Phase Shift Analysis for Alpha-alpha Elastic Scattering using Phase Function Method for Gaussian Local Potential




α-α scattering, Variational Monte-Carlo (VMC), Matrix methods, Phase Function Method (PFM)


The phase shifts for α- α scattering have been modeled using a two parameter Gaussian local potential. The time independent Schrodinger equation (TISE) has been solved iteratively using Monte-Carlo approach till the S and D bound states of the numerical solution match with the experimental binding energy data in a variational sense. The obtained potential with best fit parameters is taken as input for determining the phase-shifts for the S channel using the non-linear first order differential equation of the phase function method (PFM). It is numerically solved using 5th order Runge-Kutta (RK-5) technique. To determine the phase shifts for the ℓ=2 and 4 scattering state i.e. D and G-channel, the inversion potential parameters have been determined using variational Monte-Carlo (VMC) approach to minimize the realtive mean square error w.r.t. the experimental data.


Download data is not yet available.


B. Buck, H. Friedrich and C. Wheatley, Nuclear Physics A 275, 246 (1977).

S .A. Afzal, A. A. Z. Ahmad and S. Ali, Reviews of Modern Physics 41, 247 (1969).

P. Darriulat, G. Igo, H.G. Pugh and H.D. Holmgren, Physical Review 137, B315 (1965).

S. Ali and A.R. Bodmer, Nuclear Physics 80, 99 (1966).

A.K. Jana, J. Pal, T. Nandi and B. Talukdar, Pramana 39, 501 (1992).

M. Odsuren, K. Kato, G. Khuukhenkhuu and S. Davaa, Nuclear Engineering and Technology 49, 1006 (2017).

M. Gell-Mann and M.L. Goldberger, Physical Review 91, 398 (1953).

R. Jost and A. Pais, Physical Review 82, 840 (1951).

F. Calogero, American Journal of Physics 36, 566 (1968).

V. V. Babikov, Soviet Physics Uspekhi 10, 271 (1967).

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

J. Bhoi and U. Laha, Pramana 88, 42 (2017).

A.K. Behera, J. Bhoi, U. Laha and B. Khirali, Communications in Theoretical Physics 72, 075301 (2020).

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

U. Laha, M. Majumder and J. Bhoi, Pramana 90, 48 (2018).

O.S.K.S. Sastri, Phys. Educ. 36, 1 (2020). [Google Scholar]

A. Sharma and O.S.K.S. Sastri, Eur. J. Phys. 41, 055402 (2020).

A. Sharma, S. Gora, J. Bhagavathi and O.S.K.S. Sastri, American Journal of Physics 88, 576 (2020).

A. Sharma and O.S.K.S. Sastri (2020).

G.N. Watson, Theory of Bessel Functions (Cambridge University Press, 1945).




How to Cite

Khachi, A.; Sastri, O.; Kumar, L. .; Sharma, A. Phase Shift Analysis for Alpha-Alpha Elastic Scattering Using Phase Function Method for Gaussian Local Potential. J. Nucl. Phy. Mat. Sci. Rad. A. 2021, 9, 1-5.