• U LAHA

Articles written in Pramana – Journal of Physics

• Equivalent potentials for a nonsymmetric non-local interaction

Scattering formalisms which incorporate antisymmetrization of the projectile with respect to identical particles in the target result in a nonsymmetric non-local interaction. Such an interaction constraints the relative wavefunctions to be orthogonal to redundant states forbidden by the Pauli principle. Concentrating on the nonsymmetric non-local kernel of Saito we try to visualize the mechanisms by which a potential can ensure the required orthogonality. We achieve this by replacing the Saito kernel by an effective symmetric non-local potential. The constructed symmetric potential is found to be phase-equivalent only but not off-shell equivalent to the original kernel. This difference in the off-shell behaviour is attributed to the dynamical origin simulating the redundant states. In close analogy with one of our recent works we also derive an energy-momentum dependent equivalent to the local potential. Our solution of the pseudo inverse problem is exact and provides a basis for writing the phase—and quasiphase—equations. We present numerical results in support of this.

• Half-shellT matrix for Coulomb-modified Graz separable potential

We construct a closed form expression for the off-shell Jost function for scattering by the Coulomb-distorted Graz separable potential and express it in the ‘maximal reduced form’. Our result is particularly suitable for numerical computation. We present a case study in support of this and examine the role of Coulomb interaction in thep — p half-shell scattering in the1S0 channel.

• Phase-function method for Hulthén-modified separable potentials

We have treated the Hulthén-modified separable potentials within the framework of the phase-function method and obtained a closed form expression fors-wave scattering phase shift. Specializing to a rank one separable potential we have found out the limiting conditions in which the Hulthén-modified phase shift goes over to its Coulomb counterpart. We demonstrate the usefulness of our approach by means of a model calculation.

• On the integral representations of the Jost function and Coulomb off-shell Jost solution

The integral representations of the Jost function (on- and off-shell) are rederived by the judicious use of the transposed operator relation on the particular integrals for Jost solution and using one of these particular integrals an analytical expression for the Coulomb off-shell Jost solution is presented in the maximal reduced form.

• Hulth$\grave{e}$n potential models for $\alpha−\alpha$ and $\alpha−He^3$ elastic scattering

Simple Hulth$\grave{e}$n-type potential models are proposed to treat the $\alpha−\alpha$ and $\alpha−He^3$ elastic scattering. The merit of our approach is examined by computing elastic scattering phases through the judicious use of the phase function method. Reasonable agreements in scattering phase shifts are obtained with the standard data.

• Volterra integral equation-factorisation method and nucleus–nucleus elastic scattering

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the $\alpha−\alpha$ system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.

• Potentials and phase shifts for nucleon–light nuclei systems

Two simple models based on the Coulomb-distorted phase function and supersymmetry-inspired factorisation methods are adapted to deal with the nucleon–light nuclei elastic scattering at low energies. The first one is associated with the derivation of a closed-form expression of the scattering phase shift for motionin Coulomb-distorted separable non-local potentials. The second one deals with the development of an energy dependent phase equivalent local potential to the non-local one for s-wave and its subsequent generation of higher partial wave interactions through the formalism of supersymmetric quantum mechanics. The usefulness of our models is demonstrated through the computation of α–nucleon scattering phase shifts at low energies up to partialwaves $\ell$ = 2. Certain energy-dependent correction factors are also incorporated into energy-dependent higher partial wave potentials to achieve an excellent agreement with the standard data.

• The Fredholm determinant for Hulthén-distorted non-local separable potential: Application to $\alpha-\alpha$ elastic scattering

Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthén-distorted non-local separable potential is constructed and expressed in the maximum reduced form. Using boundary conditions (regular and irregular), two approximate energy-dependent interactions corresponding to the parent non-local potential are also constructed. The phase shifts for the $\alpha–\alpha$ elastic scattering are computed by using (i) exact expression for the Fredholm determinant and (ii) energy-dependent local interactions by exploiting the phase function method. The merits of our constructed equivalent energy-dependent potentials are judged by comparing the $\alpha–\alpha$ elastic scattering phases with our exact calculation and standard data.

• Fredholm determinants for the Hulthén-distorted separable potential

By exploiting higher partial wave solutions for the Hulthén potential, constructed via the factorisation method, closed form analytical expressions of the Fredholm determinants for motion in Hulthén plus modified Graz separable potential are constructed to study on-shell scattering up to partial wave $\scr l$= 2. Phase shifts for different states of $\alpha-^3$H and $\alpha-^3$He are obtained by exploiting the expression of the Fredholm determinant. The results are found in reasonable agreement with the standard data (Spiger and Tombrello 1967).

• Phase equivalent Coulomb-like potential

An equivalent energy-dependent local potential corresponding to Coulomb plus Graz separable potential is constructed through simple rearrangement of the Schrödinger equation. It is conjectured that local Coulomb-like potential is equally applicable for the traditional phase function method. The merit of our constructed potential is thus judged by studying nucleon–nucleon and alpha–nucleon systems through the phase function method. Good agreement in phase shift values with standard data is achieved.

• Off-shell T-matrix for the Manning–Rosen potential

New analytical expressions for the off-shell wave functions and T-matrix with the Manning–Rosen potential are constructed in terms of generalised hypergeometric functions. The off-shell T-matrices are computed for the neutron–proton and neutron–deuteron systems. The limiting behaviours of our expression for the off-shellT-matrix are verified and found correct.

• On the p−$^2$H$_1$ and p−$^{16}$O elastic scattering

We solve the wave equation with the Manning–Rosen plus rank one separable non-local potential to obtain exact analytical solutions through ordinary differential equation method. The regular, Jost and physical state solutions are found to involve special functions of mathematics. As an application of the Jost function and Fredholm determinant, the bound-state energies and the scattering phase parameters for the p−$^2$H$_1$ and p−$^{16}$O systems are computed. The results achieved are in good agreement with the other methods published earlier.

• Treatment of hadronic systems involving two potentials under a new approximation scheme

In this work, exact analytical expressions for regular solution and on-shell Jost function are calculated for nuclear Hulthén plus atomic Hulthén potential by imposing the same range approximation to both nuclear andatomic potentials. In this context, the regular solution is utilised to find expressions for the off-shell Jost function and half-shell T -matrix. The half-off-shell T -matrix and the elastic scattering phase shifts for the nucleon–nucleon and nucleus–nucleus systems are computed. Our results are found to be in good agreement with the standard data.

• Phase-equivalent potentials using SUSY transformations

The approximate phase-equivalent potentials to Manning–Rosen one are constructed using supersymmetric algebra. Using the supersymmetric factorization method, four SUSY transformations T$_1$, T$_2$, T$_3$ and T$_4$ are operated in pairs on Manning–Rosen potential to construct three different phase-equivalent potentials. These methodologies are verified by computing scattering phase shifts for different partial waves of nucleon-nucleon and α–nucleon systems using the newly constructed phase-equivalent potentials. Good agreement with standard phase-shift data prove the merits of our approaches.

• Phase function method for Hulthén-distorted separable non-local potentials in all partial waves

The scattering phase parameters for short-range local potentials can be evaluated by using the phase function method (PFM), regarded as an efficient approach for computing scattering phase shifts for quantum mechanical problems, without solving the Schrödinger equation. We adapt PFM to deal with the Hulthén-distorted separable non-local potentials and derive a closed form expression for the phase function with rigorous inclusion of electromagnetic effect. We demonstrate the usefulness of our constructed expression by calculating elastic scattering phase parameters for proton–deuteron (p–d) system which agree quite well with the previous results.

• Studies in scattering using Manning–Rosen-modified separable potential in all partial waves

The aim of this paper is to find the exact solutions of the Schrödinger equation for the Manning–Rosen plus Graz separable potential through two different approaches to the problem. We express the irregular/Jost and physical solutions in terms of the special functions of mathematical physics. Numerical results of the phase shifts are obtained by utilising the properties of the Jost function and Fredholm determinants for nucleon–nucleon and nucleon–nucleus systems. The results obtained are in good agreement with earlier works.

• Treatment of inelastic scattering within the separable interaction model

The closed-form analytical expressions for the off-shell solutions for Hulthén-distorted Yamaguchi potential are derived to deal with the charged hadron systems. To construct these solutions, the particular integrals of the non-homogeneous Schrödinger equations are utilised in conjunction with the interacting Green’s functions. The Jost functions thus obtained, both on- and off-shell, are exploited to find the half-off-shell T -matrix. The off shell Jost function exists but off-shell Jost solution for the said potential has not yet been discussed in the literature. The merits of the T -matrix are examined through some model calculations. Exploiting the expressions for on and half-shell transition matrices, the s-wave elastic and inelastic scattering cross-sections are also estimated. Our results for the proton–proton and proton–oxygen systems are in close agreement with other calculations.

• # Pramana – Journal of Physics

Volume 97, 2023
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