Abstract
The nuclear half of the interaction is defined by the Manning-Rosen potential, and the electromagnetic part by the Hulthén potential, in order to characterise the nucleon-nucleus elastic scattering. The regular solution of the relevant equation is built using an adaptation of the Frobenius approach. The associated Jost function is derived from its integral representation in terms of regular solution. Estimates of scattering phase shifts and differential cross sections for proton-oxygen system are made by exploiting the Jost function. The same physical observables are also calculated numerically by exploiting the Ricatti type equation. Our findings are in fair agreement with the earlier theoretical and experimental data.
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References
Hagen, G., Papenbrock, T., Hjorth-Jensen, M.: Ab Initio Computation of the 17F Proton Halo State and Resonances in A=17 Nuclei. Phys. Rev. Letts. 104, 182501 (2010)
Dubovichenko, S., et al.: New measurements and phase shift analysis of p16O elastic scattering at astrophysical energies. Chinese Phys. C 41, 014001 (2017)
Salisbury, S.R., Richards, H.T.: F17 Level Parameters. Phys. Rev. 126, 2147 (1962)
Gurbich, A.F.: Evaluation of non-Rutherford proton elastic scattering for oxygen Nuclear Inst. and Methods in. Phys. Res. B 129, 311 (1997)
Salisbury, S.R., Hardie, G., Oppliger, L., Dangle, R.: Proton-Oxygen Differential Scattering Cross Sections. II. Phys. Rev. 126, 2143 (1962)
Zhen-Qiang, T., Wein-Ying, R.: Proton-oxygen elastic scattering and spin effects at Tp=200 MeV in the four α-particle model. J. Phys. G: Nucl. Part. Phys. 15, 1599 (1989)
Kobayashi, S.: Elastic and Inelastic Scattering of Protons by Oxygen in the Energy Region of 6.9 MeV to 15.6 MeV. J. Phys. Soc. Japan 15, 1164 (1960)
Braun, M., Fried, T.: Elastic backscattering cross sections of protons on oxygen. Z. Phys. A 311, 173 (1983)
Blue, R.A., Haeberli, W.: Polarization of Protons Elastically Scattered by Oxygen. Phys. Rev. 137, B284 (1965)
Trachslin, W., Brown, L.: Polarization and phase shifts in 12C(p,p)12C and 16O(p,p)16O from 1.5 to 3 MeV. Nucl. Phys. A 101, 273 (1967)
Chow, H.C., Griffiths, G.M., Hall, T.H.: The 160(p, y)17F Direct Capture Cros Section with an Extrapolation to Astrophysical Energies. Can. J. Phys. 53, 1672 (1975)
Fabrici, E., et al.: Proton elastic scattering on light nuclei II. Nuclear structure effects. Phys. Rev. C 21, 844 (1980)
Amirikas, R., Jamieson, D.N., Dooley, S.P.: Measurement of (p, p) elastic cross Sections for C, O and Si in the energy range 1.0–3.5 MeV. Nucl. Instr. Meth. Phys. Res. B 77, 110 (1993)
Tilley, D.R., Weller, H.R., Cheves, C.M.: Energy levels of light nuclei A = 16–17. Nucl. Phys. A 565, 1 (1993)
Ramos, A.R., et al.: Measurement of (p, p) elastic differential cross-sections for carbon, nitrogen, oxygen, aluminium and silicon in the 500–2500 keV range at 140° and 178° laboratory scattering angles. Nucl. Instr. Meth. Phys. Res. B 190, 95 (2002)
Dubovichenko, S.: Thermonuclear processes of the Universe, NOVA Sci. Publ. (2012) https://www.novapublishers.com/catalog/product info.php? products id=31125
Dubovichenko, S.B.: Primordial nucleosynthesis of the Universe, 4th edition revised and expanded, KG: Lambert Acad. Publ. GmbH & Co., Germany (2014)
Dubovichenko, S.B., Uzikov, Yu., N.: Astrophysical S factors of reactions with light nuclei. Phys. Part. Nucl. 42, 251 (2011)
Dubovichenko, S.B.: Neutron capture by light nuclei at astrophysical energies. Phys. Part. Nucl. 44, 803 (2013)
Dubovichenko, S.B., Dzhazairov-Kakhramanov, A.V.: Examination of the astrophysical s-factors of the radiative proton capture on 2H, 6Li, 7 Li, 12C AND 13C. Int. Jour. Mod. Phys. E 21, 1250039 (2012)
Dubovichenko, S.B., Dzhazairov-Kakhramanov, A.V., Afanasyeva, N.V.: Radiative neutron capture on 9Be, 14C, 14N, 15N and 16O at thermal and astrophysical energies. Int. Jour. Mod. Phys. E 22, 1350075 (2013)
Dubovichenko, S.B., Dzhazairov-Kakhramanov, A.V., Burkova, N.A.: the radiative neutron capture on 2H, 6Li, 7Li, 12C AND 13C at astrophysical energies. Int. Jour. Mod. Phys. E 22, 1350028 (2013)
Dubovichenko, S.B., Dzhazairov-Kakhramanov, A.V.: Int. Jour. Mod. Phys. E 23, 1430012 (2014)
Bhoi, J., Laha, U.: Supersymmetry-inspired low-energy α–p elastic scattering phases. Theor. Math. Phys. 190, 69 (2017)
Bhoi, J., Laha, U.: Hulthén potential models for α−α and α−He3 elastic scattering. Pramana-J. Phys. 88, 42 (2017)
van Haeringen, H., van Wageningen, R.: Analytic T matrices for Coulomb plus rational separable potentials. J. Math. Phys. 16, 1441 (1975)
Haidenbauer, J., Plessas, W.: Separable approximations of two-body interactions Phys. Rev. C 27, 63 (1983)
Sahoo, P., Laha, U., Khirali, B.: Studies in scattering using Manning–Rosen-modified separable potential in all partial waves. Pramana-J. Phys. 96, 201 (2022)
Sahoo, P., et al.: Half-Shell T-Matrix for α-p and α-12C Scattering. Braz J. Phys. 51, 1478 (2021)
Laha, U.: Off-shell Jost solution for a Coulomb-like potential. Phys. Rev. A 74, 12710 (2006)
Laha, U.: An integral transform of Green’s function, off-shell Jost solution and T-matrix for Coulomb-Yamaguchi potential in coordinate representation. Pramana-J. Phys. 72, 457 (2009)
Laha, U.: Coulomb-modified Nuclear Scattering-off the energy shell. Lambert Academic Publishing, Saarbrücken (2010)
Laha, U., Bhoi, J.: Off-shell Jost solutions for Coulomb and Coulomb-like interactions in all partial waves. J. Math. Phys. 54, 013514 (2013)
Laha, U., Bhoi, J.: Integral transform of the Coulomb Green’s function by the Hankel function and off-shell scattering. Phys. Rev. C 88, 064001 (2013)
Laha, U., Bhoi, J.: Hadron-hadron scattering within the separable model of Interactions. Scholars’ Press, Beau Bassin (2018)
Sahoo, P., Laha, U.: Exact solutions of the Schrödinger equation for Manning-Rosen plus Yamaguchi potential. Phys. Scr. 96, 095302 (2021)
Sahoo, P., Laha, U., Khirali, B.: On the p−2H1 and p−16O elastic scattering. Pramana-J. Phys. 95, 209 (2021)
Sahoo, P., Laha, U., Behera, A.K.: p-12C and p−d Scattering within the Separable Model of Interaction. Phys. Atom. Nuclei 83, 802 (2020)
Sahoo, P., Laha, U.: Nucleon–nucleus inelastic scattering by Manning-Rosen distorted nonlocal potential. Canadian J Physics 100, 68 (2022)
Behera, A.K., Sahoo, P., Khirali, B., Laha, U.: Fredholm determinants for the Hulthén-distorted separable Potential. Pramana-J. Phys. 95, 100 (2021)
Sarkar, P., Khirali, B., Laha, U., Sahoo, P.: Exact solution of two-potential system under same range approximation and its implication. Int. J. Mod. Phys. E 30, 2150066 (2021)
Sahoo, P., Laha, U.: Treatment of hadronic systems involving two potentials under a new approximation scheme. Pramana-J. Phys. 96, 15 (2022)
Qiang, W.C., Dong, S.H.: Analytical approximations to the solutions of the Manning– Rosen potential with centrifugal term. Phys. Lett. A 368, 13 (2007)
Dong, S.H., Garcia-Ravelo, J.: Exact solutions of the s-wave Schrödinger equation with Manning-Rosen potential. Phys. Scr. 75, 307 (2007)
Diaf, A., Chouchaoni, A., Lombard, R.L.: Feynman integral treatment of the Bargmann potential. Ann. Phys. (Paris) 317, 354 (2005)
Qiang, W.C., Li, K., Chen, W.L.: New bound and scattering state solutions of the Manning-Rosen potential with the centrifugal term. J. Phys. A: Math. Theor. 42, 205306 (2009)
Manning, M.F., Rosen, N.: A potential function for the vibrations of diatomic molecules. Phys. Rev. 44, 953 (1933)
Berkdemir, C., Han, J.: Any l-state solutions of the Morse potential through the Pekeris approximation and Nikiforov-Uvarov method. Chem. Phys. Lett. 409, 203 (2005)
Hulthén, L.: On the characteristic solutions of the Schrödinger deuteron equation. Ark. Met. Astron. Fys. A 28, 5 (1942)
Sahoo, P., Laha, U., Khirali, B.: Hulthén off-shell transition matrix for nuclear systems. Chinese J. Phys. 73, 561 (2021)
Sahoo, P., Laha, U., Khirali, B., Behera, A.K.: THE ANALYTIC T-MATRIX FOR THE HULTHÉN POTENTIAL IN ALL PARTIAL WAVES. Rep. Math. Phys. 88, 295 (2021)
Slater, L.J.: Generalized Hypergeometric Functions. Cambridge University Press, London (1966)
Erdeyli, A.: Higher Transcendental Functions, vol. 1. Mc-Graw-Hill, New York (1953)
Arfken, G.: Mathematical Methods for Physicists. Acad. Press, New York (1985)
Talukdar, B., Laha, U., Das, U.: Integral representations of the Jost function. Phys. Rev. A 43, 1183 (1991)
Magnus, W., Oberhettinger, F.: Formulae and Theorems for the Special Functions of Mathematical Physics. Chelsea, New-York (1949)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals. Series and Products Academic Press, London (2000)
Jost, R.: Uber diefalschen Nullstellen der Elgen werteder S-matrix. Helv. Phys. Acta 20, 256 (1947)
Newton, R.G.: Scattering theory of waves and particles, 2nd edn. Springer Verlag, New York (1982)
Taylor, J.R.: The Quantum Theory of Non-relativistic Collisions. Dover Publications, Inc., Mineola, New York (2000)
Calogero, F.: Variable Phase Approach to Potential Scattering. Academic, New York (1967)
Laha, U., Kundu, B.: Off-shell Jost solution for scattering by a Coulomb field. Phys. Rev. A 71, 032721 (2005)
Laha, U.: Off-shell Jost solution for the Hulthén potential. Few-body syst. 59, (2018) Art. 68
Bhoi, J., Behera, A.K., Laha, U.: Off-shell Jost function for the Hulthén potential in all partial waves. J. Math. Phys. 60, 083502 (2019)
Khirali, B., Behera, A.K., Bhoi, J., Laha, U.: Regular and Jost states for the S-wave Manning-Rosen potential. J. Phys. G: Nucl. Part. Phys. 46, 115104 (2019)
Khirali, B., Behera, A.K., Bhoi, J., Laha, U.: On- and off-shell Jost functions for the Manning-Rosen potential. Phys. Scr. 95, 075308 (2020)
Behera, A.K., Laha, U., Majumder, M., Bhoi, J.: Applicability of phase equivalent energy-dependent potential-Case studies. Phys. Atom Nuclei 85, 124 (2022)
Navarro Pérez, R., Amaro, J.E., Ruiz Arriola, E.: The low-energy structure of the nucleon–nucleon interaction: statistical versus systematic uncertainties. J. Phys. G: Nucl. Part. Phys. 43, 114001 (2016)
Khirali, B., Laha, U., Sahoo, P.: Analytic transition matrix for the Manning-Rosen potential in all partial waves. Chinese J. Phys. 77, 2355 (2022)
Sahoo, P., Laha, U., Khirali, B., Bhoi, J.: Treatment of inelastic scattering within the separable interaction model. Pramana – J. Phys. 96, (2022) Art. 217
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P.S. and B.S. wrote the main manuscript text. U.L. prepared figures 1-3. All authors reviewed the manuscript.
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Sahoo, P., Swain, B. & Laha, U. Elastic Scattering of Proton from Oxygen at Astrophysical Energies. Int J Theor Phys 62, 129 (2023). https://doi.org/10.1007/s10773-023-05391-z
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DOI: https://doi.org/10.1007/s10773-023-05391-z