In an atom collision, an electron orbiting one atomic nucleus may influence what happens to an electron ~ above the various other atomic center. For example, the Coulomb repulsion between the 2 electrons may cause one or much more of the electrons to change state. One more possibility is that the electrical field that the an adverse electron weakens the ar of its positive charged atom nucleus, which consequently decreases the price at i beg your pardon transitions take ar in the 2nd atomic center. Over there are likewise other, much more subtle methods in which electrons on 2 colliding centers may impact the transition rates.
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Projectile electron lose is a procedure in i m sorry an ion interacts v an atomic or molecule target and also at least one electron is ejected native the projectile together a result of this interaction. Because that the huge majority of atomic and also molecular targets, the loss process occurs by the coulomb interaction in between the (target, Z2) nucleus and also the (projectile, Z1) electron, through the target nuclear field being attenuated by the screening of the target electrons, as shown in Fig. 1.
Fig. 1. Diagrammatic representation of first-order projectile electron lose by a target with nuclear charge Z2. As a an outcome of the nucleus-electron communication (represented through a dashed line), the projectile active electron renders a change from an initial state |ψs〉 come a final continuum state |ψf〉. The projectile nuclear charge and velocity room Z1 and v, respectively. This procedure is dubbed the screening effect.
In the projectile frame, projectile electron loss have the right to be viewed as the ionization the the projectile through the target. If the target nuclear charge is little compared through the projectile nuclear charge and also if the projectile velocity is huge compared v the Bohr velocity of the energetic projectile electron, first-order theory such together the aircraft wave Born approximation (PWBA), deserve to be offered to explain the lose process. However, the analogy through the classic ionization difficulty (Bethe, 1930), in i m sorry the ionization is due to a simple, bare, fee particle, is no sufficiently general. In most situations of interest, the target is neutral and also screening the the target nucleus plays critical role in the calculate of the electron-loss cross sections (Bates and Griffing, 1953). A neutral target can not be simulated by a bare one for the research of projectile-electron loss. In fact, the effectiveness of the screening is not the exact same for all impact parameters because that which projectile-electron loss have the right to proceed (Toburen et al., 1981). This effect, which have to be included in any realistic theoretical approach, renders the summary of the loss process significantly different from the ionization by a ceiling particle.
Another necessary difference between the ionization caused by a bare particle and also by a neutral atom is the opportunity that the target electrons likewise act together ionizing agents. It transforms out the in this case, the projectile-electron loss is due specifically to the electron-electron interaction, v the target cell nucleus acting together spectator.
The simplest theoretical approach to account for electron lose is the free-collision model or timeless impulse approximation (Bohr, 1948; Dmitriev and also Nikolaev, 1963; Bates and also Walker, 1966, 1967; Walters, 1975; Dewangan and also Walters, 1978; Meron and also Johnson, 1990; Riesselmann et al., 1991), in i m sorry the active projectile electron is claimed to be free, colliding with the target atom through a loved one velocity equal to the projectile velocity. In the impulse approximation, the projectile electron is explained by a velocity distribution, i m sorry reflects, to part extent, the tied nature the this electron. The projectile is ionized if the impulse given by the target atom come the projectile electron during the collision move an power greater 보다 the projectile ionization energy.
Recently, Lee et al. (1992) provided a different method to calculate the electron-electron donation to the loss. Viewed from the projectile frame, the target electron have the right to be thought about to interact with the projectile together a free particle if the collision time is quick compared to the orbiting time the the active projectile electron. Under this conditions, a quantum mechanical impulse-like approximation deserve to be used to calculation the electron-electron interaction component of the loss, connecting this procedure to the ionization of ion by free-electron impact.
The complete quantal treatment of the electron-electron interaction was an initial carried out by (Bates and also Griffing 1954, 1955). In this case, the free-electron theory is no used, and also both the projectile and also target electron are permitted to readjust states, in their corresponding centers, together a an outcome of the electron-electron interaction. Figure 2 provides an illustration of this mechanism, which has actually been called antiscreening by number of authors (McGuire et al., 1981; Anholt, 1986; Montenegro and also Meyerhof, 1991a) in contrast to the impact on the nucleus-electron interaction, depicted in Fig. 1, and called the screening effect. Stolterfoht (1989, 1991) discusses various feasible two-electron interactions and also notes that the antiscreening interaction have the right to be classified as a two-center scattering correlation. On the other hand, the screening impact is classified together a single-electron interaction.
Fig. 2. Diagrammatic representation of a first-order projectile electron ns mechanism due to the electron-electron communication (represented through the dashed line). While the active projectile electron goes from a state |ψs〉 come a state |ψf〉 in the continuum, the active target electron performs a simultaneous transition, which bring the target from a state |Φ0〉 come a state |Φn〉. This procedure is referred to as the antiscreening effect.
The mutual adjust of claims by the two connecting electrons in the antiscreening setting introduces additional difficulties in theoretical calculations, since two digital transitions need to be calculated and, in most cases, continuum claims are the much more likely final states. Furthermore, in most dimensions of electron loss, the final state the the target is not observed and a amount over all possible final states must be evaluated. This is a particularly an overwhelming task if the amount is brought out state through state because that targets with an ext than 2 electrons. The many widely offered procedure to circumvent this challenge is via closure (Lodge, 1969; Gillespie, 1977; McGuire et al., 1981; Anholt, 1986; Hartley and Walters, 1987; Montenegro and Meyerhof, 1991a, 1992). An approximation based on closure has two important merits besides staying clear of a state-by-state sum. First, the completeness that the atomic says is maintained, i m sorry assures that at asymptotically high energies this type of approximation is exact (Hartley and Walters, 1987). Second, the calculations use form factors based only on the target ground state tide functions, avoiding the need for excited state wave features (including the continuum) and simplifying substantially the calculations. In its crudest form, the closure technique neglects the energy differences between the various digital transitions in the target, which can be reached via the electron-electron interaction, assigning an average value come the energy transferred in all feasible transitions of the target. Back this assumption substantially simplifies the calculations, it results in a strong overestimation of the electron-electron donation to the lose in the intermediate- come low-velocity regime. Most of the recent work-related within the PWBA frame has been directed towards removing this deficiency (Anholt, 1986; Hartley and Walters, 1987; Montenegro and also Meyerhof, 1991a).
The theoretical ideologies just questioned are draft to study single-electron loss. Because that collisions involving highly charged ions, however, multiple-electron transitions room not only feasible but can have a sufficiently high probability of distorting an translate of the speculative measurements by method of a single-channel analysis. Under these circumstances, the independent-particle model (IPM) along with an impact-parameter analysis has to be widely supplied to acquire workable outcomes (see McGuire, 1992, because that a recent review the multiple-electron processes). Double-electron lose or coincided capture and also loss are instances of processes entailing electron loss where the IPM have the right to be advantageously used. An impact-parameter analysis (semiclassical theory) the electron loss was not accessible until recently (Montenegro and also Meyerhof, 1991b, 1992). Based upon time-dependent perturbation, this theory provides for the total cross part the same results as those acquired within the PWBA and shows brand-new features that the electron loss process, such together the long-range personality of the electron-electron interaction (antiscreening mode). The dominance of the electron-electron interaction at huge impact parameters can be regarded the observation of low-energy electrons in collisions, in i beg your pardon both the projectile and the target space ionized, because of the little momentum transfer linked with remote collisions (DuBois and Manson, 1990; Manson and also DuBois, 1992; Heil et al., 1991, 1992). An analysis of the ejected electron spectra v the second-order Born approximation (Jakubassa-Amundsen, 1992) support this interpretation based on impact-parameter analysis, indicating the prestige of the electron-electron interaction when the energy and the emission edge of the ejected electron decrease.
There is a second-order process associated v antiscreening the plays an important role in experiments wherein the recoil ions or the ejected electrons are at the same time measured through the projectile in electron loss collisions (Montenegro et al., 1992a; Heil et al., 1992). This process, which has actually been referred to as two-center twin ionization (Montenegro et al., 1992a), incoherent projectile-target ionization (Jakubassa-Amundsen, 1992) or uncorrelated twin inelastic scattering (Wang et al.
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, 1992), is a projectile-electron loss process due come the screened target nucleus, developing simultaneously v target ionization by the screened projectile nucleus. It results in the same last electron states as antiscreening. A understanding of the differences in between the dynamic signatures of these two processes is important in order to recognize the means in i m sorry they complete for the coincided ionization the the projectile and the target above the antiscreening threshold.