Proton-hydrogen reaction in an effectively two-body model

A model of total interaction between a proton incident to a hydrogen atom and the proton that is the nucleus of this atom is proposed. This interaction is assumed to be the sum of the short-range nuclear Reid potential and the long-range Thomas-Fermi potential induced by the Coulomb interaction of the electron with the nucleus of the hydrogen atom. The explicit low-energy asymptotic behavior of the cross section for the proton-hydrogen reaction leading to deuteron production is found. It is shown that this cross section increases in inverse proportion to the collision energy for the proton and hydrogen atom in its zero limit.     

Inelastic scattering of charged particles by atoms using the Thomas-Fermi statistical method

We describe a method of calculating the differential cross section for the inelastic scattering of charged particles by atoms based on the statistical model of the atom. For the most general form of the potential of the atom we obtain an analytical expression for the differential (with respect to the energy of the electron ejected from the atom) cross section of inelastic scattering. It is shown that the statistical method of Thomas-Fermi is applicable when the energy of the ejected electron is sufficiently high.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 92–96, September, 1986.     

Binuclear atom as the bound state of a proton and a heavy atom

The existence of a bound state of a proton and a heavy atom is predicted. The atom is described by the Thomas-Fermi method. The electrons screen the field of the proton, which suppresses the repulsive force between the proton and the atomic nucleus. On the other hand, the force of attraction between the proton and the electrons is directed along the electron density gradient (i.e., towards the nucleus). It is concluded that for Z = 80, the two forces are balanced at a distance from the nucleus of about 0.6 of the Bohr radius. It is found that the potential energy minimum of the proton with a depth of several tens of electronvolts lies in the range of negative energies (attraction). It is proposed that such a system be referred to as a binuclear atom. It is emphasized that, in contrast to molecules, in which binding with the hydrogen atom is ensured by a rearrangement of the states of the outer-shell (valence) electrons, a binuclear atom is formed as a result of the collective response of the system of inner electrons to the proton potential.     

Charge oscillations and photoabsorption of the Thomas-Fermi-Dirac-Weizsäcker atom

Following the work of Bloch and Ball et al. the theory of linear response of a hydrodynamic Thomas-Fermi model is extended to a general density dependent energy functional. The theory is applied to the Thomas-Fermi-Dirac-Weizsäcker atom. Normal mode solutions and the atomic photoabsorption cross section are calculated.     

Peculiarities of elastic scattering of intermediate-energy electrons related to their capture at quasi-stationary levels of an atom in a continuous spectrum

A theoretical model of electron scattering on an atom is constructed to study elastic atomic scattering of intermediate-energy electrons. The proposed model is based upon the combined Mensing potential with two spheres of atomic electrons, which admits analytical solutions of the radial Schröbinger equation. A procedure for matching the parameters of this scatterer to an approximate electrostatic potential of an atom in the form of a screened Coulomb potential has been determined. The screening radius of the latter potential has been calculated proceeding from the properties corresponding to the Thomas-Fermi method. A model of a scatterer determined according to the aforementioned procedure can be used to calculate the energy dependence of the cross section of elastic electron scattering on some atoms with s, p, and d shells representing elements neighboring zirconium. The main result is the establishment of factors responsible for the appearance of maxima on the energy dependences of the cross section of elastic electron scattering. These maxima are related to the resonant trapping of impinging electrons by quasi-stationary levels in a continuous spectrum.     

Calculation of free-free Gaunt factors for 1 keV electrons in a 1 keV normal density Ce plasma

We compare numerical results for free-free Gaunt factors in a hot dense cesium plasma, obtained in the average atom approximation either with a simple approximate analytic potential or with the finite temperature Thomas-Fermi model. We obtain results (for the spectrum of radiation from a 1 keV electron incident on a cesium ion in a 1 keV plasma) from an exact numerical calculation in partial waves of the relativistic electron Bremsstrahlung cross section treated as a single electron transition within these potentials. Comparison shows that Born approximation results in the same potentials fail by large factors, especially at the soft photon end of the spectrum.     

He原子和BH分子碰撞体系的转动激发能量转移

在碰撞体系He+BH的CCSD(T)二维势能面基础上,应用密耦方法,研究了 He+BH分子碰撞转动激发过程.计算了该体系的转动态-态激发的弹性和非弹性的微分和积分截面,分析了计算结果与势能面特征间的关系.结果表明: He原子以从H原子端共线形式碰撞BH分子对j=0→j'=2的激发最为有效;短程排斥对Δj=2的激发作用较大;态-态跃迁总截面出现振荡结构,长程部分分波只对j=0→j'=1的跃迁总截面有较大贡献,j'≥ 关键词： He+BH体系 转动激发 散射截面     

Cross sections of electron capture and electron capture ionization versus the impact parameter in collisions of a proton with multielectron atoms

The absolute differential cross sections of scattering of hydrogen atoms resulting from an electron capture and an electron capture ionization are measured for collisions of 4.5- and 11-keV protons with argon and xenon atoms. The range of scattering angles is 0°–2°. From the scattering differential cross section found experimentally, the probabilities of single-electron capture and electron capture ionization as a function of the impact parameter are calculated. The dependences of the incident particle scattering angle on the impact parameter (deviation function) for interactions with Ar and Xe atoms are calculated in terms of classical mechanics using the Moliére—Yukawa potential to describe the interaction of atomic particles. Analysis is given to the probabilities of electron capture and electron capture ionization versus the impact parameter and to the distribution of the electron density on different electron shells in a target atom versus a distance to the core. It is concluded that only electrons from the outer shell of the target atom are involved in the process of electron capture ionization. The cross section of electron capture ionization is calculated in the proton energy range 5–20 keV.     

10Neq+(q=1～3)的电荷损失截面

采用托马斯－费米近似和二体碰撞近似,计算了多电荷离子１０Ｎｅ＾ｑ＋与中性原子Ｈ和Ｈｅ碰撞的电荷损失截面以及电子的动量分布和离子势函数分布。     

质子与He+,Li++高能碰撞过程中电子俘获截面的理论计算

用OBK近似和CDW近似计算了H⁺+He⁺和H⁺+Li⁺⁺碰撞过程中电子俘获到激发态的分截面与俘获到基态分截面的比值，结果发现用OBK近似给出的比值和用CDW方法所给出的相应比值在高能区符合得很好．由此提出了一种用于计算高能H⁺与任一类氢离子碰撞的电子俘获总截面及任一激发态分截面的方法 关键词：     

Scattering of slow electrons by inert gas atoms. Effective polarization potential method

The problem of selecting the polarization-correlation potential V _pol for describing the interaction of electrons with atomic targets is examined. Based on the differential cross section for electron scattering by the hydrogen atom calculated using the partial wave method and the exact exchange operator, the optimal form of this potential is determined. It is demonstrated that the parameters of the potential V _pol can be determined from the condition of equality of the calculated and experimental values of the electron affinity of the hydrogen atom. For the interaction of slow electrons with inert gas atoms, the polarization parameter R _p is proposed to be determined from the known position of the Ramsauer minimum in the total elastic scattering cross section. In particular, calculations are performed for krypton and argon atoms. The results agree well with numerous experimental and theoretical published data.     

Classical binary-encounter collision theory for electron-impact ionization of ions

We calculated electron-ion impact ionization using classical binary-encounter collision theory. A differential cross section per unit energy and momentum transfer is derived for two-electron scattering. We obtain the total ionization cross section by integrating this differential cross section over the appropriate energy and momentum transfer and the bound electron-velocity distribution. To simplify the computation, we calculated the bound electron-velocity distribution in the Thomas-Fermi approximation. Comparison with other theoretical calculations shows that our results agree within 50% with the best quantum qpproximations. Our cross sections and rate coefficients, which are sufficiently accurate for many practical applications, are expressed in computationally simple form.     

Total cross sections for scattering of electrons from O2, H2O, H2, O3, CO and CO2 at 100－2000eV

A complex optical model potential rewritten by the concept of bonded atom, which considers the overlap of electron clouds, is employed to calculate the total cross sections for electron scattering from several simple molecules (O_2, H_2O, H_2, O_3, CO and CO_2) consisting of C, H and O atoms in an incident energy range of 100－2000eV by the use of the additivity rule at Hartree－Fock level. In the study, the complex optical potential composed of static, exchange, correlation polarization plus absorption contributions firstly uses the bonded-atom concept. The quantitative molecular total cross section results are compared with experimental data and with the other calculations wherever available and good agreement is obtained. It is shown that the additivity rule along with the complex optical model potential rewritten by the concept of bonded atom can be used successfully to calculate the total cross section of electron－molecule scattering above 100eV, whereas the rule together with the complex optical model potential not rewritten by the concept of bonded atom is only successfully used above 300－500eV. So, the introduction of the bonded-atom concept in the complex optical potential can improve the accuracy of the total cross section calculations.     

100～5 000 eV下电子被等电子(Z=10)分子CH4、H2O、HF及NH3散射的总截面计算

利用可加性规则,使用Roothaan-Hartree-Fock波函数,在100～5 000 eV下首次采用由束缚原子概念修正过的复光学势,对电子被等电子(Z=10)分子CH4、H2O、HF和NH3散射的总截面进行了计算.束缚原子不同于自由原子之处,是束缚原子考虑了在不同分子中电子云的不同重叠,将计算结果与实验及其它计算结果进行了比较.结果表明,利用被束缚原子概念修正过的复光学势及可加性规则进行计算,其结果的精度要比利用未被束缚原子概念修正过的复光学势及可加性规则进行计算得到的结果好.     

中高能电子被氟代甲烷散射的总截面计算

利用可加性规则,使用Hartree-Fock 波函数,采用被束缚原子概念修正过的复光学势,首次在100～5 000eV内对电子被具有较多电子数的氟代甲烷分子散射的总截面进行了计算,且将计算值与实验值及经验公式进行了比较,得出了被束缚原子概念修正过的复光学势可成功用于"电子-氟代甲烷"散射总截面计算的结论;研究了"电子-氟代甲烷"的散射总截面与目标分子总电子数及电子入射能量间的关系,初步分析了结构因子与总电荷数相关的原因,并指出了对复光学势进行进一步修正时应遵循的原则.     

Total cross sections for electrons scattering from simple molecules containing the larger atom sulfur at 30-5000eV

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds, is employed to calculate the total cross sections for electrons scattering from simple molecules （SO2, H2S, OCS, CS2 and SO3） containing the larger atom, sulfur, at 30-5000eV by using the additivity rule model at Hartree-Fock level. The quantitative molecular total cross section results are compared with those obtained in experiments and other calculations wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical model potential modified by the concept of bonded atom can give the results closer to the experiments than the one unmodified by it. So, the introduction of bonded-atom concept in complex optical model potential betters the accuracy of the total cross section calculations of electrons from the molecules containing the larger atom, sulfur.     

Binding energies and bound-free transition matrix elements for an impurity atom in a hydrogen plasma

We have obtained potentials, energy levels, and bound-free transition matrix elements for an iron impurity atom in a hydrogen plasma, under varying conditions of density and temperature, according to the Thomas-Fermi (TF) and Debye-Huckel Thomas-Fermi (DHTF) statistical average-atom models. Shape resonance features in the two models are very different.     

Is Dirichlet the physical boundary condition for the one-dimensional hydrogen atom?

It is argued that Dirichlet is the physical boundary condition at the origin for the one-dimensional hydrogen atom: The three-dimensional hydrogen atom is confined to a tube, and the limit as the diameter of the tube cross section goes to zero is taken. It is shown that the energy expectations are finite only in case of Dirichlet boundary condition.     

Semiclassical S-matrix theory for atomic fragmentation

A semiclassical scattering approach is developed which can handle long-range (Coulomb) forces without the knowledge of the asymptotic wave function for multiple charged fragments in the continuum. The classical cross section for potential and inelastic scattering including fragmentation (ionization) is derived from first principles in a form which allows for a simple extension to semiclassical scattering amplitudes as a sum over classical orbits and their associated actions. The object of primary importance is the classical deflection function which can show regular and chaotic behavior. Applications to electron impact ionization of hydrogen and electron–atom scattering in general are discussed in a reduced phase space, motivated by partial fixed points of the respective scattering systems. Special emphasis, also in connection with chaotic scattering, is put on threshold ionization. Finally, motivated by the reflection principle for molecules, a semiclassical hybrid approach is introduced for photoabsorption cross sections of atoms where the time-dependent propagator is approximated semiclassically in a short-time limit with the Baker–Hausdorff formula. Applications to one- and two-electron atoms are followed by a presentation of double photoionization of helium, treated in combination with the semiclassical S-matrix for scattering.     

Time dependent Thomas Fermi approach to atomic collisions I.

A numerical solution of the time dependent Thomas-Fermi equations introduced by Bloch is presented for the case of the scattering of a proton from an argon atom. We discuss in detail the resulting time development of the many electron density distribution and velocity fields for proton bombarding energies of 0.4, 0.9 and 2.5 MeV. Possible foundations of the model, in particular the relation to the time dependent Hartree-Fock method are indicated.