\(\boldsymbol{p}\boldsymbol{-}^{\mathbf{12}}\)C and \(\boldsymbol{p}\boldsymbol{-}\boldsymbol{d}\) Scattering within the Separable Model of Interaction

Abstract

Differential equation approach is adapted to construct exact analytical expressions for the regular, Jost, and physical states for Hulthén plus separable nonlocal potential. The Jost function and the Fredholm determinant for physical boundary condition are exploited to compute scattering phase shifts for proton–deuteron and proton–carbon systems within this two-body model of interaction. Excellent agreement in phase shift values with other sophisticated calculations is obtained.

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REFERENCES

  1. 1

    Y. Yamaguchi, Phys. Rev. 95, 1628 (1954).

    ADS  Article  Google Scholar 

  2. 2

    L. Crepinsek, C. B. Lang, H. Oberhumer, W. Plessas, and H. Zingl, Acta Phys. Austriaca 42, 139 (1975).

    Google Scholar 

  3. 3

    J. Haidenbauer and W. Plessas, Phys. Rev. C 27, 63 (1983).

    ADS  Article  Google Scholar 

  4. 4

    B. Talukdar, U. Laha, and T. Sasakawa, J. Math. Phys. 27, 2080 (1986).

    ADS  MathSciNet  Article  Google Scholar 

  5. 5

    H. van Haeringen and R. van Wageningen, J. Math. Phys. 16, 1441 (1975).

    ADS  Article  Google Scholar 

  6. 6

    B. Talukdar, U. Laha, and S. R. Bhattaru, J. Phys. A: Math. Gen. 18, L359 (1985).

    ADS  Article  Google Scholar 

  7. 7

    U. Laha and B. Talukdar, Pramana-J. Phys. 36, 289 (1991).

    Google Scholar 

  8. 8

    U. Laha, Phys. Rev. A 74, 012710 (2006).

    ADS  Article  Google Scholar 

  9. 9

    U. Laha, Pramana-J. Phys. 72, 457 (2009).

    Google Scholar 

  10. 10

    U. Laha and J. Bhoi, J. Math. Phys. 54, 013514 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11

    U. Laha and J. Bhoi, Phys. Rev. C 88, 064001 (2013).

    ADS  Article  Google Scholar 

  12. 12

    U. Laha, B. J. Roy, and B. Talukdar, J. Phys. A: Math. Gen. 22, 3597 (1989).

    ADS  Article  Google Scholar 

  13. 13

    H. van Haeringen, Charged Particle Interactions: Theory and Formulas (The Coulomb Press, Leyden, 1985).

    Google Scholar 

  14. 14

    U. Laha, Coulomb-Modified Nuclear Scattering: Off the Energy Shell (Lambert Academic, Saarbrücken, 2010).

    Google Scholar 

  15. 15

    U. Laha and J. Bhoi, Hadron-Hadron Scattering within the Separable Model of Interactions (Scholars’ Press, Beau Bassin, 2018).

  16. 16

    R. Jost, Helv. Phys. Acta 20, 256 (1947).

    Google Scholar 

  17. 17

    U. Laha, A. K. Jana, and T. Nandi, Pramana-J. Phys. 37, 387 (1991).

    Google Scholar 

  18. 18

    A. Erdeyli, Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. 1.

    Google Scholar 

  19. 19

    L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, London, 1966).

    Google Scholar 

  20. 20

    W. Magnus and F. Oberhettinger, Formulae and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1949).

    Google Scholar 

  21. 21

    G. E. Andrews, R. Askey, and R. Roy, Special Functions, Vol. 71 of Encyclopaedia of Mathematics and its Applications (Cambridge Univ. Press, London, 1999).

  22. 22

    A. W. Babister, Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations (MacMillan, New York, 1967).

    Google Scholar 

  23. 23

    W. N. Bailey, Generalised Hypergeometric Series (Cambridge Univ. Press, London, 1935).

    Google Scholar 

  24. 24

    U. Laha, C. Bhattacharyya, K. Roy, and B. Talukdar, Phys. Rev. C 38, 558 (1988).

    ADS  Article  Google Scholar 

  25. 25

    U. Laha, Few-Body Syst. 59, 68 (2018).

    ADS  Article  Google Scholar 

  26. 26

    R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1982).

    Google Scholar 

  27. 27

    J. Bhoi and U. Laha, Braz. J. Phys. 46, 129 (2016).

    ADS  Article  Google Scholar 

  28. 28

    I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, London, 2000).

    Google Scholar 

  29. 29

    U. Laha, Few-Body Syst. 61, 3 (2020).

    ADS  Article  Google Scholar 

  30. 30

    C. S. Warke and R. K. Bhaduri, Nucl. Phys. A 162, 289 (1971).

    ADS  Article  Google Scholar 

  31. 31

    B. F. Irgaziev, J.-U. Nabi, and A. Kabir, Astrophys. Space Sci. 363, 148 (2018).

    ADS  Article  Google Scholar 

  32. 32

    A. Kabir, B. F. Irgaziev, and J.-U. Nabi, Braz. J. Phys. 50, 112 (2020).

    ADS  Article  Google Scholar 

  33. 33

    C. R. Chen, G. L. Payne, J. L. Friar, and B. F. Gibson, Phys. Rev. C 39, 1261 (1989).

    ADS  Article  Google Scholar 

  34. 34

    H. L. Jackson and A. I. Galonsky, Phys. Rev. 89, 370 (1953).

    ADS  Article  Google Scholar 

  35. 35

    L. D. Knutson, L. O. Lamm, and J. E. McAninch, Phys. Rev. Lett. 71, 3762 (1993).

    ADS  Article  Google Scholar 

  36. 36

    C. Eckart, Phys. Rev. 35, 1303 (1930).

    ADS  Article  Google Scholar 

  37. 37

    J. Bhoi, A. K. Behera, and U. Laha, J. Math. Phys. 60, 083502 (2019).

    ADS  MathSciNet  Article  Google Scholar 

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Correspondence to P. Sahoo or U. Laha or A. K. Behera.

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Sahoo, P., Laha, U. & Behera, A.K. \(\boldsymbol{p}\boldsymbol{-}^{\mathbf{12}}\)C and \(\boldsymbol{p}\boldsymbol{-}\boldsymbol{d}\) Scattering within the Separable Model of Interaction. Phys. Atom. Nuclei 83, 802–810 (2020). https://doi.org/10.1134/S1063778820660072

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