**2. Decay of Gaseous Transient Anions into Dissociative Electron Attachment (DEA) and Autoionization**

In electron–molecule collisions, a TMA is formed, when an incoming electron occupies a previously unfilled orbital of a molecule for duration greater than the usual scattering time [15–17]. Since such an orbital exists at a precise energy [15], TMAs are formed at specific energies usually below 15 eV and rarely above 30 eV [15, 16]. Because of the uncertainty principle, the transient state has a width in energy, which characterizes and identifies the process in the dependence on incident electron energy of cross sections for particular energy‐ loss processes or the formation of the products or damage yields (i.e., the yield functions). Thus, at the resonance energy, corresponding to the formation of the TMA, yield functions exhibit pronounced maxima that can be superimposed on monotonically increasing back‐ ground, which results from nonresonant or direct scattering.

The formation of TMAs is well described and reviewed in the literature [15–21]. There are two major types of TMAs or "resonances" [15–17]. The first, known as a single‐particle resonance, occurs when the additional electron occupies a previously unfilled orbital of a molecule (or subunit of a large biomolecule) in its ground state. Here, the electron is temporarily trapped within an angular momentum barrier by the shape of the electron–molecule potential. Such TMAs are thus also termed shape resonances. Core‐excited resonances or "two‐particle, one‐ hole" states form when electron capture is accompanied by electronic excitation, such that two electrons occupy previously unfilled orbitals. The incident electron is in effect captured by the positive electron affinity of an excited state of the molecule or basic subunit in the case of a large biomolecule, which for DNA might include a base, sugar, or phosphate group. If a momentum barrier in the electron–molecule or electron‐subunit potential contributes to the retention of the electron in the electronically excited molecule or subunit, the transitory anion is referred to as core‐excited shape resonance. If the TMA state is dissociative and the resonance lifetime is greater than about half of the vibration period of the anion, the latter dissociates. This process is called DEA.

The decay of a TMA into dissociative channels can be understood by considering the hypo‐ thetical internuclear potential‐energy curve of a diatomic molecule AB and one of its TMA state AB‾ shown in **Figure 1**. While the following description is rigorously applicable only to diatomic molecules, it is still qualitatively valid along a specific bond of a polyatomic molecule. Assuming that only Franck–Condon (F–C) transitions are possible and that the AB‾ state is dissociative, we see from the consideration of the ground‐state nuclear wave function that electrons with energies of between *E*1 and *E*<sup>2</sup> are required to fragment AB‾. However, its fragmentation into A‾ + B is only possible if its life time is long enough to survive autode‐ tachment, which can occur for internuclear separations, *R < RC*. For *R > RC,*, AB‾ is stable against autodetachment, as electron emission is endothermic. If the TMA does not dissociate, the electron is re‐emitted into the continuum, leaving the target in vibrational, rotational, or even electronically excited states in the case of a core‐excited TMA.

applied to optimize concomitant chemoradiation therapy (CRT) by modifying the action of

In electron–molecule collisions, a TMA is formed, when an incoming electron occupies a previously unfilled orbital of a molecule for duration greater than the usual scattering time [15–17]. Since such an orbital exists at a precise energy [15], TMAs are formed at specific energies usually below 15 eV and rarely above 30 eV [15, 16]. Because of the uncertainty principle, the transient state has a width in energy, which characterizes and identifies the process in the dependence on incident electron energy of cross sections for particular energy‐ loss processes or the formation of the products or damage yields (i.e., the yield functions). Thus, at the resonance energy, corresponding to the formation of the TMA, yield functions exhibit pronounced maxima that can be superimposed on monotonically increasing back‐

The formation of TMAs is well described and reviewed in the literature [15–21]. There are two major types of TMAs or "resonances" [15–17]. The first, known as a single‐particle resonance, occurs when the additional electron occupies a previously unfilled orbital of a molecule (or subunit of a large biomolecule) in its ground state. Here, the electron is temporarily trapped within an angular momentum barrier by the shape of the electron–molecule potential. Such TMAs are thus also termed shape resonances. Core‐excited resonances or "two‐particle, one‐ hole" states form when electron capture is accompanied by electronic excitation, such that two electrons occupy previously unfilled orbitals. The incident electron is in effect captured by the positive electron affinity of an excited state of the molecule or basic subunit in the case of a large biomolecule, which for DNA might include a base, sugar, or phosphate group. If a momentum barrier in the electron–molecule or electron‐subunit potential contributes to the retention of the electron in the electronically excited molecule or subunit, the transitory anion is referred to as core‐excited shape resonance. If the TMA state is dissociative and the resonance lifetime is greater than about half of the vibration period of the anion, the latter dissociates.

The decay of a TMA into dissociative channels can be understood by considering the hypo‐ thetical internuclear potential‐energy curve of a diatomic molecule AB and one of its TMA state AB‾ shown in **Figure 1**. While the following description is rigorously applicable only to diatomic molecules, it is still qualitatively valid along a specific bond of a polyatomic molecule. Assuming that only Franck–Condon (F–C) transitions are possible and that the AB‾ state is dissociative, we see from the consideration of the ground‐state nuclear wave function that electrons with energies of between *E*1 and *E*<sup>2</sup> are required to fragment AB‾. However, its fragmentation into A‾ + B is only possible if its life time is long enough to survive autode‐ tachment, which can occur for internuclear separations, *R < RC*. For *R > RC,*, AB‾ is stable against autodetachment, as electron emission is endothermic. If the TMA does not dissociate, the

**2. Decay of Gaseous Transient Anions into Dissociative Electron**

LEEs or by increasing their numbers in cancer cells.

182 Radiation Effects in Materials

**Attachment (DEA) and Autoionization**

ground, which results from nonresonant or direct scattering.

This process is called DEA.

When the TMA state lies above the electronically excited states of the molecule, this later can acquire electronic energy, after autoionization of the anion, in addition to vibrational and rotational motion. If the electronic excited state is dissociative, then fragments A and B (**Figure 1**) are produced. Thus, both decay by autoionization into dissociative electronically excited states and DEA cause the molecule to fragment.

**Figure 1.** Born–Oppenheimer potential‐energy curves associated with dissociative electron attachment. AB represents the potential‐energy curve of the ground state of a diatomic molecule and AB‾ represents a dissociative state of a cor‐ responding transient anion. The dashed line, AB‾(s), represents the potential‐energy curve of AB*‾* within a molecular solid. *R*<sup>0</sup> is the equilibrium distance between A and B in the ground‐state AB. AB*‾* is stable against autoionization for *R* > *RC*.

Within a local complex potential–curve–crossing model, the DEA cross section may be expressed as

$$
\sigma\_{DE4}(E) = \sigma\_{CAP}.P\_s\tag{1}
$$

where *Ps* represents the survival probability of the anion against autodetachment of the electron. The capture cross section σCAP is given by:

$$\left\|\sigma\_{\mathcal{C}\mu^\circ}(E) = \lambda\_\text{e} \,\mathrm{g} \left| \chi\_\text{\nu} \right|^2 \left[ \begin{array}{c} \tilde{\mathbf{A}}\_\text{\nu} \\ \tilde{\mathbf{A}}\_\text{\nu} \end{array} \right] \tag{2}$$

where *λ<sup>e</sup>* is the de Broglie wavelength of the incident electron, *g* is a statistical factor, and χν is the normalized vibrational nuclear wave function. *Γa* and *Γ<sup>b</sup>* are the local energy widths of the AB‾ state in the F–C region and the extent of the AB‾ curve in the F–C region, respectively. The width of the transient anion state in the autodetaching region defines the lifetime *τa* toward autodetachment, *τ<sup>a</sup>* (*R*)=ћ/ Г*a*(*R*), such that the survival probability of the TMA, after electron capture, is given by

$$P\_s = \exp\left[-\int\_{\frac{R\_0}{R\_0}}^{R\_s} \frac{dt}{\tilde{\mathbf{A}}\_u(R)}\right] \tag{3}$$

where *R0* is the equilibrium bond length of the anion at energy *E* and *Rc* is the internuclear separation beyond which autodetachment is no longer possible. Hence, the DEA cross section depends exponentially on the lifetime of the TMA and the velocities of the fragments.

For further information on the mechanism of TMA formation and its effects on isolated electron–molecule systems, the reader is referred to previous works [15, 16, 22–26]. Information on resonance scattering from single layer and submonolayers of molecules physisorbed or chemisorbed on conductive surfaces can be found in the review by Palmer and Rous [20]. The following section provides information essentially on TMA formation in the condensed phase (i.e., in molecules in solids, condensed onto a dielectric surface or forming a molecular or biomolecular thin film).
