Manning-Rosen Potential Research Articles

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

The traditional phase function method is regarded as a resourceful tool for computing scattering phase shifts for quantum mechanical potential scattering involving local interactions. For the local plus a nonlocal potential the conventional phase function method does not hold good. In such a situation one has to modify it. The modified variable phase method is adapted here to treat the Manning-Rosen (MR) plus Graz nonlocal separable potential for constructing an exact expression for the phase function with rigorous inclusion of the electromagnetic effect. The merit of our analytical result is demonstrated by computing elastic scattering phase parameters and differential scattering cross sections for proton-proton (p − p) and proton-deuteron (p − d) systems which are in sensible agreement with previous works.

Critical screening parameters of one-electron systems with screened Coulomb potentials: circular Rydberg states

The critical screening parameters (λ c ) of one-electron systems in circular states under short-range screened Coulomb potentials (SCPs) are investigated using the generalized pseudospectral method. High-precision values of λ c are obtained for bound states with the principal quantum number n up to a thousand. The polynomial fittings based on the numerical values indicate that the high-Rydberg limits of the n 2-scaled critical screening parameters, i.e. , are equal to , , and , respectively, for the Debye–Hückel, Hulthén, and exponential cosine SCPs. It is surprisingly found that these high-Rydberg limits can be well-reproduced from Bohr’s correspondence principle together with the semi-classical model of the hydrogen atom. We further show that both the present numerical calculations and the semi-classical analysis can be extended to other short-range potentials such as the generalized exponential, Lennard–Jones, modified Pöschl–Teller, shifted Morse, Woods–Saxon, and Manning–Rosen potentials that attract wide interest in atomic, molecular, and nuclear physics.

Thermomagnetic properties and its effects on Fisher entropy with Schioberg plus Manning-Rosen potential (SPMRP) using Nikiforov-Uvarov functional analysis (NUFA) and supersymmetric quantum mechanics (SUSYQM) methods

Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.

Approximate arbitrary (k,l) states solutions of deformed Dirac and Schrödinger equations with new generalized Schiöberg and Manning–Rosen potentials within the generalized tensor interactionsin 3D-EQM symmetries

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space-space have recently become the object of renewed interest. In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin-orbit coupling quantum number [Formula: see text], we approximate to solve the deformed Dirac equation (DDE) for a new suggested new generalized Schiöberg and Manning–Rosen potentials within the generalized (Coulomb and Yukawa)-like tensor interactions (NGSM-GLTs). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic quantum mechanics (RQM) as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp’s shift method and standard perturbation theory using Greene–Aldrich approximation to handle [Formula: see text], [Formula: see text] and other terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers ([Formula: see text]), the mixed potential depths ([Formula: see text],[Formula: see text],[Formula: see text],[Formula: see text],[Formula: see text]), the range of the potential [Formula: see text], and noncommutativity parameters ([Formula: see text],[Formula: see text],[Formula: see text]). We recovered several potentials, including the improved Schiöberg and Manning–Rosen potentials within the improved Yukawa-like tensor interaction, the new Schiöberg and Manning–Rosen potentials within the improved Coulomb-like tensor interaction, the new Schiöberg potential within the improved Yukawa-like tensor interaction, the new Manning–Rosen potential within the improved Yukawa-like tensor interaction, and the new Schiöberg and Manning–Rosen potentials potential problems in the context of nonrelativistic extended quantum mechanics symmetries.

Approximate eigenvalue solutions with diatomic molecular potential under topological defects and Aharonov-Bohm flux field: application for some known potentials

In this paper, we determine the approximate eigenvalue bound state solution of the radial Schrodinger equation in three-dimension in the presence of the Aharonov-Bohm flux field with two-term diatomic molecular potential in point-like global monopole (PGM) defect. We analyse the effects of factors, such as topological defects, background curvature associated with topological defects as well as the potential. We also show that the energy levels shift due to the presence of the magnetic flux which gives us an analogue of the Aharonov-Bohm effect for the bound state. Finally, we apply the quantum system for some known potential models, such as q-deformed Hulthen-type potential and Manning-Rosen potential, and discussed the effects of various factors on the eigenvalue solutions.

Screening potentials derived from the central force problem in a deformed space

The action of long-range potentials can be hindered by the collective effect of free charges in a medium, a process dubbed screening. This effect is usually modeled by adding an exponential crossover to a power-law potential. We show here how these exponential cutoffs can be obtained from first principles in the central force problem through the addition of a radial deformation of space, . When considering a potential in the form , we find that the radial part of the Schrödinger equation displays an effective potential that takes the form of two well-known screening potentials, namely, the Eckart and the Manning-Rosen potentials.

Analytic transition matrix for the Manning-Rosen potential in all partial waves

The off-shell Jost and physical solutions of the Manning-Rosen potential are derived by adapting two different approaches to the problem. In contrast to the semi-classical approaches to the problem we construct exact analytical expression of the off-shell transition matrix for the Manning-Rosen potential in all partial waves by adapting pure quantum mechanical method. Our constructed expressions are in their maximal reduced form and consistent with respect to their limiting behaviors. The off-shell transition matrix satisfies the unitarity relation for positive energy. To authors’ knowledge, these results for the off-shell quantities have not yet been discussed in the literature.

More accurate ro-vibrational energies for SiF +(X 1Σ+) molecule

The most appropriate potential energy function for the X 1Σ+ state of SiF+ molecule has been specified by comparing the vibrational energies obtained via special cases of the general molecular potential (GMP) which are Morse, improved Rosen-Morse, modified Rosen-Morse, improved Manning-Rosen and Tietz potentials with the vibrational energies obtained in the presence of improved generalized Pöschl-Teller (IGPT) potential and experimental data. It has been shown that the improved Rosen-Morse potential is better than the other well-known potential energy functions in fitting experimental energies of SiF +(X 1Σ+) molecule. By using relativistic rotational-vibrational energy eigenvalue relation for Rosen-Morse potential in improved form which is acquired by solving the Dirac equation under the GMP and Pekeris type approximation, the more accurate ro-vibrational energies of SiF +(X 1Σ+) molecule have been obtained. It has been demonstrated for SiF +(X 1Σ+) molecule that in order to procure more proper ro-vibrating energies for the SiF +(X 1Σ+) molecule, a Pekeris-type approach to the centrifugal term is better than the improved Greene-Aldrich in getting more accurate ro-vibrational energies.

Nucleon–nucleus inelastic scattering by Manning–Rosen distorted nonlocal potential

Within the framework of non-relativistic quantum scattering theory, we treat the charged hadron scattering by replacing the nuclear interaction by a separable nonlocal one and the electromagnetic part by the Manning–Rosen potential. The off-energy-shell scattering is rigorously studied by this additive interaction by including the effect of electromagnetic interaction. The exact analytical expressions for the off-shell solutions and half-shell T-matrix are obtained in maximal reduced form. The half-shell T-matrix for the proton–oxygen system is computed and the resultant phase shifts are found in order.

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

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

A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in finding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.

Exact solutions of the Schrödinger equation for Manning-Rosen plus Yamaguchi potential

Exact analytical solutions of the Schrödinger equation subject to the regular, irregular and physical boundary conditions are constructed for motion in the Manning-Rosen plus Yamaguchi potential. To judge the merits of our expressions we apply them to compute scattering phase shifts for some nuclear systems and are found in order.

A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.

Off-shell Solutions and Half-shell T-matrix for the Manning–Rosen Potential

New expressions for the off-shell solutions of the Manning-Rosen potential are derived and make certain useful checks on their limiting behaviours to examine the correctness of our constructed expressions. The off-shell Jost function and the half-shell T-matrix thus obtained are found in order.

ANALYSIS OF ENERGY AND WAVE FUNCTIONS AND THE THERMODYNAMICS PROPERTIES OF THE 6-DIMENSIONAL SCHRODINGER EQUATION UNDER DOUBLE RING-SHAPE OSCILLATOR (DRSO) AND MANNING-ROSEN POTENTIALS USING SUSY QM METHOD

The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.

Prediction of thermodynamic properties of formation of HCl at temperatures 200–1000 K

In this work, the thermodynamic properties of the formation reaction of hydrogen chloride from the reactants chlorine and hydrogen are studied by employing the developed Manning-Rosen potential. A closed-form expression for the vibration part of the molecular partition function is used to calculate the vibrational contribution of the thermodynamic properties. The results obtained are used to investigate the change in the thermodynamic functions for the formation reaction of HCl at a high temperature range. The predicted results are compared with the ones obtained from the other theoretical approaches based on the harmonic and an-harmonic oscillator models.

Ro-vibrational energies of caesium molecules with the Tietz-Hua oscillator

ABSTRACT Ro-vibrational energies of caesium molecules in the excited electronic state 33∑g + have been calculated by solving the Schrödinger equation for Tietz-Hua potential by applying a Pekeris-type approximation to the centrifugal term. The obtained results are compared with those obtained via improved Manning-Rosen potential and with the experimental Rydberg–Klein–Rees (RKR) data. It has been demonstrated that the Tietz-Hua potential is one of the best potential energy functions in fitting experimental RKR data for Cs2 (33∑g +) molecule. The ro-vibrational energy levels, calculated by using Tietz-Hua potential, are in excellent agreement with the experimental data with an average deviation less than 0.001% in the most worst cases.

Analytical solutions of the Proca equation for modified Manning–Rosen potential with centrifugal term and direct coupling approaches by hypergeometric method

The Proca equation is one of the fundamental relativistic wave equations of massive vector (spin 1) boson fields. Proca equation is used to explain a relatively small particle that has a speed approaching the speed of light. The effect of photon imaginary mass to the quantum system that was coupled by noncentral potential consisting of radial, polar, and azimuthal modified Manning–Rosen potentials was investigated. The vector potential was coupled to the photon relativistic energy and the quadratic scalar potential was coupled directly to the quadratic photon mass. In the case of free space and when the vector potential was equal to scalar potential, therefore, the time-independent Proca equation reduced to a three-dimensional variable separable Schrodinger-like equation. By using variable separation method, the three-dimensional Schrodinger-like equation was resolved into three one-dimensional radial, polar, and azimuthal parts of Schrodinger-like equations. Each part of one-dimensional Schrodinger-like equation was solved using the hypergeometric differential equation through variables and wave function substitutions and resulted in the energy and wave function equations of massive photons. The relativistic energy equation of massive photons was a function of imaginary mass photon, the potential parameters, and the quantum numbers in radial, polar, and azimuthal variables. By using the Maxwell field approach, we got the correction factor for the energy function of this spin-1 particle.

Study of nucleon–nucleon and alpha-nucleon elastic scattering by the Manning–Rosen potential

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves

On- and off-shell Jost functions for the Manning-Rosen potential

The s-wave on-shell Jost solution for the Manning-Rosen potential is constructed via the ordinary differential equation approach to the problem. The corresponding off-shell Jost function is calculated by using the integral representation of the off-shell Jost function in a single channel scattering. The half off-shell T- matrix is obtained from the knowledge of the off-shell Jost function. Our constructed expressions for the Jost functions are applied to compute T-matrix, quasi-elastic phase shifts and the scattering phase shifts for the nuclear systems.