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Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands

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Abstract

A critical point symmetry (CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that the model Hamiltonian can be approximately solved with the solutions being expressed in terms of the Bessel functions of irrational orders. In particular, the CPS predicts that collective multiple chiral doublets may exist in transitional odd-odd systems.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. M. A. Caprio, Phys. Rev. C 65, 031304(R) (2002).

    Article  ADS  Google Scholar 

  4. M. A. Caprio, and F. Iachello, Nucl. Phys. A 781, 26 (2007), arXiv: nucl-th/0610026.

    Article  ADS  Google Scholar 

  5. M. A. Caprio, Phys. Rev. C 72, 054323 (2005), arXiv: nucl-th/0510059.

    Article  ADS  Google Scholar 

  6. F. Iachello, Phys. Rev. Lett. 91, 132502 (2003).

    Article  ADS  Google Scholar 

  7. D. Bonatsos, D. Lenis, D. Petrellis, and P. A. Terziev, Phys. Lett. B 588, 172 (2004), arXiv: nucl-th/0402087.

    Article  ADS  Google Scholar 

  8. N. Pietralla, and O. M. Gorbachenko, Phys. Rev. C 70, 011304(R) (2004).

    Article  ADS  Google Scholar 

  9. L. Fortunato, Phys. Rev. C 70, 011302(R) (2004), arXiv: nucl-th/0406043.

    Article  ADS  Google Scholar 

  10. L. Fortunato, S. D. Baerdemacker, and K. Heyde, Phys. Rev. C 74, 014310 (2006), arXiv: nucl-th/0607052.

    Article  ADS  Google Scholar 

  11. D. Bonatsos, D. Lenis, D. Petrellis, P. A. Terziev, and I. Yigitoglu, Phys. Lett. B 621, 102 (2005), arXiv: nucl-th/0507023.

    Article  ADS  Google Scholar 

  12. D. Bonatsos, D. Lenis, D. Petrellis, P. A. Terziev, and I. Yigitoglu, Phys. Lett. B 632, 238 (2006), arXiv: nucl-th/0510093.

    Article  ADS  Google Scholar 

  13. D. Bonatsos, D. Lenis, E. A. McCutchan, D. Petrellis, and I. Yigitoglu, Phys. Lett. B 649, 394 (2007), arXiv: nucl-th/0612101.

    Article  ADS  Google Scholar 

  14. D. Bonatsos, E. A. McCutchan, N. Minkov, R. F. Casten, P. Yotov, D. Lenis, D. Petrellis, and I. Yigitoglu, Phys. Rev. C 76, 064312 (2007), arXiv: 0807.4447.

    Article  ADS  Google Scholar 

  15. R. M. Clark, A. O. Macchiavelli, L. Fortunato, and R. Krücken, Phys. Rev. Lett. 96, 032501 (2006).

    Article  ADS  Google Scholar 

  16. Y. Zhang, Z. Hou, H. Chen, H. Wei, and Y. Liu, Phys. Rev. C 78, 024314 (2008).

    Article  ADS  Google Scholar 

  17. Y. Zhang, F. Pan, Y. A. Luo, and J. P. Draayer, Phys. Lett. B 751, 423 (2015).

    Article  ADS  Google Scholar 

  18. R. Budaca, and A. I. Budaca, Phys. Lett. B 759, 349 (2016).

    Article  ADS  Google Scholar 

  19. R. Budaca, and A. I. Budaca, Phys. Rev. C 94, 054306 (2016), arXiv: 1610.09707.

    Article  ADS  Google Scholar 

  20. Y. Zhang, F. Pan, Y. X. Liu, Y. A. Luo, and J. P. Draayer, Phys. Rev. C 96, 034323 (2017).

    Article  ADS  Google Scholar 

  21. R. F. Casten, and E. A. McCutchan, J. Phys. G-Nucl. Part. Phys. 34, R285 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. A. Bohr, Mat.-Fys. Medd. Danske Vid. Selsk. 26, 14 (1952).

    Google Scholar 

  24. L. Fortunato, Eur. Phys. J. A 26, 1 (2005), arXiv: nucl-th/0411087.

    Article  ADS  Google Scholar 

  25. D. Bonatsos, E. A. McCutchan, R. F. Casten, R. J. Casperson, V. Werner, and E. Williams, Phys. Rev. C 80, 034311 (2009), arXiv: 0909.0997.

    Article  ADS  Google Scholar 

  26. Y. Zhang, Y. X. Liu, F. Pan, Y. Sun, and J. P. Draayer, Phys. Lett. B 732, 55 (2014), arXiv: 1411.7122.

    Article  ADS  Google Scholar 

  27. Y. Zhang, F. Pan, Y. X. Liu, Y. A. Luo, and J. P. Draayer, Phys. Rev. C 90, 064318 (2014), arXiv: 1412.8557.

    Article  ADS  Google Scholar 

  28. F. Iachello, Phys. Rev. Lett. 95, 052503 (2005).

    Article  ADS  Google Scholar 

  29. F. Iachello, and P. Van Isacker, The Interacting Boson-Fermion Model (Cambridge University, Cambridge, England, 1991).

    Book  MATH  Google Scholar 

  30. C. E. Alonso, J. M. Arias, and A. Vitturi, Phys. Rev. Lett. 98, 052501 (2007), arXiv: nucl-th/0701016.

    Article  ADS  Google Scholar 

  31. C. E. Alonso, J. M. Arias, and A. Vitturi, Phys. Rev. C 75, 064316 (2007).

    Article  ADS  Google Scholar 

  32. Y. Zhang, F. Pan, Y. X. Liu, Z. F. Hou, and J. P. Draayer, Phys. Rev. C 82, 034327 (2010).

    Article  ADS  Google Scholar 

  33. Y. Zhang, F. Pan, Y. X. Liu, Y. A. Luo, and J. P. Draayer, Phys. Rev. C 84, 034306 (2011).

    Article  ADS  Google Scholar 

  34. Y. Zhang, F. Pan, Y. X. Liu, and J. P. Draayer, Phys. Rev. C 84, 054319 (2011).

    Article  ADS  Google Scholar 

  35. Y. Zhang, F. Pan, Y. A. Luo, Y. X. Liu, and J. P. Draayer, Phys. Rev. C 86, 044312 (2012).

    Article  ADS  Google Scholar 

  36. F. Iachello, A. Leviatan, and D. Petrellis, Phys. Lett. B 705, 379 (2011), arXiv: 1111.0781.

    Article  ADS  Google Scholar 

  37. Y. Zhang, L. Bao, X. Guan, F. Pan, and J. P. Draayer, Phys. Rev. C 88, 064305 (2013).

    Article  ADS  Google Scholar 

  38. S. Quan, Z. P. Li, D. Vretenar, and J. Meng, Phys. Rev. C 97, 031301(R) (2018), arXiv: 1803.02142.

    Article  ADS  Google Scholar 

  39. D. Bucurescu, and N. V. Zamfir, Phys. Rev. C 95, 014329 (2017).

    Article  ADS  Google Scholar 

  40. D. Bucurescu, and N. V. Zamfir, Phys. Rev. C 98, 024301 (2018), arXiv: 1808.00526.

    Article  ADS  Google Scholar 

  41. K. Nomura, R. Rodríguez-Guzmán, and L. M. Robledo, Phys. Rev. C 97, 064314 (2018), arXiv: 1803.07802.

    Article  ADS  Google Scholar 

  42. K. Nomura, T. Nikšić, and D. Vretenar, Phys. Rev. C 96, 014304 (2017), arXiv: 1704.07101.

    Article  ADS  Google Scholar 

  43. K. Nomura, T. Nikšić, and D. Vretenar, Phys. Rev. C 94, 064310 (2016), arXiv: 1610.00469.

    Article  ADS  Google Scholar 

  44. S. Frauendorf, and S. J. Meng, Nucl. Phys. A 617, 131 (1997).

    Article  ADS  Google Scholar 

  45. J. Meng, and S. Q. Zhang, J. Phys. G-Nucl. Part. Phys. 37, 064025 (2010), arXiv: 1002.0907.

    Article  ADS  Google Scholar 

  46. K. Starosta, T. Koike, C. J. Chiara, D. B. Fossan, D. R. LaFosse, A. A. Hecht, C. W. Beausang, M. A. Caprio, J. R. Cooper, R. Krücken, J. R. Novak, N. V. Zamfir, K. E. Zyromski, D. J. Hartley, D. L. Balabanski, J. Zhang, S. Frauendorf, and V. I. Dimitrov, Phys. Rev. Lett. 86, 971 (2001).

    Article  ADS  Google Scholar 

  47. Z. P. Li, T. Nikšić, D. Vretenar, and J. Meng, Phys. Rev. C 81, 034316 (2010), arXiv: 1003.4109.

    Article  ADS  Google Scholar 

  48. B. W. Xiong, and Y. Y. Wang, Atomic Data Nuc. Data Tables 125, 193 (2019).

    Article  ADS  Google Scholar 

  49. A. D. Ayangeakaa, U. Garg, M. D. Anthony, S. Frauendorf, J. T. Matta, B. K. Nayak, D. Patel, Q. B. Chen, S. Q. Zhang, P. W. Zhao, B. Qi, J. Meng, R. V. F. Janssens, M. P. Carpenter, C. J. Chiara, F. G. Kondev, T. Lauritsen, D. Seweryniak, S. Zhu, S. S. Ghugre, and R. Palit, Phys. Rev. Lett. 110, 172504 (2013), arXiv: 1302.0401.

    Article  ADS  Google Scholar 

  50. I. Kuti, Q. B. Chen, J. Timár, D. Sohler, S. Q. Zhang, Z. H. Zhang, P. W. Zhao, J. Meng, K. Starosta, T. Koike, E. S. Paul, D. B. Fossan, and C. Vaman, Phys. Rev. Lett. 113, 032501 (2014), arXiv: 1407.2769.

    Article  ADS  Google Scholar 

  51. 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).

    Article  ADS  Google Scholar 

  52. D. Tonev, M. S. Yavahchova, N. Goutev, G. de Angelis, P. Petkov, R. K. Bhowmik, R. P. Singh, S. Muralithar, N. Madhavan, R. Kumar, M. Kumar Raju, J. Kaur, G. Mohanto, A. Singh, N. Kaur, R. Garg, A. Shukla, T. K. Marinov, and S. Brant, Phys. Rev. Lett. 112, 052501 (2014).

    Article  ADS  Google Scholar 

  53. E. O. Lieder, R. M. Lieder, R. A. Bark, Q. B. Chen, S. Q. Zhang, J. Meng, E. A. Lawrie, J. J. Lawrie, S. P. Bvumbi, N. Y. Kheswa, S. S. Ntshangase, T. E. Madiba, P. L. Masiteng, S. M. Mullins, S. Murray, P. Papka, D. G. Roux, O. Shirinda, Z. H. Zhang, P. W. Zhao, Z. P. Li, J. Peng, B. Qi, S. Y. Wang, Z. G. Xiao, and C. Xu, Phys. Rev. Lett. 112, 202502 (2014).

    Article  ADS  Google Scholar 

  54. N. Rather, P. Datta, S. Chattopadhyay, S. Rajbanshi, A. Goswami, G. H. Bhat, J. A. Sheikh, S. Roy, R. Palit, S. Pal, S. Saha, J. Sethi, S. Biswas, P. Singh, and H. C. Jain, Phys. Rev. Lett. 112, 202503 (2014), arXiv: 1310.7731.

    Article  ADS  Google Scholar 

  55. C. M. Petrache, B. F. Lv, A. Astier, E. Dupont, Y. K. Wang, S. Q. Zhang, P. W. Zhao, Z. X. Ren, J. Meng, P. T. Greenlees, H. Badran, D. M. Cox, T. Grahn, R. Julin, S. Juutinen, J. Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, # Aktas, A. Ertoprak, H. Liu, S. Matta, P. Subramaniam, S. Guo, M. L. Liu, X. H. Zhou, K. L. Wang, I. Kuti, J. Timár, A. Tucholski, J. Srebrny, and C. Andreoiu, Phys. Rev. C 97, 041304 (2018).

    Article  ADS  Google Scholar 

  56. T. Roy, G. Mukherjee, M. A. Asgar, S. Bhattacharyya, S. Bhattacharya, C. Bhattacharya, S. Bhattacharya, T. K. Ghosh, K. Banerjee, S. Kundu, T. K. Rana, P. Roy, R. Pandey, J. Meena, A. Dhal, R. Palit, S. Saha, J. Sethi, S. Thakur, B. S. Naidu, S. V. Jadav, R. Dhonti, H. Pai, and A. Goswami, Phys. Lett. B 782, 768 (2018).

    Article  ADS  Google Scholar 

  57. B. Qi, H. Jia, C. Liu, and S. Y. Wang, Sci. China-Phys. Mech. Astron. 62, 012012 (2019).

    Article  Google Scholar 

  58. S. Guo, C. M. Petrache, D. Mengoni, Y. H. Qiang, Y. P. Wang, Y. Y. Wang, J. Meng, Y. K. Wang, S. Q. Zhang, P. W. Zhao, A. Astier, J. G. Wang, H. L. Fan, E. Dupont, B. F. Lv, D. Bazzacco, A. Boso, A. Goasduff, F. Recchia, D. Testov, F. Galtarossa, G. Jaworski, D. R. Napoli, S. Riccetto, M. Siciliano, J. J. Valiente-Dobon, M. L. Liu, G. S. Li, X. H. Zhou, Y. H. Zhang, C. Andreoiu, F. H. Garcia, K. Ortner, K. Whitmore, A. Ataç-Nyberg, T. Bäck, B. Cederwall, E. A. Lawrie, I. Kuti, D. Sohler, T. Marchlewski, J. Srebrny, and A. Tucholski, Phys. Lett. B 807, 135572 (2020).

    Article  Google Scholar 

  59. B. F. Lv, C. M. Petrache, Q. B. Chen, J. Meng, A. Astier, E. Dupont, P. Greenlees, H. Badran, T. Calverley, D. M. Cox, T. Grahn, J. Hilton, R. Julin, S. Juutinen, J. Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, P. Ruotsalainen, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, A. Ertoprak, H. Liu, S. Guo, M. L. Liu, J. G. Wang, X. H. Zhou, I. Kuti, J. Timár, A. Tucholski, J. Srebrny, and C. Andreoiu, Phys. Rev. C 100, 024314 (2019), arXiv: 1907.12809.

    Article  ADS  Google Scholar 

  60. P. Ring, and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980).

    Book  Google Scholar 

  61. J. Peng, J. Meng, and S. Q. Zhang, Phys. Rev. C 68, 044324 (2003), arXiv: nucl-th/0308080.

    Article  ADS  Google Scholar 

  62. A. A. Raduta, A. C. Gheorghe, P. Buganu, and A. Faessler, Nucl. Phys. A 819, 46 (2009), arXiv: 0811.3511.

    Article  ADS  Google Scholar 

  63. J. H. Lee, J. Korean Phys. Soc. 63, 1907 (2013).

    Article  ADS  Google Scholar 

  64. Y. X. Chen, H. Jiang, W. T. Dong, Y. Zhang, F. Pan, and Y. A. Luo, Nucl. Phys. A 987, 90 (2019).

    Article  ADS  Google Scholar 

  65. S. Q. Zhang, B. Qi, S. Y. Wang, and J. Meng, Phys. Rev. C 75, 044307 (2007), arXiv: nucl-th/0703047.

    Article  ADS  Google Scholar 

  66. J. M. Vehn, F. S. Stephens, and R. M. Diamond, Phys. Rev. Lett. 32, 1383 (1974).

    Article  ADS  Google Scholar 

  67. B. Qi, S. Q. Zhang, S. Y. Wang, J. M. Yao, and J. Meng, Phys. Rev. C 79, 041302 (2009).

    Article  ADS  Google Scholar 

  68. S. Pascu, G. Căta-Danil, D. Bucurescu, N. Mărginean, C. Müller, N. V. Zamfir, G. Graw, A. Gollwitzer, D. Hofer, and B. D. Valnion, Phys. Rev. C 81, 014304 (2010).

    Article  ADS  Google Scholar 

  69. S. Pascu, N. V. Zamfir, G. Căta-Danil, and N. Mărginean, Phys. Rev. C 81, 054321 (2010).

    Article  ADS  Google Scholar 

  70. F. Iachello, and A. Arima, The Interacting Boson Model (Cambridge University, Cambridge, 1987).

    Book  Google Scholar 

  71. K. Starosta, C. J. Chiara, D. B. Fossan, T. Koike, T. T. S. Kuo, D. R. LaFosse, S. G. Rohoziński, C. Droste, T. Morek, and J. Srebrny, Phys. Rev. C 65, 044328 (2002).

    Article  ADS  Google Scholar 

  72. Y. Khazov, A. A. Rodionov, S. Sakharov, and B. Singh, Nucl. Data Sheets 104, 497 (2005).

    Article  ADS  Google Scholar 

  73. R. F. Casten, and N. V. Zamfir, Phys. Rev. Lett. 85, 3584 (2000).

    Article  ADS  Google Scholar 

  74. M. S. Fetea, R. B. Cakirli, R. F. Casten, D. D. Warner, E. A. McCutchan, D. A. Meyer, A. Heinz, H. Ai, G. Gürdal, J. Qian, and R. Winkler, Phys. Rev. C 73, 051301(R)} (2006).

    Article  ADS  Google Scholar 

  75. R. A. Bark, A. M. Baxter, A. P. Byrne, G. D. Dracoulis, T. Kibédi, T. R. McGoram, and S. M. Mullins, Nucl. Phys. A 691, 577 (2001).

    Article  ADS  Google Scholar 

  76. E. Grodner, J. Phys.-Conf. Ser. 366, 012022 (2012).

    Article  Google Scholar 

  77. C. Droste, S. G. Rohoziński, K. Starosta, L. Próchniak, and E. Grodner, Eur. Phys. J. A 42, 79 (2009).

    Article  ADS  Google Scholar 

  78. B. Qi, S. Q. Zhang, J. Meng, S. Y. Wang, and S. Frauendorf, Phys. Lett. B 675, 175 (2009), arXiv: 0812.4597.

    Article  ADS  Google Scholar 

  79. Q. B. Chen, J. M. Yao, S. Q. Zhang, and B. Qi, Phys. Rev. C 82, 067302 (2010), arXiv: 1008.4865.

    Article  ADS  Google Scholar 

  80. J. Meng, J. Peng, S. Q. Zhang, and S. G. Zhou, Phys. Rev. C 73, 037303 (2006), arXiv: nucl-th/0510071.

    Article  ADS  Google Scholar 

  81. S. Y. Wang, Chin. Phys. C 44, 112001 (2020), arXiv: 2009.02864.

    Article  ADS  Google Scholar 

  82. I. Hamamoto, Phys. Rev. C 88, 024327 (2013), arXiv: 1307.2970.

    Article  ADS  Google Scholar 

  83. K. Nomura, R. Rodríguez-Guzmán, and L. M. Robledo, Phys. Rev. C 101, 014306 (2020), arXiv: 1908.03322.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Liaoning Normal University, Dalian, 116029, China

    Yu Zhang

  2. Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Institute of Space Sciences, Shandong University, Weihai, 264209, China

    Bin Qi

  3. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing, 110871, China

    Shuang-Quan Zhang

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Correspondence to Yu Zhang, Bin Qi or Shuang-Quan Zhang.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11875158, 11675094, and 11875075). Fruitful discussions with Qi-Bo Chen, Jie Meng, Feng Pan, Yuan-Yuan Wang and Peng-Wei Zhao are acknowledged.

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Zhang, Y., Qi, B. & Zhang, SQ. Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands. Sci. China Phys. Mech. Astron. 64, 122011 (2021). https://doi.org/10.1007/s11433-021-1766-4

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