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.

Spin-dependant tunneling to the surface states of titanium dioxide

Results of the simulation of spin-dependant tunneling of electrons to the surface states of the titanium dioxide, which are created by adsorbed organic impurities are performed. Tunneling transparency for sunlight generated electrons is calculated by the Phase function method. A ferromagnetic film is considered to be an injector of spin-dependent electrons to the titanium dioxide. It is shown that electron spin polarization at the surface states reaches 10–25 %. It can contribute to the spin enhanced catalysis peeling a surface from organic impurities.

Field Emission in Silicon Vacuum Nanostructure

Transmission coefficient and field emission current in a silicon vacuum nanostructure with a pyramidal cathode were calculated as a function of applied voltage, size of the cathode and distance between the anode and cathode by the phase function method. The field emission current density in the range of 1–10 A/cm2 was found to be achieved by varying the distance between the anode and cathode in the range of 15–25[Formula: see text]nm and the applied voltage in the range of 1.2–2.3[Formula: see text]V.

Nucleon-Nucleon Potentials and Computation of Scattering Phase Shifts

<p>By judicious exploitation of supersymmetry formalism of quantum mechanics higher partial wave nucleon-nucleon potentials are generated from its ground state interactions. The nuclear Hulthen potential and the corresponding ground state wave function with the parameters of Arnold and MacKellar are used as the starting point of our calculation. We compute the scattering phase shifts for our constructed potentials through Phase Function Method to examine the merit of our approach to the problem.</p>