X.Q. Zhang, W.C. Ma, J.D. Cole, M.W. Drigert, I.Y. Lee, J.O. Rasmussen, Y.X. Luo, M.A. Stoyer, Phys. Atomic Nuclei 69, 7 (2006)

    Article  Google Scholar 

  63. S. Rab, Nucl. Data Sheets 63, 1 (1991)

    Article  ADS  Google Scholar 

  64. A.R. Farhan, B. Singh, Nucl. Data Sheets 110, 1917 (2009)

    Article  ADS  Google Scholar 

  65. L.-J. Wang, F.-Q. Chen, Y. Sun, Phys. Lett. B 808, 135676 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank M. Caprio for illuminating discussions concerning the SO(5) selection rules. The work was partly supported by the US DoE grant DE-FG02-95-ER4093. The authors (JS, GHB, JAS and NR) acknowledge Science and Engineering Research Board (SERB), Department of Science and Technology, Govt. of India for providing financial support under Project no. CRG/2019/004960 to carry out a part of this research work.

Author information

Authors and Affiliations

  1. Department of Physics, Islamic University of Science and Technology, Awantipora, 192122, India

    S. Jehangir & N. Rather

  2. Department of Physics, SP College, Srinagar, Jammu and Kashmir, 190001, India

    G. H. Bhat

  3. Department of Physics, University of Kashmir, Srinagar, 190006, India

    G. H. Bhat & J. A. Sheikh

  4. Physics Department, University of Notre Dame, Notre Dame, Indiana, 46556, USA

    S. Frauendorf & W. Li

  5. Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai, 400005, India

    R. Palit

Authors
  1. S. Jehangir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. H. Bhat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. A. Sheikh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Frauendorf
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Palit
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. N. Rather
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Michael Bender.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jehangir, S., Bhat, G.H., Sheikh, J.A. et al. Triaxial projected shell model study of \(\gamma \)-bands in atomic nuclei. Eur. Phys. J. A 57, 308 (2021). https://doi.org/10.1140/epja/s10050-021-00620-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-021-00620-7

Search

Navigation