Phase Shift Analysis for Neutron-Alpha Elastic Scattering Using Phase Function Method with Local Gaussian Potential


  • Lalit Kumar Central University of Himachal Pradesh
  • Anil Khachi
  • Prof. O.S.K.S Sastri,



n-α scattering, Phase Function Method (PFM), Gaussian potential, cross-section


Background: The nucleon-nucleus scattering has been studied using Gaussain potential with
spin-orbit term of Thomas type to fit the experimental scattering phase shifts (SPS). Recently,
Hulthen potential without spin-orbit term has been utilised for studying α–nucleon scattering with phase function method (PFM).
Purpose: The main objectives of this paper are:
1. To obtain the best possible interaction potentials that best describe the neutron-α elastic
SPS in various channels.
2. To compute the partial cross-sections for scattering p-states and the total cross-section for
the reaction.
Methods: The local interaction potential is modeled using Gaussian function. The non-local
spin orbit term is chosen to be proportional to derivative of local potential. The phase function method has been numerically solved using 5th order Runge-Kutta method to compute the SPS. The model parameters are varied in an iterative fashion to minimise the mean absolute percentage error (MAPE) w.r.t. the experimental SPS.
1. The SPS for S, P and D channels have been obtained with MAPE values less than 3%.
2. The partial cross-sections for p 1/2 and p 3/2 have been plotted and the respective resonance energies and FWHM have been found to be in reasonable agreement with values in literature.
3. The total cross-section for the reaction has been determined and found to be matching well with experimental findings.
Conclusions: Gaussian potential with associated spin-orbit term has been shown to be a
reasonably good choice for explaining the n-α scattering reaction.


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Author Biographies

Anil Khachi,

Research Scholar at Central University of Himachal Pradesh

Prof. O.S.K.S Sastri,,

Prof. of Physics, DPAS, Central University of Himachal Pradesh


T.A. Tombrello and G.C. Phillips, Nucl. Phys., 20, 648-662, (1960).

A.N. Mitra, V.S. Bhasin and B.S. Bhakar, Nuclear Physics (Netherlands) Divided into Nucl.

Phys. A and Nucl. Phys. B, 38, 316-321, (1962).

E. van der Spuy, Nucl. Phys., 8, 381-414 (1956).

H. Kanada, S. Naagata, S. Otsuki, and Y. Sumi, Prog. Theor. Phys., 30, 475-493, (1963).

P.E. Hodgson, Adv. Phys., 25, 1-39, (1958).

C.L. Critchfield and D.C. Dodder, Phys. Rev., 76, 602, (1949).

J.L. Gammel and R.M. Thaler, Phys. Rev., 109, 2041, (1958).

L. Brown, W. Haeberli and W. Tr ¨ achslin, Nucl. Phys. A, 90, 339-352, (1967).

A. Houdayer et al., Phys. Rev. C, 18, 1985, (1978).

J. Berger et al., Phys. Rev. Lett., (1976); Erratum, 37, 1651, (1976).

L.G. Votta, P.G. Roos, N.S. Chant and R. Woody, Phys. Rev. C, 10, 520–528, (1974).

Y.C. Tang, in Topic in Nuclear Physics II, Lecture Notes in Physics, 145, 571-692, (1981).

R. Kamouni and D. Baye, Nucl. Phys. A, 791, 68-83, (2007).

G.R. Satchler, L.W. Owen, A.J. Elwyn, G.L. Morgan, and R.L. Walter, Nucl. Phys. A, 112,

, (1968).

J. Dohet-Eraly and D. Baye, Phys. Rev. C, 84, 014604 (2011)

G.L. Morgan and R.L. Walter, Phys. Rev., 168, 1114, (1968).

U. Laha and J. Bhoi, Phys. Rev. C, 91, 034614, (2015).

J. Bhoi and U. Laha, Brazilian Journal of Physics, 46, 129-132, (2016).

A.K. Behera, J. Bhoi, U. Laha and B. Khirali, Commun. Theor. Phys., 72, 075301, (2020).

B. Buck, H. Friedrich, C. Wheatley, Nucl. Phys. A, 275, 246-268, (1977).

S.Y. Igashov, A.M. Shirokov, Bull. Russ. Acad. Sci. Phys., 71, 769–775 (2007).

A. Khachi, L. Kumar, A. Sharma and O.S.K.S. Sastri, J. Nucl. Phys. Mat. Sci. Rad. A., 9,

-5, (2021).

A. Sharma and O.S.K.S. Sastri,Int. J. Quantum Chem., 121, e26682, (2021).

A. Bohr and B.R. Mottelson, Nuclear Structure (World Scientific, Singapore, 1998).

F. Calogero, American Journal of Physics, (1968).

V.V. Babikov, Sov. Phys. Usp., 10, 271, (1967).

P.M. Morse, W.P. Allis, Phys. Rev., 44, 269, (1933).

M. Odsuren, K. Katō, M. Aikawa and T. Myo, Phys. Rev. C., 89, 034322, (2014).

A. Csoto and G.M. Hale, Phys. Rev. C, 55, 536, (1997).

J.E. Bond and F.W.K. Firk, Nucl. Phys. A, 287, 317-343, (1977).

A.I. Mazur et al, Phys. Rev. C, 79, 014610, (2008).

K. Shibata, J. Nucl. Sci. Technol., 27, 81-88, (1990).




How to Cite

Kumar, L.; Khachi, A.; Sastri, O. Phase Shift Analysis for Neutron-Alpha Elastic Scattering Using Phase Function Method With Local Gaussian Potential. J. Nucl. Phy. Mat. Sci. Rad. A. 2022, 9, 215-221.