Glauber Approximation Research Articles

Double-ionization fraction of the Glauber cross sections for proton and helium collisions.

Differential cross sections for single and double ionization for p+He collisions at 0.3, 0.7, and 1 MeV are calculated using the Glauber approximation. The angular dependence of the fraction of double ionization shows a sharp peak at a scattering angle of 0.8 mrad, which is slightly smaller than the experimental finding. The peak values decrease slowly with increasing collision energies, in accordance with the experiment, but the absolute values are about twice as large. The analysis of the present result shows that the peak of the fraction is caused mainly by the structure of the single-ionization cross section rather than the double-ionization cross section.

Coulomb Dissociation of the Weakly-Bound Nucleus 11Li

Dissociation cross sections are calculated for the reaction llLi+Tar~et (with charge ZTe)->9Li + X by using the Glauber approximation, modified suitably for two-neutron removal reactions. It is found that the effect of finite qJ., the transverse component of momentum transfer, alters target· charge dependence of the Coulomb dissociation cross section as OC rx ZTl.74, while· the normal depen­ dence OC rx ZT2 is obtained if no such effect is included. Using a technique of secondary radioactive beams, Kobayashi et al.

Target-charge dependence of the Coulomb dissociation cross section of 11Li

Dissociation cross sections are calculated for the reaction 11 Li + Target → 9 Li + X within the Glauber approximation. The present Glauber calculation well reproduces experimental cross sections: the nuclear dissociation cross section has a target-mass dependence quite similar to the one obtained by Kobayashi et al. based on the factorization model and the Coulomb dissociation cross section has a target-charge dependence of Z 1.74, close to the experimentally deduced one. The suppression of the Coulomb dissociation cross section, compared with the normal Z 2 dependence, comes from the effect of finite q ⊥, the transverse component of momentum transfer.

Nuclear transparency to intermediate-energy nucleons from (e,e'p) reactions.

A simple relation between the nucleon-nucleon scattering cross sections in vacuum and in nuclear matter is proposed. It consistently takes into account the velocity dependence of the nuclear mean field and Pauli blocking, and is shown to be fairly accurate. It is used to study the mean free path of nucleons in nuclear matter and the imaginary part of the optical potential. It is also used with the local density approximation and the correlated Glauber approximation to calculate the transparency of nuclei as measured by (e,e'p) reactions. The Pauli blocking, velocity dependence of the nuclear mean field, and the ground-state correlations increase the transparency, and all the three effects are necessary to explain the observed transparencies of $^{12}\mathrm{C}$, $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, and $^{181}\mathrm{Ta}$ for recoiling 180 MeV protons.

Algebraic-eikonal approach to the electron-molecule-collision process: Vibrational excitation and quadrupole interaction.

The vibrational excitation mechanism has been included in the algebraic-eikonal approach to the electron--polar-molecule collision process. A dipole operator that can induce vibrational transitions has been used, and a technique for the evaluation of the matrix elements required for the calculation of the scattering amplitude in the Glauber approximation has been developed. In addition to the long-range dipole interaction, the quadrupole interaction has been included in the same framework in order to improve the potential description of the collision process. Numerical calculations are shown for electron-induced rotational-vibrational excitation through the dipole and dipole-plus-quadrupole interactions.

Doubly differential cross sections for ionization of helium by electron impact.

The Glauber approximation is used to calculate doubly differential cross sections (DDCS's) for electron-impact ionization of helium at incident energies of 100, 300, and 500 eV. Angular dependences of the cross sections are presented for the primary (scattered) electrons. The present calculation is done for the case where the energy of the primary electron is large compared with that of the secondary (ejected) electron. A comparison is made of the present DDCS with the results of other calculations and experiment.

Elastic scattering of electrons and positrons from rubidium.

The elastic scatterings of electrons and positrons from rubidium are calculated at intermediate energies in the Born, Glauber, modified Glauber (MG), and eikonal-Born-series approximations. The results of differential cross sections (DCS) for elastic scattering obtained within these various methods of approximation are presented with discussion. The modified Glauber results predict the existence of structures for the DCS, similar to those of scattering from potassium and sodium. Furthermore, the structures in this case persist even at a scattering energy as high as 500 eV. The DCS in the modified Glauber approximation at small scattering angles are used to estimate the ``effective'' total cross sections for positron and electron scatterings from rubidium. The effective MG total cross sections are found to be in better agreement with experimental data.

Deuteron fragmentationd+a→p+x at relativistic energies and the role of the target nucleus

The modified phase-space model for the description of inelastic hadronic and nuclear reactions is applied todp, dd, anddC collisions at 9 GeV/c. Inclusive proton spectra are calculated as an incoherent superposition of processes classified by the number of projectile and target nucleons participating in the interaction. The corresponding integrated cross sections are evaluated in the Glauber approximation. For given numbers of participants the probability of observing a definite final channel is assumed to be proportional to the phase-space factor modified by a transition matrix element that is based on statistics, thermodynamics, and the quark picture of hadrons. By using conventional wave functions and taking particle production into account the overall features of the proton spectra at 0‡ and 8‡ are satisfactorily reproduced. With increasing target mass the properties of the target nucleus become important for the correct description of the spectra.

Effects of short-range correlations and three-body force on proton-3He scattering at high energy

Proton-3He elastic scattering is studied within the framework of the Glauber approximation at 1 GeV. The short-range correlations and the three-body force effects are studied. These effects are considered through a ground state wavefunction of the target nucleus. The results are discussed and compared with experimental data.

Comparison of the total cross sections for positron (electron) collisions with alkali-metal atoms

The total cross sections for electron and positron collisions with sodium and potassium are calculated in the modified Glauber (MG) approximations, employing the Szazs-McGinn wavefunctions within the frozen-core approach. While the present values of total cross sections for electron and positron collisions are found to be consistent with those previously obtained in the model-potential approach, the positron and electron MG cross sections of the present calculation merge with each other at a rather low energy, as was observed in experiments by Stein et al. (1988-90).

Generalized oscillator strength for the 3s-3p and 2p-3s transitions in the sodium atom.

The generalized oscillator strengths for the 3s-3p and 2p-3s excitation processes have been obtained from the related differential cross sections, measured at 1-keV impact energy and normalized to the first-Born-approximation (FBA) result for the 3s-3p process at the scattering angle of 2\ifmmode^\circ\else\textdegree\fi{}. Theoretical values for the 3s-3p excitation process were also determined using the Glauber approximation, both considering the interaction of the incident electron with the atomic electrons not directly involved in the excitation process and (N-1) nuclear charges and by neglecting this interaction. FBA results were determined for both the 3s-3p and 2p-3s processes. Theoretical values for the elastic differential cross section were also determined.

Ionization of atoms by fully stripped ions in the glauber approximation

We report a method of evaluation of cross sections for single and double ionization of atoms by fully stripped ions. The method is based on the Glauber approximation. In the case of a hydrogenic target the probability amplitude turns out to be a simple two-dimensional integral which can be evaluated numerically with convenience.

Elastic nucleon-antinucleon scattering arising from two-gluon exchange diagrams

Contributions of two-gluon exchange diagrams to the elastic NN interaction at intermediate energy are compared with that from qq pair annihilation and creation with the former being calculated via the Glauber approximation. The necessary input of the qq scattering amplitude is obtained from the Richardson qq potential with some modifications. Results show that the former cannot be less important than the latter in all the calculated cases.

Erratum: Elastic and inelastic electron and positron scatterings from metastable hydrogen

The elastic and inelastic electron and positron scatterings from metastable hydrogen H(2{ital s}) are calculated by using the Wallace and Glauber approximations (Phys. Rev. Lett. 27, 622 (1971); Ann. Phys. (N.Y.) 78, 190 (1973); {ital Lectures} {ital in} {ital Theoretical} {ital Physics}, edited by W. F. Brittin (Interscience, N.Y. 1959), Vol. 1, pp. 315--414). The general expressions for the Wallace amplitude, which are valid for any {ital s}-{ital s} and {ital s}-{ital p} collision process, are given. A comparison of the results of angular distributions for electron and positron scatterings from the metastable 2{ital s} state of hydrogen reveals some significant differences in their behavior when compared to the case of scattering from the ground 1{ital s} state.

Elastic and inelastic electron and positron scatterings from metastable hydrogen.

The elastic and inelastic electron and positron scatterings from metastable hydrogen H(2s) are calculated by using the Wallace and Glauber approximations [Phys. Rev. Lett. 27, 622 (1971); Ann. Phys. (N.Y.) 78, 190 (1973); Lectures in Theoretical Physics, edited by W. F. Brittin (Interscience, N.Y. 1959), Vol. 1, pp. 315--414]. The general expressions for the Wallace amplitude, which are valid for any s-s and s-p collision process, are given. A comparison of the results of angular distributions for electron and positron scatterings from the metastable 2s state of hydrogen reveals some significant differences in their behavior when compared to the case of scattering from the ground 1s state.

Total cross sections for positron collisions with rubidium

The total cross sections for positron and electron collisions with rubidium are calculated in the energy range 15-1000 eV, employing the modified Glauber approximation. The MG total cross sections are found to be in reasonably good agreement with experimental data at energies below 100 eV, and consistent with the total cross sections calculated at energies below 30 eV in the close-coupling approximations.

Spin-isopin hadronic response in the Glauber theory

Spin-isospin surface response functions are calculated in the random phase approximation framework with a harmonic oscillator basis and tested on the ( p, p′) and ( 3He, t) reactions in the quasi-elastic peak region. The cylindrical geometry of the reactions is implemented in the Glauber approximation and turns out to be relevant in accounting for the shift of the quadi-elastic peak observed at high transferred momenta in the ( 3He, t) reaction.

Recent advances in the spin-isospin nuclear responses

The Random Phase Approximation formalism for the spin-isospin nuclear response functions is presented and applied to deep inelastic electron and proton scattering and to charge-exchange reactions. The reaction mechanism for hadron scattering on nuclei is treated in the one-step Glauber approximation which is also shortly revisited.

Single nucleon removal in relativistic nuclear collisions.

We implement a simple approach to the inclusive cross section for single nucleon removal by relativistic nucleons and nuclei. We first develop the projectile and target dependence of the mean number, {ital N}({ital b}), of nucleon-nucleon collisions as a function of impact parameter in the peripheral region. Using the Glauber approximation, we obtain a simple parametrization for a critical impact parameter {ital b}{sub {ital c}} such that the reaction cross sections for both {ital N}-{ital B} and {ital A}-{ital B} collisions are well represented by {pi}{ital b}{sub {ital c}}{sup 2}. Further study of the {ital b} dependence of {ital N}({ital b}) around {ital b}={ital b}{sub {ital c}} allows us to develop a parametrization of single nucleon abrasion cross sections. Next, we employ the Weizsacker-Williams approximation with {ital b}{sub {ital c}} as the cutoff impact parameter to calculate the Coulomb contribution to the single nucleon removal process. The results are compared with recent data which suggest that the Weizsacker-Williams approximation is inadequate for heavy projectiles. Using our estimates for the nuclear contribution, we find that the data yields good agreement with the Weizsacker-Williams results for virtually all projectile-target combinations. We therefore conclude that the measured deviations from the Weizsacker-Williams results domore » not represent new physics, but rather reflect uncertainties in the estimation of the nuclear contribution to the single nucleon removal process. As an elementary example of the possible new physics that may be observed in this process, we calculate the contributions from a coherent nuclear process and the possible interference effects. For heavy projectiles, we find that the interference effects are comparable to the present experimental uncertainties.« less

Post collision interaction effects in the ionisation of helium by electron impact

The authors present triply differential cross sections for electron impact ionisation of helium for a coplanar asymmetric geometry at incident energies of 256 and 600 eV. The calculation is based on the Glauber approximation (GA). The effect of post collision interaction (PCI) is incorporated in the GA using a classical method. The angular distributions of the ejected electrons predicted by the present method are in reasonably good agreement with experiment. The inclusion of PCI improves the recoil distributions considerably at 256 eV.