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Lie algebra symmetries and quantum phase transitions in nuclei

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In this paper, an overview of some aspects of quantum phase transitions (QPT) in nuclei is given and they are: (i) QPT in interacting boson model (sdIBM), (ii) QPT in two-level models, (iii) critical point E(5) and X(5) symmetries, (iv) QPT in a simple solvable model with three-body forces. In addition, some open problems are also given.

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References

  1. P Van Isacker, Rep. Prog. Phys. 62, 1661 (1999)

    Google Scholar 

  2. F Iachello and A Arima, The interacting boson model (Cambridge University Press, Cambridge, 1987)

  3. F Iachello and P Van Isacker, The interacting boson–fermion model (Cambridge University Press, Cambridge, 1991)

  4. D J Rowe and J L Wood, Fundamentals of nuclear models: Foundational models (World Scientific, Singapore, 2010)

  5. V K B Kota and Y D Devi, Nuclear shell model and the interacting boson model: Lecture notes for practitioners, published by IUC-DAEF, Calcutta Centre (Kolkata, India, 1996)

  6. V K B Kota and J A Castilho Alcarás, Nucl. Phys. A 764, 181 (2006)

  7. S Lerma H et al, Phys. Rev. Lett. 99, 032501 (2007) S Lerma H, Phys. Rev. C 82, 014302 (2010)

  8. Y D Devi and V K B Kota, Z. Phys. A 337, 15 (1990); in Symmetries in Science VII edited by B Gruber and T Otsuka (Plenum, New York, 1994), p. 307; Pramana – J. Phys. 39, 413 (1992) Y Liu et al, Phys. Rev. C 59, 2511 (1999)

  9. J Jolie, Scientific American 287, 54 (2002) A Frank, P Van Isacker and J Jolie, Symmetries in atomic nuclei: from isospin to supersymmetry (Springer, Heidelberg, 2010) G Levai, J Cseh and P Van Isacker, J. Phys. G 34, 1729 (2007)

  10. Y Alhassid and A Leviatan, J. Phys. A 25, L1265 (1992) A Leviatan, Phys. Rev. Lett. 77, 818 (1996) J Escher and A Leviatan, Phys. Rev. Lett. 84, 1866 (2000) A Leviatan and P Van Isacker, Phys. Rev. Lett. 89, 222501 (2002) A Leviatan, Phys. Rev. Lett. 98, 242502 (2007) A Shirokov, N A Smirnova and P Van Isacker, Phys. Lett. B 434, 237 (1998) D Kusnezov, Phys. Rev. Lett. 79, 537 (1997)

  11. V K B Kota, Pramana – J. Phys. 48, 1035 (1997)

  12. V K B Kota, in Focus on boson research edited by A V Ling (Nova Science Publishers Inc., New York, 2006) p. 57

  13. P Cejnar, J Jolie and R F Casten, Rev. Mod. Phys. 82, 2155 (2010)

    Google Scholar 

  14. F Iachello and N V Zamfir, Phys. Rev. Lett. 92, 212501 (2004)

    Google Scholar 

  15. F Iachello, N V Zamfir and R F Casten, Phys. Rev. Lett. 81, 1191 (1998) P Cejnar and J Jolie, Phys. Rev. E 61, 6237 (2000) J Jolie, R F Casten, P von Brentano and V Werner, Phys. Rev. Lett. 87, 62501 (2001) J Jolie, P Cejnar, R F Casten, S Heinze, A Linnemann and V Werner, Phys. Rev. Lett. 89, 182502 (2002)

    Google Scholar 

  16. J M Arias, J Dukelsky and J E García-Ramos, Phys. Rev. Lett. 91, 162502 (2003)

    Google Scholar 

  17. P Cejnar, P Stransky and M Macek, Nucl. Phys. News 21(4), 22 (2011)

  18. P Cejnar and F Iachello, J. Math. Phys. 40, 581 (2007) M A Caprio, J H Skrabacz and F Iachello, J. Phys. A: Mat. Theor. 44, 075303 (2011)

  19. V K B Kota, AIP Conf. Proc. 1524, 52 (2013)

  20. V K B Kota, J. Math. Phys. 38, 6639 (1997)

  21. F Iachello, Phys. Rev. Lett. 85, 3580 (2000)

    Google Scholar 

  22. A G Ushveridze, Quasi-exactly solvable models in quantum mechanics (Institute of Physics, Bristol, 1994)

  23. F Iachello, Phys. Rev. Lett. 87, 052502 (2001)

    Google Scholar 

  24. P Van Isacker, Phys. Rev. Lett. 83, 4269 (1999) Y F Smirnov, N A Smirnova and P Van Isacker, Phys. Rev. C 61, 041302(R) (2000) J E. Garcia-Ramos, A Leviatan and P Van Isacker, Phys. Rev. Lett. 102, 112502 (2009)

  25. Yu Zhang, Feng Pan, Yu-Xin Liu, Yan-An Luo and J P Draayer, Phys. Rev. C 85, 064312 (2012)

    Google Scholar 

  26. P Van Isacker, A Bouldjedri and S Zerguine, Nucl. Phys. A 836, 225 (2010)

    Google Scholar 

  27. M A Caprio and F Iachello, Phys. Rev. Lett. 93, 242502 (2004); Ann. Phys. (N.Y.) 318, 454 (2005) J M Arias, J E Garcia-Ramos and J Dukelsky, Phys. Rev. Lett. 93, 212501 (2004) A Giannatiempo, L Fortunato and A Vitturi, Phys. Rev. C 86, 034311 (2012)

    Google Scholar 

  28. V K B Kota, Pramana – J. Phys. 60, 59 (2003)

  29. R Bijker and V K B Kota, Ann. Phys. (N.Y.) 187, 148 (1988)

    Google Scholar 

  30. V K B Kota and U Datta Pramanik, Euro. Phys. J. A 3, 243 (1998)

  31. V K B Kota, Ann. Phys. (N.Y.) 280, 1 (2000)

  32. V K B Kota and R Sahu, in: Proceedings of the Workshop on Frontiers in Gamma Ray Spectroscopy (FIG09) edited by R Palit and R Pillay, (TIFR, Mumbai, India, 2011), p. 83

  33. P Cejnar, M Macek, S Heinze, J Jolie and J Dobes, J. Phys. A. Math. Gen. 39, L515 (2006)

    Google Scholar 

  34. M A Caprio, P Cejnar and F Iachello, Ann. Phys. (N.Y.) 323, 1106 (2008)

    Google Scholar 

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Acknowledgements

Thanks are due to F Iachello, R Sahu and R Palit for many useful discussions.

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KOTA, V.K.B. Lie algebra symmetries and quantum phase transitions in nuclei. Pramana - J Phys 82, 743–755 (2014). https://doi.org/10.1007/s12043-014-0725-6

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