Abstract
In this work, exact analytical expressions for regular solution and on-shell Jost function are calculated for nuclear Hulthén plus atomic Hulthén potential by imposing the same range approximation to both nuclear and atomic potentials. In this context, the regular solution is utilised to find expressions for the off-shell Jost function and half-shell T-matrix. The half-off-shell T-matrix and the elastic scattering phase shifts for the nucleon–nucleon and nucleus–nucleus systems are computed. Our results are found to be in good agreement with the standard data.
Similar content being viewed by others
References
J Bhoi and U Laha, Theor. Math. Phys. 190, 69 (2017)
J Bhoi and U Laha, Pramana – J. Phys. 88, 42 (2017)
Y Yamaguchi, Phys. Rev. 95, 1628 (1954)
D K Ghosh, S Saha, K Niyogi and B Talukdar, Czech. J. Phys. 33, 528 (1983)
H van Haeringen, Charged particle interactions – Theory and formulas (Coulomb Press, Leiden, Netherlands, 1985)
U Laha and J Bhoi, Hadron–hadron scattering within the separable model of interactions (OmniScriptum Publishing Group, Beau Bassin, 2018)
H van Haeringen and R van Wageningen, J. Math. Phys. 16, 1441 (1975)
W Schweiger, W Plessas, L P Kok and H van Haeringen, Phys. Rev. C 27, 515 (1983)
J Haidenbauer and W Plessas, Phys. Rev. C 27, 63 (1983)
B Talukdar, U Laha and T Sasakawa, J. Math. Phys. 27, 2080 (1986)
W Glöckle, J Golak, R Skibiński and H Witała, Few-Body Syst. 47, 3 (2010)
T Takemiya, Prog. Theor. Phys. 48, 1547 (1972)
M Jetter’, H Freitag and H V von Geramb, Phys. Scr. 48, 229 (1993)
H J Korsch and R Mohlenkamp, J. Phys. B: At. Mol. Phys. 15, 2187 (1982)
H S Picker, E F Redish and G J Stephenson Jr, Phys. Rev. C 4, 287 (1971)
P U Sauer, Ann. Phys. 80, 282 (1973)
U Laha and J Bhoi, Few-Body Syst. 54, 1973 (2013)
U Laha and J Bhoi, J. Math. Phys. 54, 013514 (2013)
U Laha and J Bhoi, Phys. Rev. C 88, 064001 (2013)
L Hulthén, Ark. Mat. Astron. Fys. 29B, 1 (1942)
L J Slater, Generalized hypergeometric functions (Cambridge University Press, London, 1966)
A Erdeyli, Higher transcendental functions (McGraw-Hill, New York, 1953) Vol. 1
W Magnus and F Oberhettinger, Formulae and theorems for the special functions of mathematical physics (Chelsea, New York, 1949)
R G Newton, Scattering theory of waves and particles, 2nd edn (McGraw-Hill, New York, 1982)
B Khirali, A K Behera, J Bhoi and U Laha, J. Phys G: Nucl. and Part. 46, 115104 (2019)
R Jost, Helv. Phys. Acta 20, 256 (1947)
U Laha and B Talukdar, Pramana – J. Phys. 36, 289 (1991)
B Khirali, A K Behera, J Bhoi and U Laha, Phys. Scr. 95, 075308 (2020)
A W Babister, Transcendental functions satisfying non-homogeneous linear differential equations (MacMillan, New York, 1967)
I S Gradshteyn and I M Ryzhik, Tables of integrals, series and products (Academic Press, London, 2000)
B Khirali, U Laha and P Sahoo, Few-Body Syst. 62, 20 (2021)
R B Wiringa, V G J Stoks and R Schiavilla, Phys. Rev. 51, 38 (1995)
J Bystricky, C Lechanoine-Leluc and F Lehar, J Phys. 48, 199 (1987)
R Plaga, H W Becker, A Redder, C Rolfs, H P Trautvetter and K Langanke, Nucl. Phys. A 465, 291 (1987)
A K Behera, U Laha, M Majumder and J Bhoi, J. Kor. Phys. Soc. 74, 428 (2019)
P Tischhauser et al, Phys. Rev. C 79, 055803 (2009)
S I Ando, Eur. Phys. J. A 52, 130 (2016)
S I Ando, Phys. Rev. C 97, 014604 (2018)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sahoo, P., Laha, U. Treatment of hadronic systems involving two potentials under a new approximation scheme. Pramana - J Phys 96, 15 (2022). https://doi.org/10.1007/s12043-021-02267-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-021-02267-x
Keywords
- Atomic and nuclear Hulthén potentials
- regular solution
- off-shell Jost function
- half-off-shell T-matrix
- p–p and \(\alpha \)–\(^{12}\)C Systems