On the behaviour of the (e, 3e) total cross section for helium at high and intermediate energies

Bahati, EM; Cherkani-Hassani, H.; Defrance, Pierre; Jureta, Jozo; Kereselidze, Tamaz; Machavariani, Z. S.; Noselidze, Irakli

doi:10.1088/0953-4075/38/8/015

Cited by 12 publications

(9 citation statements)

References 45 publications

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“…In addition, the scattered electron being, by definition, the most energetic electron in the final state, we have followed the recommendations of Defrance et al [54] and Bahati et al [55] and defined the upper limits of the integration E 1 max and E 2 max as…”

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confidence: 99%

Electron-induced double ionization of isolated water molecules

2013

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Theoretical doubly differential and total cross sections for electron-induced double ionization of oriented water molecules are reported here. The calculations are performed within the first Born approximation by describing the initial molecular state by means of single-center wave functions. Furthermore, the incident (scattered) electron is described by a plane wave while a Coulomb wave function is used for modeling the two secondary ejected electrons. The contribution of each final state to the double-ionization process is analyzed, namely, in considering target electrons ejected either from similar or from different molecular subshells. Thus, secondary electron energetic distributions as well as total cross sections are reported for particular target configurations, pointing out orientation effects in the double-ionization process

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confidence: 99%

Electron-induced double ionization of isolated water molecules

2013

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“…Perhaps, it should be also emphasized that the compact trial functions are not only valuable in order to gain understanding of quantum mechanics of compact few-body systems-bound state-but they are also of interest to the collision community [12]. It turns out that simple but accurate wave functions are very useful as a starting point in the calculation of double ionization cross section by electron or radiation impact as was indicated as early as by Chandrasekhar at 1944 [13], as for recent references see, for example, [14,15] and references therein. Highly sophisticated wavefunctions with large numbers of terms and parameters are frequently non-practical since they require time-demanding computer codes to evaluate cross sections.…”

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Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus:II.Spin‐singlet (excited) and spin‐triplet (lowest) states of helium sequence

Turbiner

Vieyra

Valle

et al. 2022

Int J of Quantum Chemistry

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As a continuation of Part I (Int. J. Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges Z ≤ 20, a few ultra-compact wave functions in the form of generalized Hylleraas-Kinoshita functions are constructed, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for energies (4-5 significant digits [s.d.]) of two excited states of He-like ions: the spin-singlet (first) excited state 2 1 S and lowest spin-triplet 1 3 S state. For both states, it provides absolute accuracy for energy $10 À3 a.u., exact values for cusp parameters and also for six expectation values the relative accuracy $10 À2 . Bressanini-Reynolds observation about the special form of nodal surface of 2 1 S state of helium is confirmed and extended to He-like ions with Z > 2. Critical charges Z = Z B , where ultra-compact trial functions lose their square-integrability, are estimated: Z B (1 1 S) ≈ Z B (2 1 S) $ 0.905 and Z B (1 3 S) $ 0.902. For both excited states, the Majorana formula-the energy as the second degree polynomial in Z-provides accurately the 4-5 significant digits for Z ≤ 20.

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“…Under these conditions, the initial state of the system is characterized by the product of an incident plane wave with a molecular target wave function while the final state is described by the product of a scattered plane wave with two independent Coulomb wave functions as well as an approximate expression of the Gamov factor for modeling the electron-electron repulsion [24,25]. Finally, in order to go beyond the domain of validity of the first Born approximation and then to extend the current water molecule double ionization modeling down to the intermediate energy regime, we followed the recommendations of Behati et al who suggested to use an approximate Coulomb wave function of effective charge Z* to represent the scattered electron in the field created by the water nucleus together with the two ejected electrons [26][27][28]. In their approach, the authors simply replaced the scattered electron Coulomb wave function by the first term of the whole hypergeometric series that may then be seen as a multiplicative factor, which characterizes the influence of the effective Coulomb field on the scattered electron being not far from the target nucleus.…”

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confidence: 99%

“…Then, benefiting from the selectivity rules of the complex harmonics used in the description of the molecular wave function, we easily access to triply differential cross sections, which are then numerically integrated over the solid angle Qs as well as the ejected energies £j and E2 to provide orientation-dependent total cross sections defined as [26] In Eq. (3), let us note that the upper limits of the integration £ j max and E2mm are defined by E]mm = (£; -/ 2+) and £ 2max = £l max ~ £l with £/ = / 2+ + Es + £ , + £ 2 [26].…”

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H2Odouble ionization induced by electron impact

2015

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Double ionization of water molecules remains, still today, rarely investigated on both the experimental and the theoretical side. In this context, the present work reports on a quantum mechanical approach providing a quantitative description of the electron-induced double ionization process on isolated water molecules for impact energies ranging from the target ionization threshold up to about 10 keV. The cross section calculations are here performed within the first Born approximation framework in which the initial state of the system includes a molecular ground-state wave function expressed as a single-center linear combination of atomic orbitals while the final state of the system is characterized by two independent Coulomb wave functions used for describing the two ejected electrons coupled by a Gamov factor used for modeling the electron-electron repulsion. Besides, in order to go beyond the first Born approximation, the scattered electron is considered as a particle being in the Coulomb field of the nucleus-whose charge is screened by the ejected electrons-and then treated by an approximate Coulomb wave function. In this perturbative-type description, let us add that the passive (not ionized) electrons are considered as frozen in their molecular orbitals during the collision which permits to reduce the electron-target interaction potential to a two-active-electron problem. Comparisons with rare available experimental data are reported as well an energetic analysis in terms of mean secondary energy transfer during the double ionization process in order to demonstrate the relevance of the electron-induced double ionization process.Electron-induced interactions in water are of great impor tance in many fields of research ranging from astrophysics to cellular biology with significant impacts in radiobiology, med ical imaging, and radiotherapy, essentially due to the fact that water is commonly used as a surrogate of the living matter. In this context, it is nowadays well recognized that the "physics" stage that takes place at the first postirradiation femtoseconds plays a key role in the avalanche of events occurring throughout the water radiolysis and then appears as a decisive step in the induction of the radiation cellular damages [1], Under these conditions, accurate cross sections-related to the different electron-induced interactions on water molecules-appear as crucial input data for the numerical codes devoted to the electron track-structure description in biological matter [2]. In this context, the single collisional processes induced by electron impact in water (including the elastic and inelastic channels) have been intensively investigated on both the theo retical [3,4] and the experimental [5,6] sides. Comparatively, the electron-impact double ionization (DI) of water molecules is less documented and therefore generally neglected in the majority of existing numerical track-structure codes arguing a presupposed minor contribution in the total energy deposit pattern. However, whether it is in the wat...

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On the behaviour of the (e, 3e) total cross section for helium at high and intermediate energies

Cited by 12 publications

References 45 publications

Electron-induced double ionization of isolated water molecules

Electron-induced double ionization of isolated water molecules

Ultra‐compact accurate wave functions for He‐like and Li‐like iso‐electronic sequences and variational calculus:II.Spin‐singlet (excited) and spin‐triplet (lowest) states of helium sequence

H2Odouble ionization induced by electron impact

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