Effective Range Approximation in Variable Phase Approach for Triplet 3S1{np}^3S_1^{\{np\}} and Singlet 1S0{nn,np,pp}^1S_0^{ \{nn, np, pp\}} State

This work is a short communication where phase function method has been applied to obtain the phase shifts using Effective Range Approximation potential for $^3S_1-np$, $^1S_0-nn$, $^1S_0-np$, and $^1S_0-pp$ states. No free fitting parameters are used in calculations and reasonably good match with the experimental phase shifts is observed for E $\leq$ 20 MeV. Potentials are obtained for n-n, n-p, and p-p scattering that are exponential well-shaped.Comment: 9 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2309.1678

Phase shift, Amplitude and Wavefunctions for np-system using Morse Potential by Calogero's Approach

Phase shift(delta(r)), Amplitude(A(r)) and Wave function(u(r)) vs r (in fm) curves for various channels (S, P and D) of n-p scattering have been calculated using phase function method (PFM) method. To do this, inverse potentials obtained using the Morse function as the zeroth reference potential is employed. Recently, the GRANADA group published a comprehensive partial wave analysis of scattering data, consisting of 6713 np phase shift data points from 1950 to 2013. Using the final experimental data points from GRANADA we obtained the parameters for Morse potential by minimizing mean square error (MSE) as the cost function. Various quantum functions i.e. delta(r), A(r) and u(r) are described upto 5fm with energies Elab = [1, 10, 50, 100, 150, 250, 350].Comment: 15 pages, 7 figure

Low Energy S-Wave Proton-Deuteron Scattering Phase-Shifts using Morse Potential

Background: Study of nucleon-nucleus interaction is important to understand the stabilityof nuclei. At small lab energies ≈ 1-10 MeV, the three body 3He system can be considered asa combination of proton and deuteron two body system. The two body system can be modeled by a local central potential along with Coulomb potential to obtain phase-shifts.Purpose: Molecular Morse potential has been successfully able to calculate scattering phaseshifts of neutron-Deuteron (3He). The main objective of this paper is to test if Morse potential proves to be a good interaction potential to study proton-Deuteron (3He) scattering as well. Methods: The phase function method is solved numerically using RK-5 method for determining the S-wave scattering phase shifts (SPS) for proton-deuteron (p-D) scattering as afunction of proton laboratory energy ranging from 1-10.4 MeV. The model paramters of Morse potential have been varied to obtain best mean absolute percentage error (MAPE) w.r.t. experimental data.Results: The calculated SPS are found to have MAPE less than 3 percent w.r.t experimental phase shifts. Partial scattering cross-section has been determined using the obtained SPS.Conclusions: Morse potential has been found to be successful in explaining interactionbetween proton and deuteron

3He-α Elastic Scattering Phase Shifts in Various Channels Using Phase Function Method with Morse Potential

Background: Typically 3He-α reaction has been modeled using Gaussian and Hulthen potentials without incorporating the non-local spin-orbit interaction.Purpose: To obtain the scattering phase shifts (SPS) for α-3He radiative capture reaction for partial waves with total angular momentum J = 1/2, 3/2, 5/2, 7/2 having negative parities and J = 1/2 with positive parity, using Morse potential as the model of interaction along with the associated spin-orbit term.Methods: Phase function method is employed for determining phase shifts in an iterative fashion, by making changes to model parameters, to ensure minimisation of mean absolute percentage error (MAPE) w.r.t. the experimental SPS. Results: SPS have been obtained for 1/2+, 1/2-, 3/2-, 5/2- and 7/2- with MAPE values of 3.2, 1.0, 0.8, 17.6 and 6.5 respectively. The corresponding interaction potentials and partial cross-sections have been plotted. The resonance frequencies for the 5/2- and 7/2- scattering states are closely matching with experimental ones.Conclusions: The interaction potentials for different ℓ-channels of 7Be have been constructed by considering Morse potential and spin-orbit terms by considering experimental scattering phase shifts for 3He-alpha reaction

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

Background: The nucleon-nucleus scattering has been studied using Gaussain potential withspin-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 elasticSPS in various channels.2. To compute the partial cross-sections for scattering p-states and the total cross-section forthe reaction.Methods: The local interaction potential is modeled using Gaussian function. The non-localspin 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.Results: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 areasonably good choice for explaining the n-α scattering reaction

Triton Scattering Phase-Shifts for S-wave using Morse Potential

In this paper, the phase-shifts for neutron-dueteron (n-d) scattering have been determined using the molecular Morse potential as theoretical model of interaction. The Triton (n-d) 2S1/2 ground state initially has been chosen as -7.61 MeV to determine the model parameters using variational Monte-Carlo technique in combination with matrix methods numerical approach to solving the time independent Schrodinger equation (TISE). The obtained potential is incorporated into the phase function equation, which is solved using Runge-Kutta (RK) 4,5 order technique, to calculate the phaseshifts at various lab energies below 15 MeV, for which experimental data is available. The results have been compared with those obtained using another molecular potential named Manning-Rosen (MR) and have been observed to fare better. Finally, the Triton ground state has been chosen as its binding energy (BE), given by -8.481795 MeV, as determined from experimental atomic mass evaluation data and the calculations are repeated. It has been found that these phase-shifts from BE data are slightly better matched with experimental ones as compared to those obtained using -7.61 MeV ground state for Triton (n-d two-body system) modeled using Morse potential

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

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

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

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