Study of np-scattering for S, P and D Waves using Deng-Fan Potential by Phase Function Method

In this paper, the np - scattering phase shifts and cross section for S,P and D partial waves have been obtained for energies below the pion threshold, by considering Deng-Fan potential as model of interaction. The radial time independent Schr\"odinger equation has been analytically solved using Nikiforov - Uvarov method to obtain the energy expression for ground state of np system. Utilising this, the scattering phase shifts for $^3S_1$ have been obtained using phase function method. The phase equations for various scattering states $^1S_0$, $^1P_1$, $^3P_{0,1,2}$, $^1D_2$, and $^3D_{1,2,3}$ have been numerically solved for obtaining corresponding scattering phase shifts and their respective partial cross section. The total scattering cross sections computed at various energies are found to be closely matching with experimental data. The low energy scattering parameters determined from scattering phase shifts of $^3S_1$ and $^1S_0$ are reasonably close to experimental ones. Hence, Deng-Fan potential is a good phenomenological potential to understand the np - scattering system.Comment: 11 pages, 4 figures, 2 table

Comparative Study of alpha-alpha interaction potentials constructed using various phenomenological models

In this paper, we have made a comparative study of alpha-alpha scattering using different phenomenological models like Morse, double Gaussian, double Hulthen, Malfliet-Tjon and double exponential for the nuclear interaction and atomic Hulthen as screened coulomb potential. The phase equations for S, D and G channels have been numerically solved using 5th order Runge-Kutta Method to compute scattering phase shifts for elastic scattering region consisting of energies up to 25.5 MeV. The model parameters in each of the chosen potentials were varied in an iterative fashion to minimize the mean absolute percentage error between simulated and expected scattering phase shifts. A comparative analysis revealed that, all the phenomenological models result in exactly similar inverse potentials with closely matching mean absolute percentage error values for S, D and G state. One can conclude that any mathematical function that can capture the basic features of two body interaction would always guide correctly in construction of inverse potentials.Comment: 11 pages, 3 figures, 4 Table

Constructing Inverse Scattering Potentials for {\alpha}-{\alpha} System using Reference Potential Approach

Background: An accurate way to incorporate long range Coulomb interaction alongside short-range nuclear interaction has been a challenge for theoretical physicists. Purpose: In this paper, we propose a methodology based on the reference potential approach for constructing inverse potentials of alpha-alpha scattering. Methods: Two smoothly joined Morse potentials, regular for short-range nuclear interaction and inverted for long range Coulomb, are used in tandem as a reference potential in the phase function method to obtain the scattering phase shifts for the S, D and G states of alpha-alpha scattering. The model parameters are optimized by choosing to minimize the mean absolute percentage error between the obtained and experimental scattering phase shift values. Results: The constructed inverse potentials for S, D and G states have resulted in mean absolute percentage errors of 0.8, 0.5, and 0.4 respectively. The obtained resonances for D and G states closely match the experimental ones. Conclusion: The reference potential approach using a combination of smoothly joined Morse functions is successful in accurately accounting for the Coulomb interaction between charged particles in nuclear scattering studies.Comment: 10 pages, 4 figures, 2 Table

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

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

Inverse Potentials for all l-channels of Neutron-Proton Scattering using Reference Potential Approach

Reference potential approach (RPA) is successful in obtaining inverse potentials for weakly bound diatomic molecules using Morse function. In this work, our goal is to construct inverse potentials for all available l-channels of np-scattering using RPA. The Riccati-type phase equations for various l-channels are solved using 5th order Runge-Kutta method to obtain scattering phase shifts (SPS) in tandem with an optimization procedure to minimize mean squared error (MSE). Interaction potentials for a total of 18 states have been constructed using only three parameter Morse interaction model. The obtained MSE is < 1% for 1S0 , 3P1 and 3D1 channels and < 2% for 1P1 channel and < 0.1% for rest of the 14 channels. The obtained total scattering cross-sections at various lab energies are found to be matching well with experimental ones. This phase wave analysis study of all channels of np-scattering using RPA has been undertaken using Morse function as zeroth reference, by us, is for the first time.Comment: 10 pages, 4 Figures and 2 Table

Recalculated Viola-Seaborg Coefficients for Partial Alpha Half-lives Based on AME2016

In this paper, the systematics for obtaining the Viola-Seaborg formula (VSF) for logarithmic partial alpha half-lives (Tα1/2) have been undertaken based on the NUBASE2016 evaluation. The constants Az and Bz in Geiger-Nuttal law for determination of Tα1/2  , are obtained using gs-gs transitions data, of even-even nuclei for two sets of nuclei with Z = 84 - 102 and Z = 86 - 98 with N &gt; 126. The Viola-Seaborg co-efficients are determined for both the sets. The obtained parameters for both sets are tested on even-even nuclei for Z ranging from 104 - 118 and it is observed that first set parameters fare better. This formula for estimating α-decay half-lives of heavy nuclei can be extrapolated to predict those of super-heavy nuclei. The logarithmic half-lives Tα1/2 obtained for isotopes of Z = 121 and 122 using current modified VSF (AME2016) are compared with those obtained from theoretical considerations using Coulomb and proximity potential model (CPPM) and observed to be much larger. They are also much larger than those obtained from the previous coefficients based on AME2003 data

Deuteron Structure and Form Factors: Using Inverse Potentials for S-waves

In this paper, we determine deuteron's static properties, low energy scattering parameters, total cross-section and form factors from inverse S-wave potentials constructed using Morse function. The scattering phase shifts (SPS) at different lab energies are determined using phase function method. The model parameters are optimised using both machine learning algorithm and traditional data analysis by choosing mean squared error as cost function. The mean absolute error between experimental and obtained SPS for states 3S1 and 1S0 are found to be 0.35 and 0.70 respectively. The low energy scattering parameters are matching well with expected values. The contribution due to S-waves SPS towards total cross-section at various energies have been obtained and are matching well with experimental values. The analytical ground state deuteron wave-function (DWF) is obtained by utilizing the experimental value for Quadrupole moment. Other static properties and form factors determined from obtained DWF are found to be in close agreement with experimental ones.Comment: 29 pages, 5 Figures, 8 Table