Energy-dependent Potential Research Articles

Calculation of α-decay half-lives of 186−218Po isotopes and actinide nuclei using a new phenomenological potential

This paper is devoted to the calculations of alpha decay half-lives of [Formula: see text]Po [Formula: see text] isotopes and actinide nuclei between the atomic numbers Z = 90 and Z = 102, using an energy-dependent potential model. The [Formula: see text]-nucleus effective potential employed in this study includes a Coulomb potential, a centrifugal barrier potential, and a nuclear potential. The nuclear potential is chosen to be the energy-dependent singularized harmonic potential, typical of nuclear interactions. The role of the energy-dependent potential is very significant in this study. Indeed, when compared to the experimental data, our results are found to be improved when energy-dependent interaction potential is employed compared to when energy-independent interactions are used, especially for small values of the parameter [Formula: see text] as evidenced by the values of the root mean square deviation.

Thermo-Magnetic properties of non-relativistic particles under the effect of energy-dependent Hellmann potential

This manuscript presents an analysis of the thermal and magnetic properties of particles moving in two dimensions under the influence of an external magnetic field and Aharanov-Bohm flux, considering an energy-dependent Hellmann potential. The energy eigenvalue is obtained using the asymptotic iteration method. Next, we model the system as a canonical ensemble and derive the partition function to acquire analytical expressions for the Helmholtz free energy, entropy, mean energy, and specific heat. We observe that an increase in the external magnetic field and AB flux generally increases the energy eigenvalues, with a stronger effect at lower flux values, while energy eigenvalues decrease with an increase in the screening parameter. Additionally, Helmholtz free energy and entropy functions are sensitive to temperature, particularly in the low-temperature regime, while specific heat exhibits a Schottky anomaly. We also compute the magnetisation and susceptibility functions, finding that both magnetisation and susceptibility increase with the external magnetic field strength and the AB flux.

Saturation effect in confined quantum systems with energy-dependent potentials

Saturation effect in confined quantum systems with energy-dependent potentials

Comparison of energy-dependent and independent interactions-a case study

In the present text we construct velocity-dependent or equivalently energy-dependent potential (EDP) to an energy-independent nonlocal potential (EIP) of rank-1 by Taylor series method. The phase shifts for the nucleon-nucleon and alpha-nucleon systems are computed for these two potentials by exploiting the variable phase method and the Fredholm determinant, respectively. The velocity-dependent potential is found to be superior to central nonlocal interaction in generating the scattering phase shifts up to high energy region.

Darboux transformations for Dunkl–Schrödinger equations with energy-dependent potential and position-dependent mass

We construct arbitrary-order Darboux transformations for Schrödinger equations with energy-dependent potential and position-dependent mass within the Dunkl formalism. Our construction is based on a point transformation that interrelates our equations with the standard Schrödinger case. We apply our method to generate several solvable Dunkl–Schrödinger equations.

Inverse problem in energy-dependent potentials using semiclassical methods

Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semiclassical Wentzel-Kramers-Brillouin (WKB) method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials. Published by the American Physical Society 2024

Density and energy dependent semi-microscopic optical potential of nucleon–nucleus elastic scattering

A nonlocal velocity-dependent optical potential was used to study the angular distribution of the differential cross section of nucleon–nucleus elastic scattering. The potential parameters were calculated by fitting elastic angular distributions over a wide range of energy (10-65 MeV) and mass (12-208). The real part of the local optical potential was calculated using the CDM3Y6-Paris interaction, whereas the imaginary part was a Woods-Saxon form factor and its derivative.

Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line

Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line

Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data

We characterize the long-time asymptotic behavior of the solution of the initial value problem for the coupled complex short-pulse equation associated with the 4×4 matrix spectral problem. The spectral analysis of the 4×4 matrix spectral problem is very difficult because of the existence of energy-dependent potentials and the WKI type. The method we adopted is a combination of the inverse scattering transform and Deift-Zhou nonlinear steepest descent method. Starting from the Lax pair associated with the coupled complex short-pulse equation, we derive a basic Riemann-Hilbert problem by introducing some appropriate spectral function transformations, and reconstruct the potential parameterized from the solution of the basic Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at k→0. We finally obtain the leading order asymptotic behavior of the solution of the coupled complex short-pulse equation through a series of Deift-Zhou contour deformations.

Analysis of α + 16O elastic scattering in the semi-microscopical dispersive optical model

We study the elastic scattering cross sections of the α +16O system at 49.5, 69.5, and 80.7 MeV using the optical potentials calculated in the framework of the semi-microscopical dispersive optical model. In this model, the optical potential contains an energy-independent part calculated in the double folding model with a realistic effective nucleon-nucleon interaction, as well as an energy-dependent dynamic polarization potential, the parameters of which are adjusted to the data. The parameters of the real and imaginary parts of the dynamic polarization potential are connected by the dispersion relations.

Fusion dynamics of 9Be + 197Au reaction at near and above barrier energies

The fusion dynamics of reaction has been investigated theoretically by using classical dynamical model and the energy dependent Woods-Saxon potential (EDWSP) model. Calculations of complete fusion (CF) and total fusion (TF) cross-sections within classical dynamical model are done by using code PLATYPUS and such outputs fairly described CF, ICF and TF yields at above barrier area. However, same calculations failed to reproduce CF and TF cross-sections data at near and below barrier area. In contrast, the EDWSP calculations for CF process at above barrier area are turned out to be suppressed when referenced with CF data while data at sub-barrier energies for complete fusion are reasonably addressed by the model calculations. The EDWSP based suppression has been turned out to be smaller than reported values and with an appropriate scale factor (only at above barrier energies), EDWSP outcomes properly explain CF data in complete range of energy. Further, TF data are adequately addressed by the EDWSP based calculations, thereby, reflects the breakup of weakly bound projectile in the force field of the target isotope. Thus, the weakly bound projectile shows break up effects and partially absorbed by the target, which subsequently gives suppression of the CF yields in above barrier area.

а- бөлшектердің 9Be ядросымен соқтығысу кезіндегі серпімді шашырауының жаһандық заңдылықтары

The article investigates the characteristics of the experimental data of the elastic scattering cross section in the low-energy range of the a+9Be nuclear system. General regularities depending on the change in the energy of accelerated ions of the parameters of the obtained cross sections are established. Based on the analysis in the framework of the optical model (OM), energy-dependent optical interaction potentials in a wide range of energies were found.The energy regularity of potentials, revealed as a result of systematic analysis, makes it possible to predict with sufficient accuracy the cross-section of processes at energies at which experimental measurements were not carried out.The potential, which is a complex function of the interaction between nuclei, is an empirical measurement that describes the interaction in the scattering process.Studies of the dependence of the potential on external factors should be carried out individually for each nuclear system. Such analyses carried out in order to improve the accuracy of phenomenological theories should be based on a large array of experimental data. To clarify the truthfulness of the results of phenomenological approaches, it would be theoretically more correct to determine the global patterns of potentials and energy dependences of the full reaction cross-section.The article defines the energy dependence of the potentials and the total cross-section of the reaction based on a systematic analysis of the experimental data set in the energy range of laboratory Elab=30 - 60 MeV for the α+9Be process.Optimal values of the cross-section parameters satisfying global laws depending on the energy of the accelerating beam are found.

A Wheeler–DeWitt Quantum Approach to the Branch-Cut Gravitation with Ordering Parameters

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

Assessing the theory-data tension in neutrino-induced charged pion production: The effect of final-state nucleon distortion

Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble-chamber data and the data of the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ experiment, which are often ascribed to unspecified nuclear effects. In experimental analysis use is made of approximate treatments of nuclear dynamics, usually in a Fermi gas approach with classical treatments of the reaction mechanism, and fits are often performed by simply rescaling cross sections. To understand the origin of these tensions, check the validity of approximations, and to further advance the description of neutrino pion production on nuclei, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation to calculate the nuclear matrix elements. We include the distortion of wave functions of the final-state nucleon in a real energy-dependent potential. We compare results with and without distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ and T2K charged-pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-${Q}^{2}$ $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ ${\ensuremath{\pi}}^{+}$ data. We point out that hydrogen target data from BEBC is also overpredicted at low ${Q}^{2}$, and the data-model discrepancy is similar in shape and magnitude as what is found in comparison to $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ data. Including nucleon distortion alone cannot explain the overprediction of low-${Q}^{2}$ cross sections measured by $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial form factors might not be constrained in a satisfactory way by the Argonne and Brookhaven National Laboratories (ANL/BNL) data alone. Axial couplings and their ${Q}^{2}$ dependence should ideally be derived from more precise data on hydrogen and deuterium. Nuclear matrix elements should be tested with e.g., electron scattering data for which nucleon level physics is better constrained.

Effect of [formula omitted]-derivative on time fractional Jaulent–Miodek system under modified auxiliary equation method and exp[formula omitted]-expansion method

The time fractional Jaulent–Miodek (JM) system is investigated analytically under β-derivative in this study. The JM system is associated with energy dependent potential of the Schrödinger equation having applications in fluid dynamics, condensed matter physics, optics and engineering systems. Two reliable and proficient techniques, namely, the modified auxiliary equation method and exp(−g(Ω))-expansion method are used for extraction of exact solutions of the governing system. The impact of variation of fractional parameter is demonstrated through graphs by assigning particular values to free parameters in obtained solutions.

The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials

The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials

Dirac Equation for Energy-Dependent Potential With Energy-dependent Tensor Interaction

The relativistic symmetries of the Dirac equation were investigated with an energy-dependent tensor potential interaction for two different energy-dependent potentials under parametric Nikiforov-Uvarov method and supersymmetric quantum mechanics and shape-invariance method. It is observed that the energy-dependent tensor interaction has stronger removal effect of the energy degeneracies in both the spin and pseudospin symmetries than the non-energy-dependent tensor interaction.

Calculation of nucleon scattering on <sup>40</sup>Ca based on dispersive optical model

Spherical nucleus <sup>40</sup>Ca is important structural and alloy material nucleus. Based on important theoretical value and application prospect of nuclear data of calcium isotopes, nucleon-nucleus scattering data on <sup>40</sup>Ca nucleus, the main isotopes of natural calcium, are calculated by using dispersive optical model (DOM). The dispersive optical model potential is defined by energy-dependent real potentials, imaginary potentials, and also by the corresponding dispersive contributions to the real potential which are calculated analytically from the corresponding imaginary potentials by using a dispersion relation that follow from the requirement of causality. By fit simultaneously scattering experimental data for neutron and proton, an isospin-dependent dispersive optical model potential containing a dispersive term is derived. This derived potential in this work considers the nonlocality in the real “Hartree-Fock” potential <inline-formula><tex-math id="M5">\begin{document}$ V_{\rm{HF}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231054_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231054_M5.png"/></alternatives></inline-formula> and introduces the shell gap in the definition of nuclear imaginary volume, surface and spin-orbit potentials near the Fermi energy. This dispersive optical model potential shows a good description of nucleon-nucleus scattering data on <sup>40</sup>Ca nucleus up to 200 MeV including neutron total cross sections, neutron elastic scattering angular distributions, proton elastic scattering angular distributions, neutron analyzing powers and proton analyzing powers. In addition, the energy dependencies of calculated real volume integrals of dispersive optical model potential is shown, and a typical dispersive hump is seen around the Fermi energy. This dispersive hump behavior naturally obtained from dispersion relations, and allows the dispersion optical potential to get rid of energy dependent geometry, thus avoiding the use of a radius dependent on energy.

Existence of the transfer matrix for a class of nonlocal potentials in two dimensions

Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schrödinger equation, for a local potential v, they arise in dimensions greater than one and are generally present regardless of the details of v. The approximation in which one ignores the contributions of the evanescent waves to the scattering process corresponds to replacing v with a certain energy-dependent nonlocal potential . We present a dynamical formulation of the stationary scattering for in two dimensions, where the scattering data are related to the dynamics of a quantum system having a non-self-adjoint, unbounded, and nonstationary Hamiltonian operator. The evolution operator for this system determines a two-dimensional analog of the transfer matrix of stationary scattering in one dimension which contains the information about the scattering properties of the potential. Under rather general conditions on v, we establish the strong convergence of the Dyson series expansion of the evolution operator and prove the existence of the transfer matrix for as a densely-defined operator acting in .

Analysis of formation and decay of Ba*122,128 formed via Ni58,64+Ni64 reactions near the Coulomb barrier

The fusion mechanics of $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ and $^{64}\mathrm{Ni} +^{64}\mathrm{Ni}$ reactions is analyzed by using the energy dependent Woods-Saxon potential (EDWSP) model and the subsequent decay dynamics of $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ isotopes formed in these fusion channels is examined via the dynamical cluster-decay model (DCM). In the EDWSP model, the energy dependent nature of the Woods-Saxon potential causes modifications in the profile of the fusion barrier between fusing nuclei. Such barrier modifications lead to the lowering of the effective fusion barrier of the colliding nuclei. Hence, EDWSP outcomes satisfactorily describe the energy dependence of fusion cross sections of the chosen reactions in near- and sub-barrier energy regions. Following this, the fragmentation of compound nuclei $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ formed using the above-mentioned reactions is investigated by using the collective clusterization approach of DCM. The calculations are done for quadrupole $({\ensuremath{\beta}}_{2})$ choice of fragmentation with hot configurations having optimized orientations. The evaporation residues' cross-section data lying within beam energy $({E}_{\mathrm{beam}})$ = 171--220 MeV are nicely addressed. The comparative analysis of decaying $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ nuclei is worked out in terms of fragmentation potential and preformation probability, along with the investigation of barrier characteristics.