Photodetachment of the positronium negative ion interacting with screened Coulomb (Yukawa) potentials

The effect of screened Coulomb (Yukawa) potentials on the photodetachment cross sections of the positronium negative ion is investigated by using the asymptotic form of the bound-state wave function and a plane wave form for the final-state wave function. The required normalization constant is determined from highly accurate, completely non-adiabatic wave functions for the three-particle systems. Photodetachment cross sections for the Ps^? ion are calculated for different Debye shielding lengths (D) ranging from infinite (pure Coulomb) to D = 1.81.     

Exact solutions to the Schrödinger equation for potentials with Coulomb and harmonic oscillator terms

Exact solutions to the Schrödinger equation for potentials containing Coulomb (∼1/r) plus harmonic oscillator (∼r²) terms are found, subject to constraints on the ratio of the strengths of the Coulomb and harmonic oscillator terms. The solutions have the simple form of a product of exponential and polynomial functions.     

Electromagnetic properties of spherical and deformed configurations in theK-harmonic model of18O

Within the framework of theK-harmonic model the wave functions of the¹⁸O nucleus are constructed, which correspond to the usual spherical configuration and to the deformed one, where the two last protons and neutrons fill the deformed orbitals belonging to the (2s-1d) shell. Matrix elements of the Coulomb interaction and of the electric multipole of order 2 are calculated. Corrections for the non-orthogonality of wave functions are negligible. Corrections for the elimination of the centre-of-mass motion are surprisingly small in the Coulomb energy. They enable to reduce the effective charge usually necessary for interpreting the experimental values of the reducedE2 transition rates. The Coulomb energy is nearly independent on the deformation parameters and the other quantum numbers,E2 transition rates attain maximum values in the vicinity of their SU(3) values for 2→0 and 4→2 transitions.     

Approximate normalized wave functions for the finite-size Coulomb problem

Using perturbation methods developed previously for the finite-size energy shift, thes-state wave functions for a bound lepton in the Coulomb field of a nucleus with an arbitrary charge distribution are developed through order (Zα)². This technique allows a determination of the finite-size contribution to the normalization of the wave function up to order (Zα)², both for small separations of the lepton and nucleus and for the lepton outside the nucleus. General features of the wave function are discussea, including the transition of the Dirac problem to the (singular) point charge limit. A practical application is developed using these results.     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.     

Core polarization effects on transition densities in medium-heavy nuclei

We propose a microscopic model to study the core-polarization effects of giant resonances on the transition densities of open-shell nuclei. We use the Hartree-Fock-RPA method for the calculation of the single-particle wave functions and the response function of the giant resonances. Particle-vibration coupling is applied to take into account the core polarization effect on the valence many-body wave functions. We apply our model to the quadrupole transitions in the several medium-heavy nuclei. Valence many-body wave functions are calculated with the generalized seniority scheme and with the shell model. Results for the proton and neutron effective charges and the Coulomb form factors for the N = 82 isotones and for ¹¹⁶Sn and ¹¹⁰Pd are presented and discussed. The effective coupling hamiltonian is determined by the Skyrme interaction SGII which is used also in the HF and RPA calculations. The calculated core polarization charges show some state dependences. The average theoretical values are δe_p = 0.4–0.5 and δe_n = 0.6–0.7 compared to typical empirical values of δe_p = 0.6 and δe_n = 1.2.     

Calculation method for the continuum states of atomic systems

In the present work, we develop a calculational method of solving the scattering equations for spherically symmetric potentials by expanding the solutions on Coulomb functions. We utilize a multistep integration scheme together with the standard partial wave analysis in a region where the potential term dominates. The method applies to any physical problem expressed as [? ² + V(r) + k ²]ψ(r) = 0, while the extension of the method to more general scattering problems is briefly discussed. At present, we demonstrate a two-step Coulomb-fitted integration scheme by calculating the short-range scattering phase shifts for various potentials V (r).     

Coulomb displacement energies of the T = 1, J = 0 states of A = 42 nuclei

Coulomb displacement energies of the T = 1, J = 0⁺ and 6₁⁺ states of A = 42 nuclei are analyzed with previously known charge dependent forces and effects, and with the available HartreeFock single-particle wave functions. From the study of the Coulomb displacement energies of the 6₁⁺ states, it is found that the present knowledge on the charge dependence, including a phenomenological charge symmetry breaking force previously introduced so as to help explain the Nolen-Schiffer anomaly, gives a sufficient and consistent explanation for both single-particle and twoparticle systems. From the study of the 0⁺ states, we found that the Coulomb displacement energies of the second 0₂⁺ states can be explained with a compensation between the smaller Coulomb energies of the second lowest two-particle state and larger ones of the deformed 4p-2h state.     

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k ², where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.     

Coulomb-Korrekturen bei der inneren Bremsstrahlung

Coulomb corrections to the internal Bremsstrahlung associated with allowedβ-decay have been calculated. The Coulomb field is taken into account through the electron wave function. The corrections to the contributions of the intermediate states to the spectrum are evaluated. These corrections do not cancel out when the spectrum is normalized to the emission of oneβ-particle. Hence the corrections to the normalized spectrum are no longer small. The polarization is practically not affected by these Coulomb corrections. Numerical values for P³², S³⁵ and Y⁹⁰ are compared with experimental results. Especially in the high energy part of the spectrum the former discrepancies between theory and experimental yield are removed.     

pi-Mesonic decay of hypernuclei and pion wavefunction

The pi-mesonic decay of hypernuclei is studied by using the pion distorted waves which are the solutions of the Klein-Gordon equation with the optical potential. The distortions of the pion waves give rise to significant enhancement of theπ-decay rate compared with the pion free-wave case. Theπ-decay rates are very sensitive to the behavior of the pion wave deep inside the nucleus and therefore to the chosen pion optical potentials. There is a tendency that the enhancement is larger for theπ ^?-decay than for theπ ⁰-decay due to the combined effects of the Coulomb and optical potentials.     

Carcass functions in variational calculations for few-body systems

For variational calculations of molecular and nuclear systems involving a few particles, it is proposed to use carcass basis functions that generalize exponential and Gaussian trial functions. It is shown that the matrix elements of the Hamiltonian are expressed in a closed form for a Coulomb potential, as well as for other popular particle-interaction potentials. The use of such carcass functions in two-center Coulomb problems reduces, in relation to other methods, the number of terms in a variational expansion by a few orders of magnitude at a commensurate or even higher accuracy. The efficiency of the method is illustrated by calculations of the three-particle Coulomb systems μμe, ppe, dde, and tte and the fourparticle molecular systems H₂ and HeH⁺ of various isotopic composition. By considering the example of the _Λ ⁹ Be hypernucleus, it is shown that the proposed method can be used in calculating nuclear systems as well.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Total ionization cross section in electron-hydrogen scattering

The total ionization cross section in electron-hydrogen scattering in the energy range 20.4–68.0 eV has been calculated by a method in which the initial state of the system is treated by a distorted wave polarized orbital method and the final state is described by (1) a product of two unscreened Coulomb functions and (2) a product of a plane wave and a Coulomb function. The corresponding two sets of results using a plane wave in the incident channel have also been reported. The present results where both the electrons are represented by Coulomb waves are in closer agreement than other theoretical predictions With measured values.     

9Be(3He,n)11C and 11B(3He,n)13N Reactions at Energies below Coulomb Barrier

Angular distributions have been measured for ⁹Be(³He, n)¹¹C and ¹¹B(³He, n)¹³N reactions for the neutron group leading to the ground state at E_3He = 0.90, 1.00, 1.20, 1.40 MeV and 1.70, 1.90 MeV respectively. To fit the experimental data, the theory of two nucleon stripping reactions below the Coulomb barrier has been considered. Taking Coulomb distorted wave functions for the interacting particles in the initial channel, a closed analytical form for the differential cross-section has been obtained. The other two cases using the plane wave Born approximation and the distorted wave Born approximation are also applied to the experimental data. The agreement between the Coulomb distorted wave calculations and the experimental data is better than with the PWBA and DWBA. The spectroscopic factors are extracted by fitting the experimental data with the theoretical calculations.     

Complex-Scaling Treatment for Doubly Excited Inter-Shell Resonances in H? Interacting with Screened Coulomb (Yukawa) Potentials

The doubly-excited inter-shell resonance states of the hydrogen negative ion with screened Coulomb potentials are investigated in the framework of complex-scaling method. Highly correlated wave functions with terms up to 1078 in Hylleraas coordinates are used. The resonance parameters for the 2s3s ¹ S ^e associated with the H (N?=?2) threshold and the 3s4s ¹ S ^e state associated with the H (N?=?3) threshold for various screening strengths are reported. Comparisons are made with other available data in the literature.     

Note on relativistic coulomb wave functions

Some results on the wave functions of a Dirac particle in a point charge Coulomb field are presented. Angular momentum and parity eigenfunctions are tabulated and used to construct solutions representing asymptotically a plane wave plus incoming or outgoing spherical waves. The solutions forr → 0 are exhibited in a form closely similar to the corresponding free particle spinors and are used to construct generalizations of the Casimir projection operators for positive or negative energy particles. The various wave functions presented are useful in calculations such as nuclear beta decay in which it is necessary to take into account final (or initial) state Coulomb interactions. Because of the similarity of the wave functions to those of a free particle, calculations including rigorously all Coulomb corrections for such processes as allowed beta decay can be performed with little more effort than is involved in a calculation using only plane waves.     

Hadron wave functions in lattice QCD

Coulomb gauge quark-antiquark wave functions for the pion and the rho are calculated in the valence approximation on a lattice 8³ × 16. We use gauge group SU(2) at β of 2.431 corresponding to an inverse lattice spacing of 1100 ± 100 MeV. The wave functions fall off significantly over the size of the box, are rotationally invariant except at the box's boundary, and are nearly independent of the lagrangian quark mass.     

Application of the (G^{\prime}/G)-expansion method for the Burgers, Burgers–Huxley and modified Burgers–KdV equations

In this work, we present travelling wave solutions for the Burgers, Burgers–Huxley and modified Burgers–KdV equations. The (G′/G)-expansion method is used to determine travelling wave solutions of these sets of equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.     

Microscopic theory of substrate-induced gap effect on real AFM susceptibility in graphene

In this article, the novel (G ^′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.