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Properties of \(^{8-11}\)Be isotopes with isospin-dependent spin–orbit potential in a cluster approach

  • Regular Article – Theoretical Physics
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Abstract

The nonlocalized clustering approach is generalized to \(^{8-11}\)Be isotopes with isospin dependent spin–orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function is introduced to provide a correct description for the \(\sigma \)-binding neutron in \(^{11}\)Be. Systematic calculations for \(^{8-11}\)Be isotopes are performed and results fit well with experimental values. The low energy spectrum of \(^{11}\)Be is also obtained, especially the correct spin-parity \(1/2^{+}\) is reproduced for the intruder ground state. The exotic neutron halo structure of \(^{11}\)Be is studied by calculations of root-mean-square radii and density distribution. The spectroscopic factor is also calculated and discussed for the \(1/2^+\) ground state of \({}^{11}\)Be.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data for ground state energies of \(^{8-11}\)Be isotopes are listed in Table 1 and shown in Fig. 2. The data for the low energy spectrum of \(^{11}\)Be are shown in Fig. 4.]

References

  1. M.G. Mayer, Phys. Rev. 78, 16 (1950)

    ADS  Google Scholar 

  2. S.S.-L. Zhang, G. Vignale, Phys. Rev. Lett. 116, 136601 (2016)

    ADS  Google Scholar 

  3. A. Matos-Abiague, J. Fabian, Phys. Rev. Lett. 115, 56602 (2015)

    ADS  MathSciNet  Google Scholar 

  4. C.W. Groth, M. Wimmer, A.R. Akhmerov et al., Phys. Rev. Lett. 103, 196805 (2009)

    ADS  Google Scholar 

  5. Z. Wang, X.-L. Qi, S.-C. Zhang, Phys. Rev. Lett. 105, 256803 (2010)

    ADS  Google Scholar 

  6. B.D. Cullity, C.D. Graham, Introduction to Magnetic Materials (Wiley, Hoboken, 2011)

    Google Scholar 

  7. D.J. Griffiths, Introduction to Quantum Mechanics (Pearson Education India, New Delhi, 2005)

    Google Scholar 

  8. N. Itagaki, S. Okabe, K. Ikeda, Phys. Rev. C 62, 34301 (2000)

    ADS  Google Scholar 

  9. J. Chen, J.L. Lou, Y.L. Ye et al., Phys. Rev. C 93, 34623 (2016)

    ADS  Google Scholar 

  10. T. Aumann, A. Navin, D.P. Balamuth et al., Phys. Rev. Lett. 84, 35 (2000)

    ADS  Google Scholar 

  11. J. Winfield, S. Fortier, W. Catford et al., Nucl. Phys. A 683, 48 (2001)

    ADS  Google Scholar 

  12. N. Fukuda, T. Nakamura, N. Aoi et al., Phys. Rev. C 70, 054606 (2004)

    ADS  Google Scholar 

  13. W.Y. So, K.S. Choi, M.-K. Cheoun, K.S. Kim, Phys. Rev. C 93, 54624 (2016)

    ADS  Google Scholar 

  14. T. Otsuka, N. Fukunishi, H. Sagawa, Phys. Rev. Lett. 70, 1385 (1993)

    ADS  Google Scholar 

  15. B.A. Brown, Prog. Part. Nucl. Phys. 47, 517 (2001)

    ADS  Google Scholar 

  16. Y. Kanada-En’yo, H. Horiuchi, Phys. Rev. C 66, 024305 (2002)

    ADS  Google Scholar 

  17. H. Li, Z. Ren, Sci. China Phys. Mech. Astron. 57, 1005 (2014)

    ADS  Google Scholar 

  18. Y. Hirayama, T. Shimoda, H. Izumi et al., Nucl. Phys. A 746, 71c (2004). https://doi.org/10.1016/j.nuclphysa.2004.09.018

    Article  ADS  Google Scholar 

  19. B. Zhou, Y. Funaki, H. Horiuchi, A. Tohsaki, Front. Phys. 15, 14401 (2019)

    ADS  Google Scholar 

  20. M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, U.-G. Meißner, Rev. Mod. Phys. 90, 035004 (2018)

    ADS  Google Scholar 

  21. Z. Ren, B. Zhou, Front. Phys. 13, 132110 (2018)

    ADS  Google Scholar 

  22. A. Tohsaki, H. Horiuchi, P. Schuck, G. Röpke, Rev. Mod. Phys. 89, 011002 (2017)

    ADS  Google Scholar 

  23. P. Schuck, Y. Funaki, H. Horiuchi, G. Röpke, A. Tohsaki, T. Yamada, Phys. Scr. 91, 123001 (2016)

    ADS  Google Scholar 

  24. M. Kimura, T. Suhara, Y. Kanada-En’yo, Eur. Phys. J. A 52, 373 (2016)

    ADS  Google Scholar 

  25. Y. Funaki, H. Horiuchi, A. Tohsaki, Prog. Part. Nucl. Phys. 82, 78 (2015)

    ADS  Google Scholar 

  26. M. Ito, K. Ikeda, Rep. Prog. Phys. 77, 096301 (2014)

    ADS  Google Scholar 

  27. Y. Kanada-En’yo, M. Kimura, A. Ono, Prog. Theor. Exp. Phys. 2012, 01A202 (2012). https://doi.org/10.1093/ptep/pts001

    Article  Google Scholar 

  28. H. Horiuchi, K. Ikeda, K. Kato, Prog. Theor. Phys. Suppl. 192, 1 (2012)

    ADS  Google Scholar 

  29. M. Spieker, S. Pascu, A. Zilges, F. Iachello, Phys. Rev. Lett. 114, 192504 (2015)

    ADS  Google Scholar 

  30. V.Yu. Denisov, O.I. Davidovskaya, I.Yu. Sedykh, Phys. Rev. C 92, 014602 (2015)

  31. W. He, Y. Ma et al., Phys. Rev. Lett. 113, 032506 (2014)

    ADS  Google Scholar 

  32. Z. Yang, Y. Ye et al., Phys. Rev. Lett. 112, 162501 (2014)

    ADS  Google Scholar 

  33. Y. Ren, Z. Ren, Phys. Rev. C 85, 044608 (2012)

    ADS  Google Scholar 

  34. R. Álvarez-Rodríguez, A.S. Jensen, E. Garrido, D.V. Fedorov, Phys. Rev. C 82, 34001 (2010)

    ADS  Google Scholar 

  35. C. Xu, Z. Ren, Phys. Rev. C 73, 041301 (2006)

    ADS  Google Scholar 

  36. R.G. Lovas, R.J. Liotta, A. Insolia, K. Varga, D.S. Delion, Phys. Rep. 294, 265 (1998)

    ADS  Google Scholar 

  37. I.J. Thompson, M.V. Zhukov, Phys. Rev. C 53, 708 (1996)

    ADS  Google Scholar 

  38. A. Tohsaki, H. Horiuchi, P. Schuck, G. Röpke, Phys. Rev. Lett. 87, 192501 (2001)

    ADS  Google Scholar 

  39. T. Yamada, P. Schuck, Eur. Phys. J. A 26, 185 (2005)

    ADS  Google Scholar 

  40. B. Zhou, Y. Funaki, H. Horiuchi, Z. Ren, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, Phys. Rev. Lett. 110, 262501 (2013)

    ADS  Google Scholar 

  41. B. Zhou, Y. Funaki, H. Horiuchi, Z. Ren, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, Phys. Rev. C 89, 034319 (2014)

    ADS  Google Scholar 

  42. T. Suhara, Y. Funaki, B. Zhou, H. Horiuchi, A. Tohsaki, Phys. Rev. Lett. 112, 062501 (2014)

    ADS  Google Scholar 

  43. Y. Funaki, Phys. Rev. C 97, 021304 (2018)

    ADS  Google Scholar 

  44. M. Lyu, Z. Ren, B. Zhou, Y. Funaki, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, Phys. Rev. C 91, 014313 (2015)

    ADS  Google Scholar 

  45. M. Lyu, Z. Ren, B. Zhou, Y. Funaki, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, Phys. Rev. C 93, 054308 (2016)

    ADS  Google Scholar 

  46. Q. Zhao, Z. Ren, M. Lyu, H. Horiuchi, Y. Funaki, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, B. Zhou, Phys. Rev. C 97, 054323 (2018)

    ADS  Google Scholar 

  47. M. Lyu, K. Yoshida, Y. Kanada-En’yo, K. Ogata, Phys. Rev. C 97, 044612 (2018)

    ADS  Google Scholar 

  48. Q. Zhao, Z. Ren, M. Lyu, H. Horiuchi, Y. Kanada-En’yo, Y. Funaki, G. Röpke, P. Schuck, A. Tohsaki, C. Xu, T. Yamada, B. Zhou, Phys. Rev. C 100, 014306 (2019)

    ADS  Google Scholar 

  49. M. Lyu, K. Yoshida, Y. Kanada-En’yo, K. Ogata, Phys. Rev. C 99, 064610 (2019)

    ADS  Google Scholar 

  50. M. Lyu, T. Myo, H. Toki, H. Horiuchi, C. Xu, N. Wan, Phys. Lett. B 805, 135421 (2020)

    Google Scholar 

  51. S. Li, T. Myo, Q. Zhao, H. Toki, H. Horiuchi, C. Xu, J. Liu, M. Lyu, Z. Ren, Phys. Rev. C 101, 064307 (2020)

    ADS  Google Scholar 

  52. M. Wang, G. Audi, A.H. Wapstra et al., Chin. Phys. C 36, 1603 (2012)

    Google Scholar 

  53. J.H. Kelley, E. Kwan, J.E. Purcell et al., Nucl. Phys. A 880, 88 (2012)

    ADS  Google Scholar 

  54. I. Tanihata, H. Savajols, R. Kanungo, Prog. Part. Nucl. Phys. 68, 215 (2013)

    ADS  Google Scholar 

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

    Google Scholar 

  56. N.V. Mau, Nucl. Phys. A 592, 33 (1995)

    ADS  Google Scholar 

  57. V. Lima, J.A. Scarpaci, D. Lacroix et al., Nucl. Phys. A 795, 1 (2007)

    ADS  Google Scholar 

  58. T. Nakamura et al., Phys. Lett. B 331, 296 (1994)

    ADS  Google Scholar 

  59. S.K. Charagi, S.K. Gupta, Phys. Rev. C 41, 1610 (1989)

    ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Prof. Yanlin Ye, Prof. Kanada-En’yo, Prof. Massaki Kimura, Dr. Hantao Li, and Dr. Niu Wan for the valuable discussions. This work is supported by the National Natural Science Foundation of China (Grants No. 12035011, No. 11975167, No. 11761161001, No. 11535004, No. 11961141003, No. 11881240623, No. 11822503 and No. 11575082), the National Key Research and Development Program of China (Grants No. 2018YFA0404403 and No. 2016YFE0129300), the Science and Technology Development Fund of Macau under Grant No. 008/2017/AFJ, and the Central Universities (Grant No. 22120200101). The ECT* Trento has supported this work and this infrastructure is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 824093.

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Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Mengjiao Lyu

  2. Key Laboratory of Aerospace Information Materials and Physics, Ministry of Industry and Information Technology, Nanjing, 210016, China

    Mengjiao Lyu

  3. School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China

    Zhongzhou Ren

  4. Research Center for Nuclear Physics (RCNP), Osaka University, Osaka, 567-0047, Japan

    Hisashi Horiuchi & Akihiro Tohsaki

  5. Institute of Modern Physics, Fudan University, Shanghai, 200433, China

    Bo Zhou

  6. Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Bo Zhou

  7. Laboratory of Physics, Kanto Gakuin University, Yokohama, 236-8501, Japan

    Yasuro Funaki & Taiichi Yamada

  8. Institut für Physik, Universität Rostock, 18051, Rostock, Germany

    Gerd Röpke

  9. National Research Nuclear University (MEPhI), 115409, Moscow, Russia

    Gerd Röpke

  10. Université Paris-Saclay, CNRS-IN2P3, IJCLab, 91405, Orsay, France

    Peter Schuck

  11. Université Grenoble Alpes, CNRS, LPMMC, 38000, Grenoble, France

    Peter Schuck

  12. Department of Physics, Nanjing University, Nanjing, 210093, China

    Chang Xu

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  1. Mengjiao Lyu
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Correspondence to Mengjiao Lyu or Zhongzhou Ren.

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Communicated by David Blaschke.

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Lyu, M., Ren, Z., Horiuchi, H. et al. Properties of \(^{8-11}\)Be isotopes with isospin-dependent spin–orbit potential in a cluster approach. Eur. Phys. J. A 57, 51 (2021). https://doi.org/10.1140/epja/s10050-021-00363-5

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