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Three-Body Structure of \(^9_{\varLambda }\)Be with \(\alpha \alpha \varLambda \) Cluster Model

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Abstract

In the framework of \(\alpha +\alpha +\varLambda \) three-body cluster model, we calculate energy spectra from bound energy region to resonant energy region up to around 20 MeV with respect to \(\alpha \alpha \varLambda \) threshold. To calculate resonant states, we employ Complex Scaling method which is one of the powerful method. We obtain the states of \(^8\)Be analogue and genuine hypernuclear analogue, which are consistent with those by Yamada et al. (Prog Theor Phys Suppl 81:104, 1985). However, the calculated ordering of \(^9\)Be analogue states is quite different with their calculation. We also obtain \(2^+\) and \(4^+\) resonant states of which have been never pointed out.

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References

  1. T. Motoba, H. Bandō, K. Ikeda, Prog. Theor. Phys. Suppl. 70, 189 (1983)

    Article  Google Scholar 

  2. T. Yamada, T. Motoba, K. Ikeda, H. Bandō, Structure study of typical light hypernuclei. Prog. Theor. Phys. Suppl. 81, 104 (1985)

    Article  ADS  Google Scholar 

  3. E. Hiyama, M. Kamimura, T. Motoba, T. Yamada, Y. Yamamoto, Three-body model study of \(A=6 {-} 7\) hypernuclei: halo and skin structures. Phys. Rev. C 53, 2075 (1996)

    Article  ADS  Google Scholar 

  4. E. Hiyama, M. Kamimura, K. Miyazaki, T. Motoba, \(\gamma \) transitions in \(A=7\) hypernuclei and a possible derivation of hypernuclear size. Phys. Rev. C 59, 2351 (1999)

    Article  ADS  Google Scholar 

  5. B.-N. Lu, E. Hiyama, H. Sagawa, S.-G. Zhou, Superdeformed \(\varLambda \) hypernuclei within relativstic mean field models. Phys. Rev. C 89, 044307 (2014)

    Article  ADS  Google Scholar 

  6. M. Isaka, K. Fukukawa, M. Kimura, E. Hiyama, H. Sagawa, Y. Yamamoto, Superdeformed \(\varLambda \) hypernuclei with antisymmetrized molecular dynamics. Phys. Rev. C 89, 024310 (2014)

    Article  ADS  Google Scholar 

  7. Y. Funaki, M. Isaka, E. Hiyama, T. Yamada, K. Ikeda, Multi-cluster dynamics in \(^{13}_{\varLambda }\)C and analogy to clustering in \(^{12}\)C. Phys. Lett. B 773, 336 (2017)

    Article  ADS  Google Scholar 

  8. K. Tanida et al., Measurement of the \(B(E2)\) of \(^7_{\varLambda }\)Li and shirinkage of the hypernucelar size. Phys. Rev. Lett. 86, 1982 (2001)

    Article  ADS  Google Scholar 

  9. R.H. Dalitz, A. Gal, Supersymmetric and strangeness analog states in p-shell \(\varLambda \) hypernuclei. Phys. Rev. Lett. 36, 362 (1976)

    Article  ADS  Google Scholar 

  10. R.H. Dalitz, A. Gal, Strangeness analogue states in \(_\varLambda ^9\)Be. Ann. Phys. 131, 314 (1981)

    Article  ADS  Google Scholar 

  11. H. Akikawa et al., Hypernuclear fine structure in \(^9_{\varLambda }\)Be. Phys. Rev. Lett. 88, 082501 (2002)

    Article  ADS  Google Scholar 

  12. H. Tamura et al., \(\gamma \)-ray spectroscopy in \(\varLambda \) hypernuclei. Nucl. Phys. A 754, 58c (2005)

    Article  ADS  Google Scholar 

  13. S. Ajimura et al., Observation of spin–orbit splitting in \(\varLambda \) single-particle states. Phys. Rev. Lett. 86, 4255 (2001)

    Article  ADS  Google Scholar 

  14. H. Tamura et al., Observation of a spin-flip M1 transition in \(_\varLambda ^7\)Li. Phys. Rev. Lett. 84, 5963 (2000)

    Article  ADS  Google Scholar 

  15. M. Ukai et al., Hypernuclear fine structure in \(^{16}_\varLambda \)O and the \({\varLambda }N\) tensor interaction. Phys. Rev. Lett. 93, 232501 (2004)

    Article  ADS  Google Scholar 

  16. M. Ukai et al., Cascade \(\gamma \) decay in the \(_\varLambda ^7\)Li hypernucleus. Phys. Rev. C 73, 012501(R) (2006)

    Article  ADS  Google Scholar 

  17. O. Hashimoto, H. Tamura, Spectroscopy of \(\varLambda \) hypernuclei. Prog. Part. Nucl. Phys. 57, 564 (2006)

    Article  ADS  Google Scholar 

  18. E. Hiyama, Y. Kino, M. Kamimura, Gaussian expansion method for few-body systems. Prog. Part. Nucl. Phys. 51, 223 (2003)

    Article  ADS  Google Scholar 

  19. E. Hiyama, T. Yamada, Structure of light hypernuclei. Prog. Part. Nucl. Phys. 63, 339 (2009)

    Article  ADS  Google Scholar 

  20. D.J. Millener, Shell-model interpretation of \(\gamma \)-ray transitions in p-shell hypernuclei. Nucl. Phys. A 804, 84 (2008)

    Article  ADS  Google Scholar 

  21. D.J. Millener, Lect. Notes Phys. 724, 31 (2007)

    Article  ADS  Google Scholar 

  22. J. Aguilar, J.M. Combes, Commun. Math. Phys. 22, 269 (1971)

    Article  ADS  Google Scholar 

  23. E. Balslev, J.M. Combes, Commun. Math. Phys. 22, 280 (1971)

    Article  ADS  Google Scholar 

  24. B. Simon, Commun. Math. Phys. 27, 1 (1972)

    Article  ADS  Google Scholar 

  25. Y.K. Ho, Phys. Rep. 99, 1 (1983)

    Article  ADS  Google Scholar 

  26. N. Moiseyev, Phys. Rep. 302, 211 (1998)

    Article  ADS  Google Scholar 

  27. S. Aoyama, T. Myo, K. Kato, K. Ikeda, Prog. Theor. Phys. 116, 1 (2006)

    Article  ADS  Google Scholar 

  28. T. Myo, Y. Kikuchi, H. Masui, K. Kato, Prog. Part. Nucl. Phys. 79, 1 (2014)

    Article  ADS  Google Scholar 

  29. S. Saito, Effect of Pauli principle in scattering of two clusters. Prog. Theor. Phys. 40, 893 (1968)

    Article  ADS  Google Scholar 

  30. S. Saito, Effect of Pauli principle in scattering of two clusters. Prog. Theor. Phys. 41, 705 (1969)

    Article  ADS  Google Scholar 

  31. E. Hiyama, M. Kamimura, T. Motoba, T. Yamada, Y. Yamamoto, Three- and four-body cluster models of hypernuclei using the G-matrix \({\varLambda }N\) interaction—\(_\varLambda ^9\)Be, \(_\varLambda ^{13}\)C, \(_{\varLambda \varLambda }^6\)He and \(_{\varLambda \varLambda }^{10}\)Be -. Prog. Theor. Phys. 97, 881 (1997)

    Article  ADS  Google Scholar 

  32. E. Hiyama, M. Isaka, M. Kamimura, T. Myo, T. Motoba, Resonant states of the neutron-rich \(\varLambda \) hypernucleus \(^7_{\varLambda }\)He. Phys. Rev. C 91, 054316 (2015)

    Article  ADS  Google Scholar 

  33. E. Hiyama, R. Lazauskas, J. Carbonell, M. Kamimura, Possibility of generating a 4-neutron resonance with a \(T=3/2\) isospin 3-neutron force. Phys. Rev. 93, 044004 (2016)

    ADS  MathSciNet  Google Scholar 

  34. M. May et al., Observation of hypernuclear gamma-ray transitions in \(_\varLambda ^{7}\)Li and \(_\varLambda ^{9}\)Be. Phys. Rev. Lett. 51, 2085 (1983)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank to Prof. M. Kamimura for useful discussion. This work is supported by RIKEN-MOST project. One of the authors (E. H.) is supported by a Grants-in-Aid for Scientific Research from Monbukagakusho of Japan (18H05407, 16H03995 and 16H02180). One of the authors (Y. F.) is supported by JSPS KAKENHI Grant Number JP18K03658. The numerical calculations were performed at the Yukawa Institute Computer Facility. One of authors (Q.W.) is supported by National Natural Science Foundation of China (11475085, 11535005, 11690030) and National Major state Basic Research and Development of China (2016YFE0129300).

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Authors and Affiliations

  1. Department of Physics, H-27, Tokyo Institute of Technology, Meguro, Tokyo, 152-8551, Japan

    Jehee Lee

  2. Nishina Center for Accelerator-Based Science, Institute for Physical and Chemical Research (RIKEN), Wako, 351-0198, Japan

    Jehee Lee

  3. Department of Physics, Nanjing Univeristy, Nanjing, 210093, China

    Qian Wu, Hongshi Zong & Emiko Hiyama

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

    Yasuro Funaki

  5. Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing, 210093, China

    Hongshi Zong

  6. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190, China

    Hongshi Zong

  7. Department of Physics, Kyushu University, Fukuoka, 819-0395, Japan

    Emiko Hiyama

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  1. Jehee Lee
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  2. Qian Wu
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  3. Yasuro Funaki
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  4. Hongshi Zong
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  5. Emiko Hiyama
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Correspondence to Emiko Hiyama.

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Lee, J., Wu, Q., Funaki, Y. et al. Three-Body Structure of \(^9_{\varLambda }\)Be with \(\alpha \alpha \varLambda \) Cluster Model. Few-Body Syst 60, 30 (2019). https://doi.org/10.1007/s00601-019-1502-3

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