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.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

Coulomb energy of nuclei

The density functional determining the Coulomb energy of nuclei is calculated to the first order in e ². It is shown that the Coulomb energy includes three terms: the Hartree energy; the Fock energy; and the correlation Coulomb energy (CCE), which contributes considerably to the surface energy, the mass difference between mirror nuclei, and the single-particle spectrum. A CCE-based mechanism of a systematic shift of the single-particle spectrum is proposed. A dominant contribution to the CCE is shown to come from the surface region of nuclei. The CCE effect on the calculated proton drip line is examined, and the maximum charge Z of nuclei near this line is found to decrease by 2 or 3 units. The effect of Coulomb interaction on the effective proton mass is analyzed.     

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.     

Elastic scattering of intermediate energy protons on4He and12C

The elastic angular distribution and polarization of ～1 GeV protons on⁴He and¹²C have been analysed using the recently proposed correlation expansion for the Glauber amplitude by retaining terms up to three-body density only. The calculations include Coulomb and spin effects. Using realistic form factors for target nuclei it is found that we need to consider only up to the second-order density term to provide a satisfactory explanation of both kinds of experimental data in the available momentum transfer region. The contribution of the three-body density term is only marginal except in⁴He differential cross-section in the cm angular range 45°<θ _cm<65°.     

The process of coulomb dissociation of weakly bound relativistic nuclei and hypernuclei within the two-cluster model

Using the analogy with the problem of ionization and excitation of atoms in the propagation of relativistic charged particles through a bulk of matter, the process of Coulomb dissociation of weakly bound relativistic nuclei and hypernuclei is theoretically investigated in the framework of the two-cluster deuteron-like model. Explicit expressions for the total cross section of Coulomb disintegration of weakly bound systems are derived taking into account the corrections due to the finite size of a target nucleus. Numerical estimations for the Coulomb dissociation of relativistic hypernuclei ³H_Λ and ⁶He_Λ are performed. It is shown that, owing to a sharp dependence of the Coulomb dissociation cross section on the binding energy, experimental measurements of the cross section allow one to determine the values of binding energy for these systems. The text was submitted by the authors in English.     

<Emphasis Type="Italic">D</Emphasis>-Wave Resonances in Three-Body System Ps<Superscript>−</Superscript> with Pure Coulomb and Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited ¹ D ^e resonance states of Ps⁻ interacting with pure Coulomb and screened Coulomb (Yukawa) potentials employing highly correlated wavefunctions. For pure Coulomb interaction, in the framework of stabilization method and complex coordinate rotation method we have obtained two resonances below the n = 2 threshold of the Ps atom. For screened Coulomb interaction, we employ the stabilization method to extract resonance parameters. Resonance energies and widths for the ¹ D ^e resonance states of Ps⁻ for different screening parameter ranging from infinity (pure Coulomb case) to a small value are also reported.     

Determination of the ground state energies of the H 2 + , D 2 + and H 2 + molecular ions taking into account relativistic corrections

On the basis of determination of the asymptotic behavior of correlation functions of the corresponding field currents with the corresponding quantum numbers an analytic method for determination of the energy spectrum of three-body Coulomb system is suggested. Our results show that the constituent masses of particles, which we have defined as masses of particles in a bound state, differ from masses of particles in a free-state. The constituent mass to the free state mass relation for the electron is greater than the same mass relation for the proton, deuteron and triton. It was also found that this constituent electron mass has different values in each systems, i.e. in H ₂ ⁺ , D ₂ ⁺ and T ₂ ⁺ hydrogen molecular ions. The contributions of exchange and self-energy diagrams were taken into account in the determination of the energy spectrum of the three-body Coulomb system. Our results show that the self-energy diagram contribution is inversely proportional to the square of the constituent mass of particles. This contribution is sufficient for the electron and is negligible for the proton, deuteron and triton. When defining the energy and the wave function (WF), it is necessary to take into account the contributions of both the exchange and self-energy diagrams.     

E1 polarization in coulomb excitation of 7Li

Coulomb excitation of the 0.478 MeV $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ state of ⁷Li has been studied by a partiele-γ coincidence technique. From the dependence of the excitation probabilities on bombarding energy and scattering angle a sizeable interference contribution from E1 excitation of continuum states has been determined. General expressions for the size of the E1 polarization effect in Coulomb excitation are given and the observed magnitudes in ^6,7Li are compared with schematic model calculations.     

The Low-Energy p–d System in Pionless EFT

We summarize results presented at the 5th Asian Pacific Conference on Few Body Problems in Physics, which was held in Seoul in August 2011. We calculate low-energy quartet and doublet channel proton–deuteron scattering in the framework of pionless effective field theory. We obtain good agreement with the available phase shift analyses. Moreover, we calculate the Coulomb contribution to the ³He–³H binding energy difference in first order perturbation theory.     

Contribution of electric quadrupole and dipole-quadrupole interference terms in Coulomb breakup of 15C

The effects of electric quadrupole (E2) and dipole-quadrupole interference (E1–E2) terms in the Coulomb breakup of ¹⁵C have been investigated within the framework of eikonal approximation. The sensitivity of Coulomb breakup cross section, differential in relative energy and Longitudinal Momentum Distribution (LMD) of core fragments, towards these terms have been examined. A very small (1% of E1) contribution of E2 transition has been predicted in integrated Coulomb breakup cross section. Further it is also found that the inclusion of E2 and E1–E2 terms introduces a small asymmetry in the peak of relative energy spectrum and also increases the peak height of the spectrum. The contribution of dipole-quadrupole interference terms is clearly shown in LMD, as it introduces an asymmetry in the shape of LMD and enhances the matching between the data and predictions.     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

Improved optical potential for low and medium energy π−-4He elastic scattering

Effects of the second-order correction in multiple scattering theory and the nucleon binding correction to the optical potential are investigated in π^?-⁴He elastic scattering and total reaction cross-sections. The second-order correction includes not only nucleon-nucleon correlation effects but also the contribution from spin (isospin) double-flip processes. It is found that the latter has an ascendency over the former. We have also shown that the nucleon binding effect is very important to reproduce the energy dependence of the total elastic cross section and the total reaction cross section, especially in the low energy and resonance energy regions.     

Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

The Hellmann potential is simply a superposition of an attractive Coulomb potential ?a/r plus a Yukawa potential be^{?δ r} /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.     

The effect of p-h corrections on the proton pairing vibrations at Z=50

Recent experimental results from Cd(³He, n)Sn reactions on a variety of Cd targets indicate that the proton pairing vibration lies at an excitation energy nearly 2 MeV below the value suggested by binding energy systematics. It is shown here that this large discrepancy, which is in contrast to the case of neutron pairing vibrations, may be explained by the effects of particle-hole (p-h) interactions which are large because of the Coulomb contribution. The p-h matrix elements are obtained empirically from observed p-h separations and also calculated theoretically for both Coulomb and nuclear contributions. These average empirical matrix elements from the Cd experiments give excellent agreement to the 2p-1h states in the ¹¹⁵In(³He, n) experiment populated via L=0 transfers. The agreement in the latter case indicates a simple scaling of the interaction with the number of particles and holes.     

Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion

Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L ² towards a 1/L decay when the Coulomb energy to Fermi energy ratio increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at . Received 13 March 2000     

Possible antiferroelectric ordering of polarization with wavenumber 2kF in assumed Wigner crystal in TTF-TCNQ. Simple model analysis

We obtain electronic polarization in TCNQ^? and its contribution to the cohesive energy in the ground state of TTF-TCNQ as functions of intramolecular transfer energy t. We make a two-site model for TCNQ^? embodying its spatial extention and take account of the long range Coulomb interaction betwern electrons but neglect the intermolecular transfer energy. Value of t obtained from an interpretation of optical data strongly supports the possibility of antiferroelectric ordering.     

共面双对称几何中Li+(1s2)(e,2e)反应的理论研究

利用Berakdar理论,考虑了入射道的库仑相互作用,在共面双对称碰撞几何中,计算了能量为251eV入射电子碰撞Li⁺(1s²)(e,2e)反应的三重微分截面(TDCS),讨论了不同散射振幅对截面的贡献,分析了干涉效应及入射道库仑场对截面的影响.结果表明,它们对决定TDCS的角度分布和大小起着重要作用. 关键词：     

Energetic ion generation by Coulomb explosion in cluster gas and a low-density plastic foam with an intense femtosecond laser

The energy distributions of protons emitted from the Coulomb explosion of hydrogen clusters by an intense femtosecond laser have been experimentally obtained. Ten thousand hydrogen clusters were exploded, emitting 8.1-keV protons under laser irradiation of intensity 6 × 10¹⁶W/cm². The energy distributions are interpreted well by a spherical uniform cluster analytical model. The maximum energy of the emitted protons can be characterized by cluster size and laser intensity. The laser intensity scale for the maximum proton energy, given by a spherical cluster Coulomb explosion model, is in fairly good agreement with the experimental results obtained at a laser intensity of 10¹⁶–10¹⁷ W/cm² and also when extrapolated with the results of three-dimensional particle simulations at 10²⁰–10²¹ W/cm². Energetic proton generation in low-density plastic (C₅H₁₀) foam by intense femtosecond laser pulse irradiation has been studied experimentally and numerically. Plastic foam was successfully produced by a sol-gel method, achieving an average density of 10 mg/cm³. The foam target was irradiated by 100-fs pulses of a laser with intensity 1 × 10¹⁸ W/cm². A plateau structure extending up to 200 keV was observed in the energy distribution of protons generated from the foam target, with the plateau shape explained well by Coulomb explosion of lamella in the foam. The laser-foam interaction and ion generation were studied qualitatively by two-dimensional particle-in-cell simulations, which indicated that energetic protons are mainly generated by the Coulomb explosion. From the results, the efficiency of energetic ion generation in a low-density foam target by Coulomb explosion is expected to be higher than in a gas-cluster target.