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Background: The study of np and pp scattering, central to understanding nuclear force, remains an optional topic in many undergraduate nuclear physics curriculum. Purpose: The main thrust of this paper is to study pp scattering using the phase function method to obtain the observed S-wave phase shifts and cross-sections at various energies. Methods: The pp interaction has been modeled by choosing the Malfliet-Tjon potential for the nuclear part along with the screened Coulomb potential. The phase equation has been solved to obtain scattering phase shifts using the fourth-order RK method (RK-4). Results: The interaction potential obtained from optimized parameters matches well with the realistic Argonne V18 potential for 1S0 state of pp scattering and the scattering phase shifts as well as the cross-section for energies ranging from 1-350 MeV are in good agreement with expected data. Conclusion: Introducing the phase function method for S-wave (l=0) could bring this interesting study of nucleon-nucleon scattering to the undergraduate classroom., Comment: 18, 5 Figures, 2 Tables

An algorithm$^{\ref{Fig1}}$ has been developed with the purpose of obtaining inverse potentials, where the Riccati-type non-linear differential equation, also called phase equation, has been kept in tandem with the Variational Monte Carlo method. The optimization of Gaussian function parameters is achieved such that the experimental phase shifts are reproduced. The obtained SPS for various $\ ell$ channels has been compared with experimental ones with mean absolute percentage error (MAPE) as a measure. The model parameters have been optimised by suitable optimisation technique by looking for minimum value of MAPE. The results for $\ell$=0$^+$, 2$^+$ and 4$^+$ partial waves have been obtained, to match with experimental SPS, with MAPE values of $2.9$, $4.6$ and $6.2$ respectively for data up to $23$ MeV, while for higher states 6$^+$, 8$^+$ and 10$^+$ has MAPE of $3.2, 4.5$ and $5.9$ respectively for data from $53-120$ MeV. On extrapolation for data in range E$_{\ell ab.}$ = $23-120$ MeV, using the optimised parameters, the SPS are found to be in close agreement with experimental ones for the first three channels., Comment: 18 pages, 7 figures, 25 references

In this article, we propose a numerical approach to solve quantum mechanical scattering problems, using phase function method, by considering neutron-proton interaction as an example. The nonlinear phase equation, obtained from the time-independent Schrodinger equation, is solved using the Runge-Kutta method for obtaining S-wave scattering phase shifts for neutron-proton interaction modeled using Yukawa and Malfliet-Tjon potentials. While scattering phase shifts of S-states using Yukawa match with experimental data for only lower energies of 50 MeV, Malfliet-Tjon potential with repulsive term gives very good accuracy for all available energies up to 350 MeV. Utilizing these S-wave scattering phase shifts, low energy scattering parameters, and total S-wave cross section have been calculated and found to be consistent with experimental results. This simulation methodology can be easily extended to study scattering phenomenon using phase wave analysis approach in the realms of atomic, molecular, and nuclear physics., Comment: 19 pages, 6 figures, 2 Tables

The neutron-deuteron (nd) and proton-deuteron (pd) scattering are the simplest nucleon-nucleus scenario which throws light on understanding few body systems. In this work, real and imaginary parts of scattering phase shifts (SPS) for nd and pd scattering are obtained using optical potential, with Malfliet-Tjon (MT) model of interaction, by phase function method (PFM). The SPS for doublet 2S1/2 and quartet 4S3/2 states of nd and pd systems have been obtained for real and imaginary parts separately by solving the phase equation for l= 0, using Runge-Kutta 5 th order technique for laboratory energies up to 19 M eV . The obtained (real,imaginary) SPS for 2S1/2 and 4S3/2 states are matching with standard data with mean absolute error (MAE) of (1.32, 0.06) for 2S1/2 state and (0.19, 0.06) for 4S3/2 state of nd scattering, (1.47,0.62) for 2S1/2 state and (0.55, 0.14) for 4S3/2 state of pd scattering., Comment: 13 pages, 4 Figures and 3 Tables

The neutron and proton scattering with either deuteron or stable alpha particle can be modeled as a two particle system. In this paper, using Morse function as reference potential, inverse potentials have been computationally constructed directly from scattering phase shifts (SPS) data for light nucleon-nucleus systems. The phase equation for various l-channels has been numerically solved using 5th order Runge-Kutta (RK-5) method in each iteration within the optimization procedure to obtain best model parameters of Morse function that minimize mean absolute percentage error (MAPE). The inverse potentials for S-wave of neutron-deuteron and proton-deuteron systems have been obtained with MAPE of 1.95 and 2.05% respectively. Those corresponding to various P and D channels of neutron-alpha(n-alpha) and proton-alpha(p-alpha) systems, have been determined to less than 1.53 and 2.17% respectively. The obtained(experimental) resonance energies for p1/2 and p3/2, from their partial cross-sections plots, respectively are 4.1(4) and 0.93(0.89) for n-alpha and 5.21(5) and 1.96(1.96) for p-alpha system. While total cross-section for n-alpha has been found to be matching with values available in literature, that of p-alpha is seen to be following the correct trend., Comment: 8 pages, 8 figures, 2 Tables

Single particle energy states as described by nuclear shell model are obtained for doubly magic nuclei using Gnumeric worksheet environment. Numerov method rephrased in matrix form is utilised to solve time-independent Schrodinger equation (TISE) within mean-field approximation, described by Woods-Saxon (WS) potential along with spin-orbit term, to obtain the single particle energies for both neutron and proton states. The WS model parameters are chosen from previous simulation results performed using matrix methods technique involving sine basis, where optimization was done w.r.t available experimental single particle energies for 208Pb and 48Ca. In this paper, only the algorithm parameters, step size h and matrix size N are optimized to obtain the expected energy level sequence obtained using matrix methods. An attempt is made, by incorporating this tool within the framework of guided inquiry strategy (a constructivist approach to learning), to actively engage the students in assigning appropriate spin-parity configurations for ground states of nuclei neighbouring the doubly magic ones. It has been observed that the ground state configurations could be better predicted when energy level sequences are known for all nuclei as compared to what is usually obtained from that of 208Pb alone., Comment: 17 pages, 2 Figures, 4 Tables

Dimension-5 photon ($\gamma$) scalar ($\phi$) interaction terms usually appear in the Lagrangian of bosonic sector of unified theories of electromagnetism and gravity. This interaction makes the medium dichoric and induces optical activity. We have modelled the propagation of photons with this interaction in the environment of cold a magnetized compact star (White Dwarf (WD) or Neutron Star (NS)), assuming synchro-curvature process as the dominant mechanism of emission. We have tried to outline the polarimetric implications of photon-scalar coupling on the produced spectrum of these emissions in the stellar atmosphere. Further more assuming the 'emission-energy vs emission-altitude' relation, that is believed to hold in such (i.e. cold magnetized WD or NS) environments, we have tried to point out the possible modifications to the radiation spectrum when the same is incorporated along with dim-5 photon scalar mixing operator., Comment: Minor modifications, references added, 20 pages, 4 figures