Electron capture process

In the self-energy formalism, the probability of Auger capture per unit time r can be calculated in terms of the screened Coulomb interaction W(r,r [19] 

Using equations (9) and (10), the rate F can be written as well in terms of the response function r, m)  

Equation (11) allows to interpret the electronic excitation in the Auger process as the medium response to a dynamic fluctuation of charge between the states i(r) and p (r). From this point of view, we apply linear response theory to an external pertirrbation which is the electrostatic potential v i(r) created by such charge fluctuation. In general terms, the response function r, m) completely determines the behavior of the system in response to an external perturbation, provided that the latter is sufficiently small and thus linear theory is applicable. The imaginary part of contains 

It can be shown that the calculation of lm[ o] in real space and its subsequent substitution in the expressions for the Auger rate, equations (9) and (10), leads to die standard Fermi s golden rule for the calculation of the Auger rate when the excitations in the medium are obtained in the singleparticle approximation [22]  

more sophisticated approximation to calculate the Auger rate involves the inclusion of many-body effects in the medium excitations. This can be achieved by using the many-body response function of the interacting-electron system v(r, r, ru) [19]. In the random-phase approximation (RPA), X is obtained in a self-consistent way  

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In almost all cases X is unaffected by any changes in the physical and chemical conditions of the radionucHde. However, there are special conditions that can influence X. An example is the decay of Be that occurs by the capture of an atomic electron by the nucleus. Chemical compounds are formed by interactions between the outer electrons of the atoms in the compound, and different compounds have different electron wave functions for these outer electrons. Because Be has only four electrons, the wave functions of the electrons involved in the electron-capture process are influenced by the chemical bonding. The change in the Be decay constant for different compounds has been measured, and the maximum observed change is about 0.2%. 

For any nucHde that decays only by this electron capture process, if one were to produce an atom in which all of the electrons were removed, the effective X would become infinite. An interesting example of this involves the decay of Mn in interstellar space. For its normal electron cloud, Mn decays with a half-life of 312 d and this decay is by electron capture over 99.99% of the time. The remaining decays are less than 0.0000006% by j3 -decay and a possible branch of less than 0.0003% by /5 -decay. In interstellar space some Mn atoms have all of their electrons stripped off so they can only decay by these particle emissions, and therefore their effective half-life is greater than 3 x 10 yr. 

The eventual fate of any ion is its neutralization, either by a free electron or by a negative ion formed by electron attachment. In ethylene radiolysis at high dose rates, electron capture processes should be insignificant (29), and the recombination energy of the positive ion will become available on neutralization, a portion of which may be in the form of excitation (59). 

Recently, we have developed a full theoretical treatment of electron capture processes involving an ab initio molecular calculation of the potential energy curves and of the radial and rotational couplings followed, according to the collision energy range concerned, by a semi-classical [21-23] orquantal [24] collision treatment. 

In accordance with previous investigations [8,9], Aese experiments have shown a quite different behaviour for N (ls )than for other multicharged ions such as the isoelectronic ion [10. The single-electron capture process has been shown to be dominant on the n = 3 levels and in particular on the 3s level for collision energies lower than 50 keV. A high probability of double capture has also been observed characterized by an intense peak at X = 76.5 nm attributed to the 2s > 2s 2p P transition [4,5,7]. Furthermore,... 

A complete theoretical treatment of the + He collision should therefore take into account, first the single-electron capture process from the ground state entry channel... 

He(ls ) S and also from the metastable level Nr (ls2s)-1- He(ls ) in order to take care of the fraction of metastable ion in the incident beam, as well as the double-electron capture process from both ground and metastable ions. 

The electron capture processes are driven by non-adiabatic couplings between molecular states. All the non-zero radial and rotational eoupling matrix elements have therefore been evaluated from ab initio wavefunctions. 

In relation with these avoided crossings, the radial coupling matrix elements present sharp peaks at respectively 5.4, 6.6, 7.55 and 9.5 a.u. (Fig. 5). We may notice that these radial couplings are almost insensitive to the choice of the origin of electronic coordinates. The most sensitive one is the g23 function at short internuclear distance range, but we may expect weak translational effects for such electron capture processes dominated by collisions at large distance of closest approach. 

SINGLE-ELECTRON CAPTURE PROCESS FROM THE GROUND STATE... 

Assuming the contribution of the potential energy curves which have not been taken into account to be almost constant with the collision energy, such calculations could provide a relative estimate of the variation of the double capture cross-sections with the collision energy. The results presented in Fig. 7 seem to be coherent with this hypothesis and to corroborate a cascade effect for the double electron capture process. 

Mathematical models of the electron-capture process are based on the stirred reactor model of Lovelock [145] and the kinetic model of Wentworth [117,142,146] as further modified by others [129,134-136,147-150]. The ionization ch2uaber is considered... 

Capture, K-Electron—Electron capture from the K shell by the nucleus of the atom. Also loosely used to designate any orbital electron capture process. 

The vacancy left in the low-energy K-shell will be filled by an electron from a higher level with the resultant emission of radiations of extra nuclear origin, X-rays, which are distinguished from the accompanying nuclear y radiation. It should be noted that the n p criterion is the same for both positron and electron capture processes and it is not unusual to find both occurring with different atoms of the same nuclide. 

According to ESR spectra, cyclobutanone and tetramethylene sulfone undergo dissociative electron capture process (Scheme 3.34 for cyclobutanone) in argon matrices and yield distonic anion-radicals (Kasai 1991, Koeppe and Kasai 1994). 

B4++ He reaction. This collisional system has been investigated theoretically within the framework of the semiclassical close-coupling formalism using different model potential approaches [2,3] which lead to a discrepancy of about a factor 5 for the double capture cross section values. We have thus performed an alternative study of this system by means of a full molecular expansion method, focusing our attention on the double electron capture process. 

This work provides accurate potential energy curves as well as coupling matrix elements for the B2+/H and B4+/ He systems. From the molecular point of view, it appears important to involve all levels correlated to the entry channels in the collision dynamics and, in particular, to take into account rotational effects, which might be quite important. The results concerning the double electron capture process in the (B4+ + He) collision point out the limitations ofthe potential approach model, especially to account for open shell levels, for which more elaborate calculations are necessary. 

The formation of C5H5Co was observed at low ionizing energy, and is probably formed by a dissociative electron capture process. 

The EH calculations agree with the CNDO results if a planar nondefect geometry is used. When the model containing defects serves as the lattice, electron-capture processes are favored at the expense of Ag+ capture at the Ag center, as shown in Table XIII. This leads to the alternative pathway shown in Fig. 24, and would explain a dependence of photochemistry on surface-defect structure. 

This definite failure to find G is importantlybecause Gaydoni has suggested that this appearance potential might correspond to the production of 0+ and C. Finally, O, without kinetic energy, is produced at 9-5 eV. Earlier workers obtained 0 at voltages between 9 3 and 9-5. The production of 0 at such low energies can only be due to a dissociative electron capture process... 

Iodine Isotope. There are many radioactive isotopes of iodine. Four are commercially available. For most purposes, one of these, I, is the most useful because it has a reasonable half-life (60 days), it decays to a stable isotope, and it decays by an electron capture process that results in a cascade of low energy electrons and the emission of X-rays and y-rays. 

Stuckey and Kiser considered this and related mechanisms and recognized that Z in its ground state would not bind an electron when Z is F, Cl, Br, 0 or CN. Therefore, they concluded that it was very unlikely that Z formation occurs by a simple electron-capture process with the ground state of Z, te. 

That is, a fast ion, formed by electron impact and accelerated toward the plasma surface, excites the H ion to form H , and then the H ion reacts via a third body electron capture process to form the ion inferred from the experiments. Only the ions formed at the surface of the plasma could be accelerated through the same potential drop as the primary H ions. Further, Schnitzer and Anbar argue that since there is no significant change in the Ha ion current as the ion source pressure is varied, the formation of does not occur within the... 

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