The current state of the theory and its application to low-energy electron-molecule collisions is reviewed. The emphasis is on elastic scattering and vibrational and rotational excitation of small diatomic and polyatomic molecules. New and traditional theoretical approaches are described, and the results of calculations are compared with existing experimental measurements.

The theory of electron-molecule collisions

A general study has been made of the bound states of a charged particle in a static field which behaves as the dipole form asymptotically. When the field is that of either a point dipole plus a sufficiently repulsive spherical core, or a finite dipole, the existence of bound states of the charged particle depends only on the value of the reduced dipole moment K (equation (5)). It is shown that each symmetry class of states has its own threshold value of K such that states of that symmetry exist if, and only if, K exceeds the critical minimum. There is an infinite number of states of given symmetry when there are any. Critical values of K < 100 are calculated. When the potential has an arbitrary form at short range (but still has the dipole form at long range), the situation remains much the same as above, with the exception that sufficient attraction at short range will allow some states to exist for any value of the dipole moment.

Bound states of a charged particle in a dipole field

High-resolution threshold photodetachment of ${\mathrm{H}}_{2}$C-CH${\mathrm{O}}^{\ensuremath{-}}$ has resulted in the observation of \ensuremath{\sim}50 narrow resonances (some 20 MHz full width at half maximum). These resonances are due to autodetachment from a diffuse negative-ion complex consisting of an electron weakly bound (\ensuremath{\sim}5 ${\mathrm{cm}}^{\ensuremath{-}1}$) by the dipolar electric field of the neutral. Electric fields of 70 V/cm are adequate to detach the electron from the lower (bound) levels where autodetachment is not possible. Such states should exist for all neutrals with dipole moments greater than about 2 D.

Observation of dipole-bound states of negative ions

The spectra of electronically excited states of strongly polar negative ions are discussed in terms of general features that may be predicted for such systems. The general properties are then studied through a systematic treatment of lithium halide and lithium hydride anions. Only one or two excited electronic levels exist for these systems, and the binding energies are so low that a limited number of bound rotational levels are associated with each of the excited states. For the states of lowest binding energies, abnormal rotational level spacings are demonstrated. Also, a discussion is given of the implictions for electron scattering and photodetachment studies, of the higher lying dipole states which cross over into the continuum.

Excited states of polar negative ions

Ground-state energy eigenvalues and eigenfunctions are obtained by a variational method for an electron in the field of a finite, stationary, permanent electric dipole. The dipole moments studied cover the range from the minimum value required for binding (${D}_{min}=0.6393 e{a}_{0}$) to $D=400 e{a}_{0}$, where the system is equivalent to the hydrogen atom perturbed slightly by a distant stationary negative charge. The eigenvalues obtained agree with those reported by Wallis, Herman, and Milnes, who determined them by another method in the range $D=0.84e{a}_{0} \mathrm{to} 30e{a}_{0}$. The normalized eigenfunctions display the manner in which the electronic charge density changes from that of the hydrogen atom at very large $D$ to a flat distribution approaching that which is characteristic of a zero-energy continuum state as the minimum moment is approached from above. Optimized variational wave functions for different values of $D$ are presented for use in other calculations. Contour maps and profiles of electronic charge density are shown for a number of values of $D$. Mean values of the powers -1, 1, and 2 of the distances of the electron from the dipole charges are also calculated.

Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

Minimum dipole moment required to bind an electron to a finite dipole

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Minimum dipole moment required to bind an electron to a finite dipole