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Journal of Physics B Atomic Molecular and Optical Physics

Evidence of virtual dipole-supported states in electron scattering by methyl chloride

I. I. Fabrikant, R. S. Wilde

Published Jan 1, 1999• 14 citations
Publisher

Abstract

A previously detected negative-ion dipole-supported state of is identified as a virtual state whose energy is about eV at J=K=0 , where J and K are the rotational angular momentum and its component about the symmetry axis. For higher J and low K the S -matrix poles in the complex energy plane move off the real axis and typically do not correspond to quasibound states, i.e. there is no time delay in scattering. If K is close to J , the S -matrix poles correspond to quasibound states and may appear as Feshbach resonances.

DOI
10.1088/0953-4075/32/2/007

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A previously detected negative-ion dipole-supported state of is identified as a virtual state whose energy is about eV at J=K=0 , where J and K are the rotational angular momentum and its component about the symmetry axis. For higher J and low K the S -matrix poles in the complex energy plane move off the real axis and typically do not correspond to quasibound states, i.e. there is no time delay in scattering. If K is close to J , the S -matrix poles correspond to quasibound states and may appear as Feshbach resonances.
A detailed study is made of the nature of rotational Feshbach resonances in the elastic scattering of extremely-low-energy electrons by diatomic polar molecules. The bound-state properties of an electron in the field of a dipole rotator, determined previously, are used in establishing the resonance behavior of elastic-scattering phase shifts in the energy region below the first rotational excitation threshold. Feshbach resonances of very narrow widths are found in partial-wave scattering channels with total angular momenta greater than zero when the strength of the interaction potentials is somewhat less than that necessary to yield bound states of the same symmetry type, and very much less than those necessary to yield a "bound state" of the projected Hamiltonian QHQ\mathrm{QHQ}QHQ. The latter implies a non-negligible value of the resonance energy shift for polar molecules.
A virtual state of an electron interacting with a molecule indicates that a new bound state with a large sss-wave component is about to appear. In the picture of fixed nuclei, the bound state is caused to appear or disappear by a small displacement of the nuclei. When the nuclear vibrations are taken into account, it is shown, for the example of e+HCle+\mathrm{HCl}e+HCl, that nuclear-excited Feshbach resonances occur at energies just below the vibrational thresholds.
Potassium atoms in selected high-lying np Rydberg states (80 {<=} n {<=} 400) are being used as a tool to examine electron-polar molecule collisions at ultra-low energies ({approximately}80 {mu}eV - 1 meV). This energy regime has not been investigated previously and is of interest because the corresponding electron de Broglie wavelength is large, {approximately}1300 - 330 {Angstrom}, and because the collision time is comparable to the period of molecular rotation. A variety of target molecules has been studied, including simple rotors such as HF, and more complex species such as NH{sub 3}, CH{sub 3}I, CH{sub 2}Br{sub 2} and C{sub 6}H{sub 5}NO{sub 2}. These targets encompass a range of dipole moments and rotational behavior, but analysis of the data shows that in each case the cross section {sigma}({epsilon}) for rotationally-inelastic electron-polar molecule scattering varies approximately as 1/{epsilon} where {epsilon} is the electron energy. Such threshold behavior is not predicted by the Born approximation and possible reasons for this discrepancy will be discussed. In the case of NH{sub 3}, the data show that near-resonant energy transfer associated with transitions between different inversion levels is an important process leading to collisional state changing.
A simple expansion of the scattering length in terms of SSS-matrix poles is derived for the angular momenta l>0l>0l>0. This expression shows that the dominant role in the low-energy collisions is played by the poles lying close to the origin of the complex momentum plane. Among these poles a peculiar class of virtual states is found to respond very weakly to the scaled perturbation potentials and thus resistant to producing trajectories in the complex momentum plane. Properties and an impact on low-energy collisions of these resistant virtual states are discussed.
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g., parity-time-symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension) possessing one of four certain symmetries, the poles of the SSS-matrix eigenvalues in the complex momentum plane are symmetric about the imaginary axis, i.e., they are complex-conjugate pairs on the complex-energy plane. This applies even to states which are not bounded eigenstates of the system, i.e., antibound or virtual states, resonances, and antiresonances. The four Hamiltonian symmetries are formulated as the commutation of the Hamiltonian with specific antilinear operators. Example potentials with such symmetries are constructed and their pole structures and scattering properties are calculated.