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Fermions in a mixed vector-scalar double-step potential via continuous chiral transformation

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Abstract.

The behaviour of fermions in the background of a double-step potential is analyzed with a general mixing of scalar and vector couplings via continuous chiral-conjugation transformation. Provided the vector coupling does not exceed the scalar coupling, a Sturm-Liouville approach for the double-step potential shows that the transmission coefficient exhibits oscillations and that a finite set of intrinsically relativistic bound-state solutions might appear as poles of the transmission amplitude in a strong coupling regime. An isolated bound-state solution resulting from coupled first-order equations might also come into sight. It is also shown that all those possible bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time. Furthermore, we show that due to the additional mass acquired by the fermion from the scalar background the high localization of the fermion in an extreme relativistic regime does not violate the Heisenberg uncertainty principle.

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References

  1. J. Bell, H. Ruegg, Nucl. Phys. B 98, 151 (1975)

    Article  ADS  Google Scholar 

  2. P.R. Page et al., Phys. Rev. Lett. 86, 204 (2001)

    Article  ADS  Google Scholar 

  3. J.N. Ginocchio, Phys. Rep. 414, 165 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  4. J.N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997)

    Article  ADS  Google Scholar 

  5. J.N. Ginocchio, A. Leviatan, Phys. Lett. B 425, 1 (1998)

    Article  ADS  Google Scholar 

  6. G.A. Lalazissis et al., Phys. Rev. C 58, R45 (1998)

    Article  ADS  Google Scholar 

  7. J. Meng et al., Phys. Rev. C 58, R628 (1998)

    Article  ADS  Google Scholar 

  8. K. Sugawara-Tanabe, A. Arima, Phys. Rev. C 58, R3065 (1998)

    Article  ADS  Google Scholar 

  9. J.N. Ginocchio, Phys. Rep. 315, 231 (1999)

    Article  ADS  Google Scholar 

  10. S. Marcos et al., Phys. Rev. C 62, 054309 (2000)

    Article  ADS  Google Scholar 

  11. P. Alberto et al., Phys. Rev. Lett. 86, 5015 (2001)

    Article  ADS  Google Scholar 

  12. S. Marcos et al., Phys. Lett. B 513, 306 (2001)

    Article  Google Scholar 

  13. J.N. Ginocchio, A. Leviatan, Phys. Rev. Lett. 87, 072502 (2001)

    Article  ADS  Google Scholar 

  14. P. Alberto et al., Phys. Rev. C 65, 034307 (2002)

    Article  ADS  Google Scholar 

  15. J.N. Ginocchio, Phys. Rev. C 66, 064312 (2002)

    Article  ADS  Google Scholar 

  16. C. Ti-Sheng et al., Chin. Phys. Lett. 20, 358 (2003)

    Article  ADS  Google Scholar 

  17. S.G. Zhou et al., Phys. Rev. Lett. 91, 262501 (2003)

    Article  ADS  Google Scholar 

  18. G. Mao, Phys. Rev. C 67, 044318 (2003)

    Article  ADS  Google Scholar 

  19. R. Lisboa et al., Phys. Rev. C 69, 024319 (2004)

    Article  ADS  Google Scholar 

  20. A. Leviatan, Phys. Rev. Lett. 92, 202501 (2004)

    Article  ADS  Google Scholar 

  21. J.Y. Guo, Phys. Lett. A 338, 90 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  22. P. Alberto et al., Phys. Rev. C 71, 034313 (2005)

    Article  ADS  Google Scholar 

  23. J.Y. Guo et al., Phys. Rev. C 72, 054319 (2005)

    Article  ADS  Google Scholar 

  24. J.Y. Guo et al., Nucl. Phys. A 757, 411 (2005)

    Article  ADS  Google Scholar 

  25. C. Berkdemir, Nucl. Phys. A 770, 32 (2006)

    Article  ADS  Google Scholar 

  26. Q. Xu, S.J. Zhu, Nucl. Phys. A 768, 161 (2006)

    Article  ADS  Google Scholar 

  27. X.T. He et al., Eur. Phys. J. A 28, 265 (2006)

    Article  ADS  Google Scholar 

  28. R.V. Jolos, V.V. Voronov, Phys. At. Nucl. 70, 812 (2007)

    Article  Google Scholar 

  29. S. Chun-Yan et al., Chin. Phys. Lett. 26, 122102 (2009)

    Article  ADS  Google Scholar 

  30. H. Liang et al., Eur. Phys. J. A 44, 119 (2010)

    Article  ADS  Google Scholar 

  31. R. Lisboa et al., Phys. Rev. C 81, 064324 (2010)

    Article  ADS  Google Scholar 

  32. S. Shun-Yan, J.M. Yao, Chin. Phys. C. 34, 1425 (2010)

    Article  ADS  Google Scholar 

  33. H. Liang et al., Phys. Rev. C 83, 041301(R) (2011)

    Article  ADS  Google Scholar 

  34. S. Chun-Yan et al., Chin. Phys. Lett. 28, 092101 (2011)

    Article  ADS  Google Scholar 

  35. B.N. Lu et al., Phys. Rev. Lett. 109, 072501 (2012)

    Article  ADS  Google Scholar 

  36. A.S. de Castro, P. Alberto, Phys. Rev. A 86, 032122 (2012)

    Article  ADS  Google Scholar 

  37. P. Alberto et al., Phys. Rev C 87, 031301(R) (2013)

    Article  ADS  Google Scholar 

  38. P. Alberto et al., J. Phys.: Conf. Ser. 490, 012069 (2014)

    ADS  Google Scholar 

  39. P. Alberto et al., Phys. Rev. C 75, 047303 (2007)

    Article  ADS  Google Scholar 

  40. R. Jackiw, C. Rebbi, Phys. Rev. D 13, 3398 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  41. W.P. Su et al., Phys. Rev. Lett. 42, 1698 (1979)

    Article  ADS  Google Scholar 

  42. J. Goldstone, F. Wilczek, Phys. Rev. Lett. 47, 986 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  43. M.J. Rice, E.J. Mele, Phys. Rev. Lett. 49, 1455 (1982)

    Article  ADS  Google Scholar 

  44. R. Jackiw, G. Semenoff, Phys. Rev. Lett. 50, 439 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  45. F. Charmchi, S. Gousheh, Phys. Rev. D 89, 025002 (2014)

    Article  ADS  Google Scholar 

  46. F. Charmchi, S. Gousheh, Nucl. Phys. B 883, 256 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  47. W.M. Castilho, A.S. de Castro, Ann. Phys. (N.Y.) 340, 1 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  48. W.M. Castilho, A.S. de Castro, Ann. Phys. (N.Y.) 346, 164 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  49. W.M. Castilho, A.S. de Castro, J. Phys.: Conf. Ser. 630, 012029 (2015)

    ADS  Google Scholar 

  50. A.S. de Castro, W.G. Pereira, Phys. Lett. A 308, 131 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  51. L.P. de Oliveira, A.S. de Castro, Can. J. Phys. 90, 481 (2012)

    Article  ADS  Google Scholar 

  52. L.P. de Oliveira, A.S. de Castro, Int. J. Mod. Phys. E 24, 1550031 (2015)

    Article  ADS  Google Scholar 

  53. A.S. de Castro et al., Phys. Rev. C 73, 054309 (2006)

    Article  Google Scholar 

  54. S. Watanabe, Phys. Rev. 106, 1306 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  55. B.F. Touschek, Nuovo Cimento 5, 754 (1957)

    Article  MathSciNet  Google Scholar 

  56. A.S. de Castro, Ann. Phys. (N.Y.) 316, 414 (2005)

    Article  ADS  Google Scholar 

  57. A.S. de Castro, M. Hott, Phys. Lett. A 342, 53 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  58. W. Greiner, Relativistic Quantum Mechanics, Wave Equations (Springer, Berlin, 1990)

  59. P. Strange, Relativistic Quantum Mechanics with Applications in Condensed Matter and Atomic Physics (Cambridge University Press, Cambridge, 1998)

  60. A.J. Niemi, G. Semenoff, Phys. Rep. 135, 99 (1986)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. UNESP - Campus de Guaratinguetá, Departamento de Física e Química, 12516-410, Guaratinguetá SP, Brazil

    W. M. Castilho & A. S. de Castro

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  1. W. M. Castilho
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  2. A. S. de Castro
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Correspondence to W. M. Castilho.

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Castilho, W.M., de Castro, A.S. Fermions in a mixed vector-scalar double-step potential via continuous chiral transformation. Eur. Phys. J. Plus 131, 94 (2016). https://doi.org/10.1140/epjp/i2016-16094-6

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  • DOI: https://doi.org/10.1140/epjp/i2016-16094-6

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