Skip to main content
SpringerLink
Log in

The Fredholm determinant for Hulthén-distorted non-local separable potential: Application to \( \alpha {-}\alpha \) elastic scattering

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthén-distorted non-local separable potential is constructed and expressed in the maximum reduced form. Using boundary conditions (regular and irregular), two approximate energy-dependent interactions corresponding to the parent non-local potential are also constructed. The phase shifts for the \( \alpha \)–\(\alpha \) elastic scattering are computed by using (i) exact expression for the Fredholm determinant and (ii) energy-dependent local interactions by exploiting the phase function method. The merits of our constructed equivalent energy-dependent potentials are judged by comparing the \( \alpha \)–\(\alpha \) elastic scattering phases with our exact calculation and standard data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. E Rutherford and J Chadwick, Phil. Mag. 4, 605 (1927)

    Google Scholar 

  2. N P Heydenberg and G M Temmer, Phys. Rev. 104, 123 (1956)

    ADS  Google Scholar 

  3. J L Russell, G C Phillips and C W Reich, Phys. Rev. 104, 135 (1956)

    ADS  Google Scholar 

  4. C M Jones, G C Phillips and P D Miller, Phys. Rev. 117, 525 (1960)

    ADS  Google Scholar 

  5. N Berk, F E Steigert and G L Salinger, Phys. Rev. 117, 531 (1960)

    ADS  Google Scholar 

  6. J R Dunning, A M Smith and F E Steigert, Phys. Rev. 121, 580 (1961)

    ADS  Google Scholar 

  7. R Chiba, H E Conzett, H Morinaga, N Mutsuro, K Shoda and M Kimura, J. Phys. Soc. Jpn. 16, 1077 (1961)

    ADS  Google Scholar 

  8. T A Tombrello and L S Senhouse, Phys. Rev. 129, 2252 (1963)

    ADS  Google Scholar 

  9. P Darriulat, G Igo, H G Pugh and H D Holmgren, Phys. Rev. 137, B315 (1965)

    ADS  Google Scholar 

  10. R R Haefner, Rev. Mod. Phys. 23, 228 (1951)

    ADS  Google Scholar 

  11. E van der Spuy and H J Pienaar, Nucl. Phys. 7, 397 (1958)

    Google Scholar 

  12. G Igo, Phys. Rev. 117, 1079 (1960)

    ADS  Google Scholar 

  13. O Endo, I Shimodaya and J Hiura, Prog. Theor. Phys. (Kyoto) 31, 1157 (1964)

    ADS  Google Scholar 

  14. S Ali and A R Bodmer, Nucl. Phys. 80, 99 (1966)

    Google Scholar 

  15. S Ali and S A Afzal, Nuovo Cimento 50, 355 (1967)

    ADS  Google Scholar 

  16. V I Kukulin, V G Neudatchin and Y F Smirnov, Nucl. Phys. A 245, 429 (1975)

    ADS  Google Scholar 

  17. B Buck, H Friedrich and C Wheatley, Nucl. Phys. A 275, 246 (1977)

    ADS  Google Scholar 

  18. H Friedrich, Phys. Rep. 74, 209 (1981); Phys. Rev. C 30, 1102 (1984)

  19. L Marquez, Phys. Rev. C 28, 2525 (1983)

    ADS  Google Scholar 

  20. P Mohr et al, Z. Phys. A 349, 339 (1994)

    ADS  Google Scholar 

  21. S Elhatisari, D Lee, G Rupak, E Epelbaum, H Krebs, T A Lähde, T Luu and Ulf-G Meißner, Nature 528, 111 (2015)

    ADS  Google Scholar 

  22. E Caurier, P Navrátil, W E Ormand and J P Vary, Phys. Rev. C 64, 051301 (2001)

    ADS  Google Scholar 

  23. T Yoshida, N Shimizu, T Abe and T Otsuka, J. Phys. Conf. Ser. 454, 012050 (2013)

    Google Scholar 

  24. T Myo, A Umeya, K Horii, H Toki and K Ikeda, Prog. Theor. Exp. Phys. 2014, 033D01 (2014)

  25. V M Datar et al, Phys. Rev. Lett. 111, 062502 (2013)

    ADS  Google Scholar 

  26. J Bhoi and U Laha, Phys. At. Nucl. 79, 370 (2016)

    Google Scholar 

  27. J Bhoi and U Laha, Pramana – J. Phys. 88: 42 (2017)

    Google Scholar 

  28. M Rahaman, D Husain and S Ali, Phys. Rev. C 10, 1 (1974)

    ADS  Google Scholar 

  29. U Laha, N Haque, T Nandi and G C Sett, Z. Phys. A 332, 305309 (1989)

    Google Scholar 

  30. U Laha, M Majumder and J Bhoi, Pramana – J. Phys. 90: 48 (2018)

    Google Scholar 

  31. M Coz, L G Arnold and A D Mac Kellar, Ann. Phys. (N. Y.) 59, 219 (1970)

  32. L G Arnold and A D MacKellar, Phys. Rev. C 3, 1095 (1971)

    ADS  Google Scholar 

  33. F Calogero, Variable phase approach to potential scattering (Academic Press, New York, 1967)

    MATH  Google Scholar 

  34. B Talukdar, G C Sett and S R Bhattaru, J. Phys. G 11, 591 (1985)

    ADS  Google Scholar 

  35. R G Newton, Scattering theory of waves and particles (McGraw-Hill, New York, 1982)

    MATH  Google Scholar 

  36. H van Haeringen, Charged particle interactions – Theory and formulas (The Coulomb Press, Leyden, 1985)

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  41. L J Slater, Generalized hypergeometric functions (Cambridge University Press, London, 1966)

    MATH  Google Scholar 

  42. A Erdeyli, Higher transcendental functions (McGraw-Hill, New York, 1953) Vol. 1

  43. W Magnus and F Oberhettinger, Formulae and theorems for the special functions of mathematical physics (Chelsea, New York, 1949)

    MATH  Google Scholar 

  44. A W Babister, Transcendental functions satisfying non-homogeneous linear differential equations (MacMillan, New York, 1967)

    MATH  Google Scholar 

  45. W N Balley, Generalised hypergeometric series (Cambridge University Press, London, 1935)

    Google Scholar 

  46. U Laha, S Ray, S Panda and J Bhoi, Theor. Math. Phys. 193, 1498 (2017)

    Google Scholar 

  47. B Talukdar, D Chatterjee and P Banerjee, J. Phys. G 3, 813 (1977)

    ADS  Google Scholar 

  48. G C Sett, U Laha and B Talukdar, J. Phys. A 21, 3643 (1988)

    ADS  MathSciNet  Google Scholar 

  49. U Laha, S Das and J Bhoi, Turk. J. Phys. 41, 447 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Institute of Technology, Jamshedpur, 831 014, India

    U Laha, A K Behera & M Majumder

  2. Department of Physics, Veer Surendra Sai University of Technology, Burla, 768 018, India

    J Bhoi

Authors
  1. U Laha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A K Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M Majumder
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J Bhoi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to U Laha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laha, U., Behera, A.K., Majumder, M. et al. The Fredholm determinant for Hulthén-distorted non-local separable potential: Application to \( \alpha {-}\alpha \) elastic scattering. Pramana - J Phys 94, 144 (2020). https://doi.org/10.1007/s12043-020-02012-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-020-02012-w

Keywords

PACS Nos

Search

Navigation