Classical and quantum scattering by a Coulomb potential

For relativistic energies the small-angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contains the classical terms which are independent of that charge. The difference in classical and quantum cross sections may be partly attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this effect. The text was submitted by the authors in English.     

A model study on the nuclear photoeffect

In a simple model of a spinless particle moving in a finite square well potential influences of final state Born approximation and of various approximations in the electromagnetic operators on photoabsorption differential, total and integrated cross sections are investigated. While the Born approximation is very poor in all respects, the long wave length approximation turns out to be the best and reproduces the total cross section quite well. However, appreciable deviations occur in the differential cross section at intermediate energies. The integrated cross section slightly exceeds the classical sum rule resulting from nonanalyticity of the forward compton scattering amplitude, as is discussed in the limiting case of theδ-potential.     

Rearrangement collisions for high energies (linear model)

The high energy behaviour of the cross section for particle exchange in a three particle collision is investigated for arbitrary masses and a rather general class of potentials. For convenience we use a linear model. It is shown that in general the first and second Born approximation provide the leading terms for high energies. If the exchanged mass is “small” the interaction between the two heavy masses cancels. The wave treatment and the impact parameter version give identical results. For particular mass ratios either the first or the second Born approximation provides the leading term. Then even backscattering can be dominant. The high energy results agree with the asymptotic expansion for two exactly solvable cases.     

Inner-shell ionization of atoms by electron,positron and photon impacts

Plane wave Born approximation with Coulomb, relativistic and exchange corrections is employed to obtain L1-, L2- and L3-subshell ionization cross sections of several atoms due to electron and positron impacts for projectile energy varying from the threshold of ionization to 60 times the threshold energy. Photoionization cross sections for all the three L-subshells of the atoms are also calculated using the hydrogenic approximation for the atomic wave functions. For L3-subshell the present cross sections due to electron impact are in good agreement with a number of experimental data for different atoms over the entire energy range investigated. For L1- and L2-subshells the present calculations yield qualitative agreement with the experimental data. The agreement between the present results and the limited experimental data for positron impact is also satisfactory. The hydrogenic approximation for the L-subshell photoionization is found to be good at small photon energies but it underestimates the cross sections at large photon energies.     

M X‐ray production cross sections for heavy elements by proton impact

We present in this paper, M‐shell ionization cross sections and M X‐ray production cross sections calculated within the Energy loss, Coulomb deflection, Perturbed Stationary State and Relativistic effects (ECPSSR) theory for elements with 72 ≤ Z ≤ 90 for protons with 0.1–4.0 MeV energy. Our results are compared to the plane wave Born approximation (PWBA) predictions, the relativistic plane‐wave Born approximation including corrections for binding and Coulomb deflection effect (RPWBA‐BC) results and the ECPSSR calculations from earlier works. On the other hand, semiempirical and empirical M X‐ray production cross sections are deduced from the polynomial fitting of the available experimental data collected from different sources. A comparison is made between the different sets of results. The differences between the above calculations and the experimental results are pointed out and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.     

Relativistic coulomb collisions and the virtual radiation spectrum

We evaluate the Coulomb-excitation cross sections in relativistic heavy-ion collisions by means of the plane-wave Born approximation. The final total cross section is shown to be equal to that obtained by a semiclassical method. As a byproduct the virtual photon spectrum for similar electromagnetic processes is derived. Comparison with other methods is performed.     

Radiative corrections to chiral amplitudes in quasiperipheral kinematics

Chiral amplitudes for two-jet processes in quasiperipheral kinematics are calculated at the Born and one-loop correction levels. The amplitudes of subprocesses describing the interaction of a virtual and a real photon with the creation of a charged fermion pair for various chiral states are considered in detail. Similar results are presented for the Compton subprocess with a virtual photon. Contributions of the emission of virtual, soft, and hard real additional photons are explicitly taken into account. The relevant cross sections expressed in terms of impact factors are in agreement with the structure function approach in the leading logarithmic approximation. Contributions of the next-to-leading terms are represented in analytic form. Estimation of accuracy is discussed. The text was submitted by the authors in English.     

低能质子引起的金LX射线相对产生截面

对于能量为０．５－１ＭｅＶ的入射质子，在计算中采用ＡｕＬ１次壳层荧光产额的实验值代替相应的Ｄｉｒａｃ－Ｈａｒｔｒｅｅ－Ｓｌａｔｅｒ值时，使用ＲＰＷＢＡ－ＢＣ（经结合能和库仑歪曲修正的相对论平面波玻恩近似）电离截面计算得到的金原子ＬＸ射线相对产生截面与测量值相符。以前报道的对ＲＰＷＢＡ－ＢＣ截面的各种修正都是不需要的     

量子力学中的二维散射问题

研究了量子力学中的二维散射问题，讨论了分波法和Ｂｏｍ近似法，并计算了一些实例。     

Kinetic Approach to the Electrical Conductivity in a Partially Ionized Hydrogen Plasma

The electrical conductivity is investigated for a partially ionized hydrogen plasma, starting from a generalized quantum kinetic equation with three particle collision integrals. To take into account plasma effects, screened potentials are used. The transport cross sections of the considered two and three particle scattering processes are calculated by perturbative solution of the Lippmann-Schwinger equations for the T-matrices up to the second Born approximation. In connection with a mass action law the influence of the electron-electron and the elastic electron-atom scattering is discussed. The pressure ionization (Mott-effect) is described by a minimum-behaviour of the electrical conductivity.     

Radiative corrections to very high energy electron-proton scattering

A “leading log” analysis of radiative corrections to inclusive ep scattering at HERA energies is presented. Neutral current weak interactions are considered at the level of the Born cross section as well as of the modifications of vertex and vacuum polarization parts. The leading log approximation has been also improved in the single hard and multiple soft photon emission by appropriate kinematical considerations. Some numerical results are presented for polarized electron and positron beams.     

On Born approximation in black hole scattering

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner–Nordström and Reissner–Nordström–de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.     

SEMI‐empirical and empirical formulas for calculation of K‐shell ionization cross sections by proton impact: a comparison

According to the plane wave Born approximation (PWBA) and the binary encounter approximation (BEA) models, it is possible to fit the cross sections obtained with any atomic element at any particle energy using a scaling law for a K‐shell. The semi‐empirical K‐shell ionization cross sections are then deduced by fitting the available experimental data normalized to their corresponding theoretical values. For the empirical K‐shell ionization cross sections, a third‐order polynomial was used to fit the same experimental data for protons. Our results are compared with the predictions of the ECPSSR theory and with other earlier works. Good agreement is obtained, but it is emphasized that the ultimate solution is to deduce the cross sections by fitting the available experimental data for each element separately. Copyright © 2008 John Wiley & Sons, Ltd.     

2γ and 3γ annihilation as calibration processes for high energy <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> colliders

Born differential cross sections and the lowest-order radiative correction to them are obtained in the kinematics of large-angle final photon emissions in high-energy electron-positron annihilation processes. Taking into account the possible emission of real soft and hard photons in collinear kinematics, we show the validity of the Drell-Yan form of the differential cross section with the nonsinglet structure functions of the initial leptons. The leading and next-to-leading contribution to the cross sections is obtained. The relevant numerical estimations are presented. The text was submitted by the authors in English.     

Pair production in the gravitational field of a cosmic string

We show that many elementary particle physics processes, such as pair production by a high energy photon, that take place in Minkowski space only if a non-uniform external field provides for momentum non-conservation, do occur in the space-time around a straight cosmic string, even though the space is locally flat and there is no local gravitational potential. We exemplify this mechanism through the evaluation of the cross section per unit length of string for the decay of a massless scalar particle into a pair of massive particles. The cross sections for this kind of processes are typically small. Nevertheless, it is interesting to realize how these reactions occur due to topological properties of space, rather than to the action of a local field.     

On the role of the magnetic dipolar interaction in cold and ultracold collisions: numerical and analytical results for NH(3Σ−) + NH(3Σ−)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important below a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.     

Charge transfer in H~ H and H~ He~ collisions at intermediate and high energies using an asymptotic two-state atomic expansion method

ＣｈａｒｇｅｔｒａｎｓｆｅｒｉｎＨ＋＋ＨａｎｄＨ＋＋Ｈｅ＋ｃｏｌｉｓｉｏｎｓａｔｉｎｔｅｒｍｅｄｉａｔｅａｎｄｈｉｇｈｅｎｅｒｇｉｅｓｕｓｉｎｇａｎａｓｙｍｐｔｏｔｉｃｔｗｏｓｔａｔｅａｔｏｍｉｃｅｘｐａｎｓｉｏｎｍｅｔｈｏｄ▲ＺｈｏｕＸｉａｏｘｉ...     

Bremsstrahlung produced by colliding particles in an external electric field

We have used the nonrelativistic dipole Born approximation to study bremsstrahlung from two colliding charged particles in a uniform electric field. We have calculated the differential cross sections for photon emission as the system transitions into various states of internal motion. We find the cross sections exhibit spatial anisotropy due to the uniform electric field, and that oscillations can arise that are probably due to interference effects between the colliding particles.Khabarovskii State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–50, July, 1994.     

Emission in the final state in processes with the production of charged pions and light leptons

The Drell-Yan form is proposed for the decay widths of heavy quarks and cross sections for high-energy scattering with the production of charged pions and light leptons including radiative corrections in the final state in the leading logarithmic approximation. The corresponding spectral distributions are given in terms of the convolution of the cross section (decay width) in the Born approximation with the structure functions of pions and leptons. The pion structure function is given in the explicit form.