On excitation and loss of an electron by incident ions in relativistic collisions with atoms

The excitation and loss of an electron by ions in relativistic collisions with atoms are studied in first-order perturbation theory. General expressions are obtained for the cross sections for the excitation and loss of an electron. In the limit of nonrelativistic collision velocities these expressions pass into the well-known nonrelativistic results. It is shown that, in contradistinction to the nonrelativistic collisions, in ultrarelativistic collisions the screening of the nucleus of the target atom by the atomic electrons is very important for excitation and loss of an electron by ions even for collisions of heavy ions with light atoms. Our computational results for the cross section for electron loss are in good agreement with existing experimental data.     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

Nonresonant photocreation of electron-positron pair on a nucleus in the field of a pulsed light wave

The nonresonant Coulomb photocreation of electron-positron pair on a nucleus in the field of a pulsed light wave is theoretically investigated. The approximation is examined when pulsewidth is considerably greater than the characteristic time of wave oscillations. The interaction of an electron and a positron with a Coulomb potential of a nucleus is considered in the first order of perturbation theory (the Born approximation). An analytic expression for the nonresonant differential cross section was obtained for the range of moderately strong fields in the case relativistic and nonrelativistic energies. It is shown, that the nonresonant cross section of Coulomb photocreation of nonrelativistic pair in the field of a pulsed light wave is two times larger than the cross section of Coulomb photocreation in the absence of an external field.     

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.     

Explicit designs of spin chains for perfect quantum state transfer

For the process of electron-electron (e-e) bremsstrahlung the momentum and energy distributions of the recoiling electrons are calculated in the laboratory frame. In order to get the differential cross section and the photon spectrum for target electrons which are bound to an atom, these formulae are multiplied by the incoherent scattering function and numerically integrated over the recoil energy. The effect of atomic binding is most pronounced at low energies of the incident electrons and for target atoms of high atomic numbers. The results are compared to those of previous calculations.     

Intermediate mass fragments emitted in the reaction Ag+14N at 100, 160 and 250 MeV bombarding energy

The fragments produced in the reaction between a ¹⁴N beam of various energies and a natural Ag target have been studied. The atomic numbers of the fragments have been identified up to Z = 17 by means of a E-ΔE counter telescope. The cross sections, the kinetic energy distributions as well as the angular distributions have been measured for each atomic number. The kinetic energy distributions show two components: a high-energy component (quasi-elastic), prevailing at angles close to the grazing angles and for atomic numbers close to Z = 7, and a low-energy component (relaxed), at energies close to the Coulomb repulsion energy, present at all angles and for all the Z. A detailed study of the relaxed components of the kinetic energy seems to account for both them means and the widths of these distributions on a purely statistical basis. The cross sections of the relaxed components appear to be quite large at low Z and to decrease rapidly to a fairly constant value in the region of 10 ≦ Z ≦ 17. A marked even-odd alternation in the cross sections is observed. The angular distributions are strongly forward peaked for Z < 7. For Z > 7 the forward peaking decreases rapidly until, for Z > 13, the limiting form 1/sinθ is attained. Evidence for the existence of a diffusion process along the mass asymmetry coordinate is discussed.     

Coulomb and photo cross sections for nucleon emission from relativistic O projectiles

Coulomb cross sections for nucleon emission out of ¹⁶O projectiles scattered with laboratory energies of 2.1, 60 and 200 GeV/nucleon on various target nuclei are calculated in first-order perturbation theory by using the corresponding photo cross sections. The photo cross sections are obtained with an 1-particle-1-hole basis in the giant resonance region and with the quasi-deuteron model up to photon energies of 140 MeV. Whereas the 2.1 GeV/nucleon results agree well with the experimental data points, the 60 and 200 GeV/nucleon cross sections are roughly one quarter lower than the measured ones, because also photons with energies higher than 140 MeV contribute at these incident energies.     

Coulomb breakup of light nuclei in the field of a heavy ion at relativistic collision energies

A simple method for calculating the amplitude and the cross section for the Coulomb breakup of a light nucleus into two fragments in the field of a heavy ion at relativistic collision energies is proposed on the basis of time-dependent perturbation theory. It is shown that the resulting amplitude for the process in question has a correct nonrelativistic limit. The contribution of the longitudinal component of the Coulomb field of a heavy ion tends to zero in the ultrarelativistic limit. A specific implementation of the method is demonstrated by taking the example of the Coulomb breakup reaction ²⁰⁸Pb(⁸B, ⁷Bep)²⁰⁸Pb at various collision energies. The results are found to be in agreement with experimental data.     

The contribution of the central region of the electron energy spectrum to the total double photoionization cross section of helium in the asymptotic nonrelativistic energy region

The double photoionization of helium at high photon energies is considered using a nonrelativistic approach. The central region of the energy spectrum and its contribution to the total process cross section and to the ratio between the double and single ionization cross sections are studied. Interelectronic interaction in the initial state is included exactly, whereas the interaction between the fast outgoing electrons is calculated by perturbation theory. A detailed derivation of the expression for the cross section ratio between double and single ionizations is given. The corresponding results obtained by other authors are analyzed and corrected.     

Integrated Cross Sections of High-Energy <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> Pair Electroproduction by an Electron in an Atomic Field

The integrated cross sections of e⁺e^– pair electroproduction by an ultrarelativistic electron in an atomic field are studied. The importance of various contributions to the integrated cross sections is discussed. The Coulomb corrections have turned out to make a large contribution to both differential and integrated cross sections even at moderate values of the nuclear charge number. The interaction of the electron emitting a virtual photon with the atomic field is shown to contribute significantly to the cross sections differential with respect to the electron transverse momentum. However, this interaction affects only slightly the cross section differential only with respect to the positron transverse momentum.     

K-shell X-ray production for fluorine ions on target elements Ti to La

The production of target atomK-shell X-rays has been studied for 2 to 28 MeV fluorine ions incident on thin solid targets of 14 elements with atomic numbers Z₂=22 to 57. Total X-ray production cross sections, energy shifts ofK _α andK _β lines andK _α/K _β intensity ratios were measured with a Si(Li) detector. The results of cross section measurements are compared with theoretical predictions of inner shell ionization. In most cases, satisfactory agreement between measured cross sections and theoretical Coulomb ionization cross sections, corrected for the perturbation of the target atom by the projectile charge and for relativistic effects, was obtained.     

Experiments on screening effect in deuteron fusion reactions at extremely low energies

The enhanced electron screening effect in nuclear reactions taking place in dense astrophysical plasmas is extremely important for determination of stellar reaction rates in terrestrial laboratories as well as in prediction of cross sections enhancement in interiors of stars such as White and Brown Dwarfs or Giant Planets. This effect resulting in reduction of the nuclear Coulomb potential by the atomic electrons has been confirmed in many laboratory experiments. Unfortunately, experimental screening energies are much higher than the theoretical predictions and the reason for that remains unknown. Here, we present absorbing results of the experiment studying d + d nuclear reactions in different deuterized metallic targets under ultra high vacuum conditions. The total cross sections and angular distributions of the ²H(d,p)³H and ²H(d,n)³He reactions have been measured using a deuteron beam of energies between 8 and 30 keV provided by the electron cyclotron ion source. The atomic cleanness of the target surface has been secured by combining Ar sputtering of the target and Auger electrons spectroscopy. Due to application of an on-line analysis method, the homogeneity of the implanted deuteron densities could be continuously monitored. We will discuss probable causes of the large discrepancy between theoretical and experimental data.     

Studies of In-Medium Nucleon-Nucleon Collision Cross Section in the Nonrelativistic Energy Region

At nonrelativistic energy region, by using Skyrme interaction, nucleon-nucleon collision cross sections in medium and their relations with densities and energies have been studied. It is found that under PauLi correction, nucleon-nucleon collision cross section in medium is larger than free nucieon-nucleon collision cross section.     

Relativistic calculations of inelastic collisions between electrons and atoms

The Feynman S-matrix formalism is used to consider the inelastic collisions of electrons with a hydrogen atom. The two leading Feynman diagrams are calculated, and the 1s-2s transition is treated in detail. Results are given for scattering amplitudes at energies of 1.0–8.0 (atomic units) and for various scattering angles, as well as the differential cross sections for direct scattering in the energy region 1.36–118.5 keV. On the basis of comparison with nonrelativistic calculations, we conclude that relativistic effects are appreciable and increase with energy. Total cross sections are calculated in both nonrelativistic and relativistic approximations. The difference between them increases with energy and is 15–20% for energies of 20–50 keV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–12, August, 1977.     

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.     

The interaction potential of the He+-Au system determined from Rutherford backscattering data

The potential-internuclear-distance dependences for the He⁺-Au system are obtained by processing measurements of particle scattering cross sections at various collision energies. The potential is shown to be independent of the collision velocity. The values obtained made it possible to introduce a correction for the difference of the above potential from the Coulomb one involved in the Rutherford backscattering method, and thus to improve the measurement accuracy. The obtained data on the screening constants enable estimation of the screening effect on the increase in the nucleosynthesis cross sections.     

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable. nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy. The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.     

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy.The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite digerent mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially,it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections, induced by the halo nuclei due to the very weak binding and the very extended density distribution.     

Near-barrier fusion of the ⁸B + ⁵⁸Ni proton-halo system

Fusion cross sections were measured for the exotic proton-halo nucleus ?B incident on a ??Ni target at several energies near the Coulomb barrier. This is the first experiment to report on the fusion of a proton-halo nucleus. The resulting excitation function shows a striking enhancement with respect to expectations for normal projectiles. Evidence is presented that the sum of the fusion and breakup yields saturates the total reaction cross section.