Neutron-Proton Scattering Phase Shifts in S-Channel using Phase Function Method for Various Two Term Potentials

Authors

DOI:

https://doi.org/10.15415/jnp.2021.91015

Keywords:

n-p Scattering, Phase Function Method (PFM), Matrix Methods

Abstract

The scattering phase shifts for n-p scattering have been modeled using various two term exponential type potentials such as Malfliet-Tjon, Manning-Rosen and Morse to study the phase shifts in the S-channels. As a first step, the model arameters for each of the potentials are determined by obtaining binding energy of the deuteron using matrix methods vis-a-vis Variational Monte-Carlo (VMC) technique to minimize the percentage error w.r.t. the experimental value. Then, the first order ODE as given by phase function method (PFM), is numerically solved using 5th order Runge-Kutta (RK-5) technique, by substituting the obtained potentials for calculating phase shifts for the bound 3S1 channel. Finally, the potential parameters are varied in least squares sense using VMC technique to obtain the scattering phase-shifts for each of the potentials in the 1S0 channel. The numerically obtained values are seen to be matching with those obtained using other analytical techniques and a comparative analysis with the experimental values up to 300 MeV is presented.

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References

F. Gross and A. Stadler, Phys. Rev. C 78, 014005 (2008). https://doi.org/10.1103/PhysRevC.78.014005

R. A. Arndt et al., Phys. Rev. D 28, 97 (1983). https://doi.org/10.1103/PhysRevD.28.97

R. A. Arndt, R. H. Hackman and L. D. Roper, Phys. Rev. C 15, 1002 (1977). https://doi.org/10.1103/PhysRevC.15.1002

Y. Hideki, S. Sakata and M. Taketani, in proceedings of the Physico-Mathematical Society of Japan. 3rd Series (1938): 319-340.

J. Bhoi and U. Laha, Brazilian Journal of Physics 46, 129 (2016). https://doi.org/10.1007/s13538-015-0388-x

R. A. Malfliet and J. A. Tjon, Nuclear Physics A 127, 161 (1969). https://doi.org/10.1016/0375-9474(69)90775-1

A. K. Behera, J. Bhoi, U. Laha and B. Khirali, Communications in Theoretical Physics 72, 075301 (2020). https://orcid.org/0000-0003-4544-2358

C. Eckart, Physical Review 35, 1303 (1930). https://doi.org/10.1103/PhysRev.35.1303

P. M. Morse, Physical review 34, 57 (1929). https://doi.org/10.1103/PhysRev.34.57

N. Rosen and P. M. Morse, Physical Review 42, 192 (1932). https://doi.org/10.1103/PhysRev.42.210

A. M. Lane and R. G. Thomas, Reviews of Modern Physics 30, 257 (1958). https://doi.org/10.1103/RevModPhys.30.257

R. Jost and A. Pais, Physical Review 82, 840 (1951). https://doi.org/10.1103/PhysRev.82.840

M. Gell-Mann and M. L. Goldberger, Physical Review 91, 398 (1953). https://doi.org/10.1103/PhysRev.91.398

P. Darriulat, G. Igo, H. G. Pugh and H. D. Holmgren, Physical Review 137, B315 (1965). https://doi.org/10.1103/PhysRev.137.B315

S. Ali and A. R. Bodmer, Nuclear Physics 80, 99 (1966). https://doi.org/10.1016/0029-5582(66)90829-7

J. D. Reber and J. D. Brandenberger, Physical Review 163, 1077 (1967). https://doi.org/10.1103/PhysRev.163.1077

S. A. Afzal, A. A. Z. Ahmad and S. Ali, Reviews of Modern Physics 41, 247 (1969). https://doi.org/10.1103/RevModPhys.41.247

B. Buck, H. Friedrich and C. Wheatley, Nuclear Physics A 275, 246 (1977). https://doi.org/10.1016/0375-9474(77)90287-1

A. K. Jana, J. Pal, T. Nandi and B. Talukdar, Pramana 39, 501 (1992). https://doi.org/10.1007/BF02847338

F. Calogero, American Journal of Physics 36, 566 (1968). https://doi.org/10.1119/1.1975005

V. V. Babikov, Soviet Physics Uspekhi 10, 271 (1967). https://doi.org/10.1070/PU1967v010n03ABEH003246

P. Tischhauser et al., Phys. Rev. C 79, 055803 (2009). https://doi.org/10.1103/PhysRevC.79.055803

V. I. Zhaba, Journal of Physical Studies 19, 4201 (2015).

B. A. Jugdutt and F. Marsiglio, American Journal of Physics 81, 343 (2013). https://doi.org/10.1119/1.4793594

O. S. K. S. Sastri, Phys. Educ. 36, 1 (2020).

A. Sharma and O. S. K. S. Sastri, Eur. J. Phys. 41, 055402 (2020). https://doi.org/10.1119/10.0001041

A. Sharma, S. Gora, J. Bhagavathi and O. S. K. S. Sastri, American Journal of Physics 88, 576 (2020). https://orcid.org/0000-0003-1405-5283

A. Sharma and O. S. K. S. Sastri, (2020). https://indiarxiv.org/5a6by/

D. Hestenes, American Journal of Physics 55, 440 (1987). https://doi.org/10.1119/1.15129

O. S. K. S. Sastri, A. Sharma, J. Bhardwaj, S. Gora, V. Sharda and Jithin B. P., Physics Education 36, 1 (2020).

G. N. Watson, A treatise on the theory of Bessel functions (Cambridge: The University Press; New York, The Macmillan Company, 1944).

M. Naghdi, Physics of Particles and Nuclei 45, 924 (2014). https://doi.org/10.1134/S1063779614050050

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Published

2021-08-31

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