Distributions Of Double-differential Cross Sections Research Articles

Electron emission cross sections for collisions of heavy ions with atomic targets

A theoretical study of the double-differential cross sections (DDCS) for ejection of electron from hydrogen atom in ground state by the impact of $$\hbox {C}^{6+}$$ ion with energy values 1 and 2.5 MeV/amu is presented. For the final state, we use a continuum distorted wave that contains the product of two Coulomb distortions due to the projectile–electron and target–electron Coulombic interactions for which it is called the two-Coulomb-wave (2CW) model. In this paper, the energy and angular distributions of DDCS for electron emission from atomic hydrogen have been investigated. The ejected electrons are influenced by the combined fields of the target and the projectile ion. Comprehensive comparisons are made between the three-Coulomb-wave model (Jana et al. in Eur Phys J D 66:243, 2012) and the present 2CW model. The emitted electron, the incident projectile ion and the residual ion are considered to be in the same plane. It is found that the two-centre effect has a major influence on the observed forward–backward angular asymmetry in the angular distribution of electron emission spectra. The region of the binary encounter peak is analysed in detail. The present computed results have been compared with the available experimental results as well as other theoretical calculations based on the first Born approximation and the continuum distorted wave eikonal initial state approximation. Moreover, the present computed results are in better agreement with the available experimental data for electron emission cross sections.

Energy and angular distributions of electron emission from diatomic molecules by bare ion impact

The three-Coulomb wave model has been used extensively to study the energy and angular distributions of double-differential cross sections (DDCS) of electron emissions from hydrogen and nitrogen molecules by bare ion impact at intermediate and high energies. In the present model, we have expressed the molecular triple differential cross section in terms of the corresponding atomic triple differential cross section multiplied by the occupation number and the average Rayleigh interference factor, which accounts for the two-center interference effect. Here we have used an active electron approximation of the molecule as a whole in the initial channel. To account for the effect of passive electrons, we have constructed a model potential that satisfies the initial conditions and the corresponding wavefunction has been calculated from the model Hamiltonian of the active electron in the target. In the final channel, we have used a hydrogenic model with an effective nuclear charge that is calculated from its binding energy. In this model, the correlated motion of the particles in the exit channel of the reaction is considered by an adequate product of three-Coulomb functions. The emitted electron, the incident projectile ion and the residual ion are considered to be in same plane. The obtained results are compared with other recent theoretical and experimental findings. There is an overall agreement of the calculations with the experimental data for electron emission cross sections.

Electron DDCS in ionization of H2O by 72 MeV O8+ ions: comparison with CDW-EIS post and prior forms

We have measured energy and angular distributions of double differential cross-sections (DDCS) for electron emission in ionization of water molecule under the impact of 72-MeV O8+ ions. The DDCS values have been compared with a state-of-the-art CDW-EIS calculation for both the prior and post forms of scattering matrix. The prior form of the CDW-EIS model produces better quantitative agreement with the experimental data.

Energy and angular distributions of the low-energy electron emission in collisions of 4 MeV/u bare F ions with He atoms

The energy and angular distributions of double-differential cross sections (DDCS) of electron emission from He in collisions with 4 MeV/u F9 + ions are reported. The derived single-differential distributions and the total cross sections are also reported. The measured distributions of the low-energy electrons between 1 and 400 eV over a wide angular range between 20° and 160° are compared with the state-of-the-art quantum mechanical models. The first Born (B1) and the continuum distorted wave-eikonal initial state (CDW-EIS) approximations are used for this purpose. The DDCS for a given angle was found to fall by a few orders of magnitude over the electron energy range studied. The CDW-EIS model provides excellent agreement with the energy distributions and the angular distributions. The electron energy dependence of the forward–backward asymmetry parameter shows monotonically increasing behaviour. This has been explained very well in terms of the CDW-EIS model, which includes the two-centre effect. A large deviation from the B1 is also observed. We have also derived the single-differential distributions in terms of the angle as well as the electron energy. These distributions are also well reproduced by the CDW-EIS model.

Ionization of molecular hydrogen by 5 MeV/u bare fluorine ion and electron interference

Electrons emitted from H2 in collisions with 5 MeV/u F9 + ions were measured in the energy range from 1 to 300 eV and a wide range of emission angles between 20° and 160°. The measured energy and angular distributions of double-differential cross sections (DDCSs) of these electrons are compared with the molecular continuum distorted wave-eikonal initial state (CDW-EIS) calculation. The observed energy and angular distributions can be explained, in general, with the help of the two-centre effect which is included in the CDW-EIS model. In addition, the DDCS ratios of molecular-to-atomic hydrogen exhibit an oscillatory structure which is discussed in terms of Young-type electron interference. We have obtained the frequencies of such oscillations and studied their angular dependence. The single-differential cross sections (SDCSs) are deduced by integrating the DDCSs over solid angle and emission energy. We demonstrate that the SDCS ratio spectra also preserve the signature of interference to some extent. The asymmetry parameter, derived only from the molecular cross sections for forward and backward angles, shows an oscillatory behaviour as a function of electron velocity. This is understood in terms of the interference effect superimposed with the post-collisional two-centre effect.

Investigation of IVGRs via theNi(t,He)Co reaction

A 130 MeV primary tritium beam, newly developed at the superconducting cyclotron AGOR, has been used for the investigation of 1ħω and 2ħω isovector giant resonances in58Co via theτ+ channel. The angular distributions of double-differential cross sections have been extracted betweenEx = 7 and 30 MeV fromθlab = 0° to 6°. A DWBA analysis with normal-mode (NM) wave functions and a multipole-decomposition analysis (MDA) indicate strength for the monopole resonances (dominated by the spin-flip transition) fragmented between 10 and 27 MeV excitation energy, in rather good agreement with preliminary RPA calculations.

Investigation of IVGRs via the 58Ni(t, 3He) 58Co reaction

A 130 MeV primary tritium beam, newly developed at the superconducting cyclotron AGOR, has been used for the investigation of 1ħω and 2ħω isovector giant resonances in 58Co via the τ + channel. The angular distributions of double-differential cross sections have been extracted between E x = 7 and 30 MeV from θ lab = 0° to 6°. A DWBA analysis with normal-mode (NM) wave functions and a multipole-decomposition analysis (MDA) indicate strength for the monopole resonances (dominated by the spin-flip transition) fragmented between 10 and 27 MeV excitation energy, in rather good agreement with preliminary RPA calculations.

Angular and energy distributions of ejected electrons in the direct and resonance He(e, 2e)He+ reactions

Angular and energy distributions of ejected electrons in the direct and resonance He(e, 2e)He+ reactions are studied. It is shown that the first Born approximation (FBA) can be used to described ejected electron characteristics at incident energies E0>or=500 eV and ejection energies Eb<or=40 eV. It is also shown that the anisotropy of ejected electrons and the predominance of higher-order multipole terms are due to the peculiarities of the angular distributions of double-differential cross sections under different kinematical conditions. Under the conditions of FBA validity the profiles of the overlapping 1P and 1D autoionization resonances (AIR) in the ejection spectra of the He(e, 2e)He+ reaction are investigated by using the resonance structure of the angular coefficients. The resonance structure of the angular coefficients might provide more detailed information on the profiles and interaction mechanism of the 1P and 1D AIR at different multipoles L. Calculations carried out in the concrete structure model are compared with the available experimental data and theoretical estimates.