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.     

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.     

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.     

Critical electron state in heavy-ion collisions

The results of a calculation of the electron wave function for the critical state (? = ?m_ec²) and of some related quantities are presented. The effect of the finite nuclear size on the critical internuclear distance R_cr is taken into account. The calculations are performed by means of the variational method for nuclei with charges 85 ? Z ? 100. The error of the WKB method for strong Coulomb fields is found to be a few percent.     

Spectral properties of quantum dots influenced by a confining potential model

We obtain the exact energy spectra and corresponding wave functions of the spherical quantum dots for any (n,l) state in the presence of a combination of pseudo-harmonic, Coulomb and linear confining potential terms within the exact analytical iteration method (EAIM). The interaction potential model under consideration is labeled as the Cornell modified-plus-harmonic (CMpH) type which is a correction form to the harmonic, Coulomb and linear confining potential terms.     

Electron capture in collisions between negative and positive ions

Collisions between negative and positive atomic ions are investigated. The ionic wave function is expressed in terms of the Coulomb Green’s function. Normalizing this function allows the system of two ions to be described completely. The exchange matrix elements turn out to be the sums of products of the Coulomb wave functions over degenerate states. These sums are expressed in terms of the quadratic form of the wave function for a state with zero angular quantum numbers, l=m=0. The nonadiabatic coupling of quasi-crossing terms with other terms of the system is analyzed; this effect significantly increases the cross section for single-electron capture.     

Theory of the Trojan-Horse method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.     

Coulomb and strong interactions for Bose-Einstein correlations

We present an analytical formula for the Bose-Einstein correlations (BEC) which includes effects of both Coulomb and strong final state interactions (FSI). It was obtained by using Coulomb wave function together with the scattering partial wave amplitude of the strong interactions describing data on thes-wave phase shift. We have proved numerically that this method is equivalent to solving Schrödinger equation with Coulomb and thes-wave strong interaction potentials. As an application we have analysed, using our formula which includes the degree of coherence and the long range correlation, the data fore ⁺ e ^? annihilations. We have found that the degree of coherence present in our formula approaches approximately unity whereas the long range correlation parameter becomes approximately zero. These results suggest that the physical meanings of the fractional degree of coherence and the long range correlation observed in various other analyses can most probably be attributed to FSI.     

Li+低能(e,2e)反应角分布

利用修正的BBK理论，考虑入射道的库仑相互作用及出射电子的交换对称性，在共面-等能分享-垂直角度碰撞几何中，分别计算了能量为79.6，105.6，227.6和375.6eV的入射电子碰撞Li⁺(1s²)(e，2ｅ)反应三重微分截面(TDCS).结果表明：在接近阈能的碰撞中，两出射电子连线平行于入射电子方向时，TDCS最大；两出射电子连线垂直于入射电子方向时，TDCS最小；入射电子能量达5倍的电离阈能时，主要为单次双体碰撞，而且入射道库仑场对决定低能碰撞的TDCS起着重要作用. 关键词：     

Scalar Charged Particle in Presence of Magnetic and Aharonov–Bohm Fields Plus Scalar–Vector Killingbeck Potentials

The generalized form of Killingbeck potential is an attractive Coulomb term plus a linear term and a harmonic oscillator term, i.e. ?a/r + br + λr ², which has a useful application in quarkonium spectroscopy. The ground state energy with the corresponding wave function are obtained for any arbitrary m-state in two-dimensional Klein–Gordon equation with equal mixture of scalar–vector Killingbeck potentials in the presence of constant magnetic and singular Ahoronov–Bohm flux fields perpendicular to the plane where the interacting charged particle is confined. The analytical exact iteration method is used in our solution. We obtain the energy eigensolutions for particle and antiparticle corresponding to S(r) = V(r) and S(r) = ?V(r) cases, respectively. Some special cases like the Coulomb, harmonic oscillator potentials and the nonrelativistic limits are found in presence and absence of external fields.     

Sum rules for the bound-free transition form factors in hydrogenlike atoms

The product of two bound-free transition form factors of the type 〈k¦exp(i q·r)¦nlm〉 is analytically summed-up over all the degenerate stateslm. Using the genuine Coulomb wave 〈r¦k〉, together with the hydrogenlike wavefunction 〈r¦nlm〉, exact analytical expressions are derived for the sum rule. The results are conveniently expressed in terms of the finite linear combination of easily generated Appell and Lauricella hypergeometric polynomials of two and three variables. This highly desirable sum rule is most frequently required in broad applications within the distorted wave theory of particle-atom scattering.     

Approximate scattering solutions of the dirac equation for electron-nucleus processes in light nuclei

Scattering solutions of the second-order Dirac equation for the case of the Coulomb potential and which are correct to first order in the coupling constantZe ²/hc are investigated and found to describe pure Coulomb scattering equally well as the Sommerfeld-Maue wave functions. Errors introduced by the use of these solutions are studied in a numerical calculation of cross sections for nuclear electric-quadrupole excitation by high-energy electrons. The use of these wave functions is suggested for simplified calculations of lowest-order Coulomb corrections to Born approximation results for various electron-nucleus processes.     

Ab initio studies on magnetism and hybridization of the ternary germanide

We perform a theoretical investigation on the magnetism and orbital hybridization in ternary germanide Ce₃Ni₂Ge₇ using the full-potential linearized augmented plane wave method (FP_LAPW) based on the density functional theory (DFT). The calculation with local spin density approximation (LSDA) predicts that there are two states for the Ce atoms due to the different environment: one (Ce₁) is near the nonmagnetic state and the other (Ce₂) is localized and magnetic. The orbital hybridization plays a key role in determining the state of Ce. On adding on-site Coulomb potential to the localized Ce₂-4f orbit, the magnetic moment obtained from our calculation fits well with the experimental value.     

Geometric bounds of energy of many-particle quantum-mechanical systems

The energy bounds are constructed for the ground state of many-particle Coulomb and gravitational systems using the method of a model Schrödinger equation for a correlated exponential wave function. The method is based on geometric inequalities for average values of cosines of the angles of the triangles formed by triples of particles and does not require calculations of the wave functions. Two-sided energy bounds for an n-particle gravitational system are derived by using this method.     

Density functional theory study on the magnetic properties of Co3O4 with normal spinel structure

The magnetic properties of Co₃O₄ with a normal spinel structure were investigated via the full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). The exchange and correlation effects between electrons were treated with a standard generalized gradient approximation (GGA) from Perdew–Burke–Ernzerhof (PBE), as a function of the on-site Coulomb U term, the GGA−PBE+U method, and a B3PW91 hybrid functional with different Hartree–Fock exchange admixtures. Were calculated all of these exchange–correlation (XC) functionals both with and without spin–orbit coupling (SOC). The objective for these calculations was to predict the ground-state magnetic structure of Co₃O₄ crystal using different XC functionals and to investigate the influence that SOC had on these results. All of our calculations confirmed that the collinear antiferromagnetic (AFM) order was energetically more favorable than the ferromagnetic (FM) one, which agrees with experimental findings. This conclusion was not influenced by the XC functional type employed or whether the spin–orbit effect was used. Thus, the present work does not confirm the recent DFT plane wave pseudopotential results that when including spin–orbit effects, the calculations determined that the collinear FM state had lower energy than the AFM one.     

New microscopic wave function of ��-condensation

We explain how to treat a microscopic wave function of ??-condensation taking a 3??-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, R?pke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an ??-gas nature thanks to ??-condensation as an excited state of ??-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3??-condensation.     

Coherent states of the inverted Caldirola-Kanai oscillator with time-dependent singularities

The coherent states for a system of time-dependent singular potentials coupled to inverted CK (Caldirola-Kanai) oscillator are investigated by employing invariant operator method and Lie algebraic approach. We considered Coulomb potential and inverse quadratic potential as singularities of the system. The spectrum of quantum states is discrete for λ < 0 while continuous for λ ? 0. The probability densities for both Fock state and coherent state are converged to the center as time goes by according to the dissipation of energy. We confirmed that the probability density in the coherent state oscillates back and forth like a classical wave packet.     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Shape of recombination lines for exciton complexes in quantum dots with in-plane electric field

We study electron–hole recombination lines of exciton (X) and exciton complexes (X−, X+, 2X) in planar quantum dots with the electric field oriented within the plane of confinement. A model of a two-dimensional circular infinite quantum well is applied and the ground state of the complexes is found using an exact diagonalization method. We demonstrate that for each of the exciton complexes the recombination lines become non-monotonic for some material and sample parameters as a result of Coulomb interactions. A phase diagram for the line shape is presented. The relation of the exact results to the mean field approach is also discussed.     

Sums of products of Coulomb wave function over degenerate states

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green’s function G(r, r′, E), where the energy parameter E approaches an atomic energy level: E → E _n , E _n = ?Z ²/2n ². The Green’s function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem.