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On Mass Polarization Effect in Three-Body Nuclear Systems

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Abstract

The mass polarization effect is considered for different three-body nuclear AAB systems having a strongly bound AB and unbound AA subsystems. We employ the Faddeev equations for calculations and the Schrödinger equation for analysis of the contribution of the mass polarization term of the kinetic-energy operator. For a three-boson system the mass polarization effect is determined by the difference of the doubled binding energy of the AB subsystem \(2E_{2}\) and the three-body binding energy \(E_{3}(V_{AA}=0)\) when the interaction between the identical particles is omitted. In this case: \(\left| E_{3}(V_{AA}=0)\right| >2\left| E_{2}\right| \). In the case of a system complicated by isospins(spins), such as the kaonic clusters \( K^{-}K^{-}p\) and \(ppK^{-}\), a similar evaluation is impossible. For these systems it is found that \(\left| E_{3}(V_{AA}=0)\right| <2\left| E_{2}\right| \). A model with an AB potential averaged over spin(isospin) variables transforms the latter case to the first one. The mass polarization effect calculated within this model is essential for the kaonic clusters. In addition we have obtained the relation \(|E_3|\le |2E_2|\) for the binding energy of the kaonic clusters.

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References

  1. C. Froese Fischer, T. Brage, P. Jönsson, Computational Atomic Structure, An MCHF Approach (IOP, Bristol, 1997)

    MATH  Google Scholar 

  2. B. Bransden, C. Joachain, Physics of Atoms and Molecules, 2nd edn. (Pearson Education, Harlow, 2003)

    Google Scholar 

  3. D. Hughes, C. Eckart, The effect of the motion of the nucleus on the spectra of Li I and Li II. Phys. Rev. 36, 694–698 (1930)

    Article  ADS  MATH  Google Scholar 

  4. S.S. Prasad, A.L. Stewart, Isotope shift in Li and B2+. Proc. Phys. Soc. 87, 159–164 (1966)

    Article  ADS  Google Scholar 

  5. N.C. Handy, A.M. Lee, The adiabatic approximation. Chem. Phys. Lett. 252, 425 (1996)

    Article  ADS  Google Scholar 

  6. N. Yamanaka, Calculation of mass polarization for the and states in Li-like ions. J. Phys. B At. Mol. Opt. Phys. 32, 1597–1605 (1999)

    Article  ADS  Google Scholar 

  7. F. Rolim, J.P. Braga, J.R. Mohallem, Unified description of chemical bonding in H2 isotopomers, including Ps2, \(\mu \)2 and bi-excitons. Chem. Phys. Lett. 322, 139 (2000)

    Article  ADS  Google Scholar 

  8. T. Koga, H. Matsuyama, Nuclear mass corrections for atoms and ions. Chem. Phys. Lett. 366, 601–605 (2002)

    Article  ADS  Google Scholar 

  9. G.W.F. Drake, M.M. Cassar, R. Nistor, Ground-state energies for helium, \(\text{ H }^{-}\), and \(\text{ Ps }^{-}\). Phys. Rev. A 65, 054501 (2002)

    Article  ADS  Google Scholar 

  10. T. Koga, H. Matsuyama, Nuclear mass corrections for atoms and ions. Chem. Phys. Lett. 366, 601 (2002)

    Article  ADS  Google Scholar 

  11. A.K. Bhatia, R.J. Drachman, The mass polarization effect in He-like ions: first and second order. J. Phys. B At. Mol. Opt. Phys. 36, 1957 (2003)

    Article  ADS  Google Scholar 

  12. H. Nakashima, H. Nakatsuji, Solving the electron and electron-nuclear Schrdinger equations for the excited states of helium atom with the free iterative-complement-interaction method. J. Chem. Phys. 128, 154107–7 (2008)

    Article  ADS  Google Scholar 

  13. J.R. Mohallem, L.G. Diniz, A.S. Dutra, Separation of motions of atomic cores and valence electrons in molecules. Chem. Phys. Lett. 501, 575 (2011)

    Article  ADS  Google Scholar 

  14. J.R. Mohallem, F. Rolim, C.P. Goncalves, A molecular model for positron complexes: long-range effects on 2\(\gamma \) pair-annihilation rates. J. Phys. B At. Mol. Opt. Phys. 37, 1045 (2004)

    Article  ADS  Google Scholar 

  15. T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318-6 (2013)

    Article  ADS  Google Scholar 

  16. D.K. Zhang, D.W. Kidd, K. Varga, Excited biexcitons in transition metal dichalcogenides. Nano Lett. 15, 70027005 (2015)

    ADS  Google Scholar 

  17. E. Courtade et al., Charged excitons in monolayer \(\text{ WSe }_{2}\): experiment and theory. arXiv:1705.02110

  18. I.N. Filikhin, A. Gal, Light \(\varLambda \varLambda \) hypernuclei and the onset of stability for \(\varLambda \varXi \) hypernuclei. Phys. Rev. C 65, 041001(R)–4 (2002)

    Article  ADS  Google Scholar 

  19. E. Hiyama, M. Kamimura, T. Motoba, T. Yamada, Y. Yamamoto, Four-body cluster structure of \(A=7-10\) double-hypernuclei. Phys. Rev. C 66, 024007–13 (2002)

    Article  ADS  Google Scholar 

  20. A. Dote, Double-pole structure on a prototype of kaonic nuclei \(K^{-}pp\). In: Presented at HYP2015, Tohoku University Centennial Hall, 7–11 September (2015)

  21. A. Dote, T. Inoue, T. Myo, Application of a coupled-channel complex scaling method with Feshbach projection to the \(K^-pp\) system. Prog. Theor. Exp. Phys. https://doi.org/10.1093/ptep/ptv039

  22. J.-L. Basdevant, A. Martin, J.-M. Richard, T.T. Wu, Optimized lower bounds in the three-body problem. Nucl. Phys. B 393, 111–125 (1993)

    Article  ADS  MATH  Google Scholar 

  23. L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer Academic, Dordrecht, 1993), p. 398

    Book  MATH  Google Scholar 

  24. H.P. Noyes, H. Fiedeldey, in Three-Particle Scattering in Quantum Mechanics, ed. by J. Gillespie, J. Nuttall (W. A. Benjamin, New York, 1968), p. 195

  25. A.A. Kvitsinsky, Yu.A. Kuperin, S.P. Merkuriev, A.K. Motovilov, S.L. Yakovlev, N-body quantum problem in configuration space. Fiz. Elem. Chastits At. Yadra, 17, 267–317 (1986) (in Russian). http://www1.jinr.ru/Archive/Pepan/1986-v17/v-17-2.htm

  26. I.N. Filikhin, A. Gal, V.M. Suslov, Faddeev calculations for the \(A=5,6\varLambda \varLambda \)-hypernuclei. Phys. Rev. C 68, 024002–8 (2003)

    Article  ADS  Google Scholar 

  27. I. Filikhin, A. Gal, V.M. Suslov, Cluster models of \(_{\varLambda \varLambda }^6\)He and \(_{\varLambda }^9\)Be hypernuclei. Nucl. Phys. A 743, 194–207 (2004)

    Article  ADS  Google Scholar 

  28. I.N. Filikhin, V.M. Suslov, B. Vlahovic, A new prediction for the binding energy of the \(^{7}\varLambda \)He hypernucleus. J. Phys. G: Nucl. Part. Phys. 31, 389–400 (2005)

    Article  ADS  Google Scholar 

  29. R.A. Malfliet, J.A. Tjon, Solution of the Faddeev equations for the triton problem using local two-particle interactions. Nucl. Phys. A 127, 161–168 (1969)

    Article  ADS  Google Scholar 

  30. J.L. Friar, B.F. Gibson, G. Berthold, W. Glöckle, Th Cornelius, H. Witala, J. Haidenbauer, Y. Koike, G.L. Payne, J.A. Tjon, W.M. Kloet, Benchmark solutions for a model three-nucleon scattering problem. Phys. Rev. C 42, 1838–1840 (1990)

    Article  ADS  Google Scholar 

  31. I.N. Filikhin, V.M. Suslov, B. Vlahovic, Charge symmetry breaking effect for \(^3\)H and \(^3\)He within s-wave approach. Int. J. Mod. Phys. E 25, 1650042–9 (2016)

    Article  ADS  Google Scholar 

  32. R.Ya. Kezerashvili, S.M. Tsiklauri, I. Filikhin, V.M. Suslov, B. Vlahovic, Three-body calculations for the \(K^-pp\) system within potential models. J. Phys. G Nucl. Part. Phys. 43, 065104–065118 (2016). arXiv:1508.07638

    Article  ADS  Google Scholar 

  33. T. Yamazaki, Y. Akaishi, Basic \({\bar{K}}\) nuclear cluster, \(K^-pp\), and its enhanced formation in the \(p+p\rightarrow K^++X\) reaction. Phys. Rev. C 76, 045201–16 (2007)

    Article  ADS  Google Scholar 

  34. T. Hyodo, W. Weise, Effective \({\bar{K}}N\) interaction based on chiral SU(3) dynamics. Phys. Rev. C 77, 035204–14 (2008)

    Article  ADS  Google Scholar 

  35. D. Jido, Y. Kanada-Enyo, \(K{\bar{K}}N\) molecule state with \(I=1/2\) and \(J^P=1/2^+\) studied with a three-body calculation. Phys. Rev. C 78, 035203–10 (2008)

    Article  ADS  Google Scholar 

  36. Y. Kanada-Enyo, D. Jido, \({\bar{K}}{\bar{K}}N\) molecular state in a three-body calculation. Phys. Rev. C 78, 025212-10 (2008)

    ADS  Google Scholar 

  37. M. Bayar, J. Yamagata-Sekihara, E. Oset, \({\bar{K}}NN\) system with chiral dynamics. Phys. Rev. C 84, 015209–9 (2011)

    Article  ADS  Google Scholar 

  38. I. Filikhin, V.M. Suslov, B. Vlahovic, An \(\alpha \)-cluster model for \(_\varLambda ^9\)Be spectroscopy. Phys. At. Nucl. 76, 355–364 (2013)

    Article  Google Scholar 

  39. Y.C. Tang, R.C. Herndon, \(\varLambda \varLambda \) Potential from analysis of \(_{\varLambda \varLambda }\text{ Be }^{10}\). Phys. Rev. 138, 637–643 (1965)

    Article  ADS  Google Scholar 

  40. B.F. Gibson, A. Goldberg, M.S. Weiss, Effects of \(\varLambda -\varSigma \) coupling in \(^{4}\varLambda \)H, \(^{4}\varLambda \)He, and \(^{4}\varLambda \)He. Phys. Rev. C 6, 741–748 (1972)

    Article  ADS  Google Scholar 

  41. S. Maeda, E.W. Schmid, in Few-Body Problems in Physics, vol. II, ed. by B. Zeitnitz (Elsevier, Amsterdam, 1984), p. 379

  42. K.S. Myint, S. Shinmura, Y. Akaishi, \(\varLambda \varLambda -{\varXi } N\) coupling effects in light hypernuclei. Eur. Phys. J. A 16, 21–26 (2003)

    Article  ADS  Google Scholar 

  43. Y. Kurihara, Y. Akaishi, H. Tanaka, Central repulsion of \(\varLambda -\alpha \) interaction with hard-core \(\varLambda -N\) potential. Prog. Theor. Phys. 71, 561–568 (1984)

    Article  ADS  Google Scholar 

  44. K.A. Olive et al., Particle data group. Review of particle physics. Chin. Phys. C 38, 090001 (2014)

    Article  ADS  Google Scholar 

  45. R.Ya. Kezerashvili, S.M. Tsiklauri, I.N. Filikhin, V.M. Suslov, B. Vlahovic, \({\bar{K}}pp\) and \({\bar{K}}{\bar{K}}p\) Clusters. EPJ Web Conf. 113, 07005-4 (2016)

    Google Scholar 

  46. J.L. Friar, B.F. Gibson, G.L. Payne, Configuration space Faddeev calculations. V. Variational bounds. Phys. Rev. C 24, 2279–2289 (1981)

    Article  ADS  Google Scholar 

  47. A. Dote, T. Hyodo, W. Weise, Variational calculation of the \(ppK^-\) system based on chiral SU(3) dynamics. Phys. Rev. C 79, 014003–16 (2009)

    Article  ADS  Google Scholar 

  48. A. Dote, T. Inoue, T. Myo, Fully coupled-channels complex scaling method for the \(K^{-}pp\) system. Phys. Rev. C 95, 062201 (2017)

    Article  ADS  Google Scholar 

  49. Y. Ichikawa et al., Observation of the \(K^-pp\)-like structure in the \(d(\pi ^+, K^+)\) reaction at 1.69 GeV. Prog. Theor. Exp. Phys. 2015, 021D018 (2015)

    Article  Google Scholar 

  50. A. Gal, MESON2016–concluding remarks. EPJ Web Conf. 130, 01030–01038 (2016). arXiv:1609.04570v2

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Science Foundation Grant Supplement to the NSF grant HRD-1345219 and NASA (NNX09AV07A). R. Ya. K. partially supported by MES RK, the Grant 3106/GF4.

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Authors and Affiliations

  1. North Carolina Central University, Durham, NC, 27707, USA

    I. Filikhin, V. M. Suslov & B. Vlahovic

  2. Physics Department, New York City College of Technology, The City University of New York, Brooklyn, NY, 11201, USA

    R. Ya. Kezerashvili

  3. The Graduate School and University Center, The City University of New York, New York, NY, 10016, USA

    R. Ya. Kezerashvili

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  1. I. Filikhin
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  4. B. Vlahovic
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Correspondence to I. Filikhin.

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Filikhin, I., Kezerashvili, R.Y., Suslov, V.M. et al. On Mass Polarization Effect in Three-Body Nuclear Systems. Few-Body Syst 59, 33 (2018). https://doi.org/10.1007/s00601-018-1353-3

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