Pressure shifts and electron scattering lengths in atomic and molecular gases

Abstract

Photoabsorption or photoionization spectra of CH3I are discussed as a function of perturber pressure for 11 different binary gas mixtures consisting of CH3I and each one of 11 different gaseous perturbers. Five of the perturbers were rare gases and six were nondipolar molecules. The energy shifts of CH3I Rydberg states become independent of n, the principal quantum number, for n≥10. The energy shifts for n≥10 vary in a linear fashion with perturber number density. The electron scattering lengths for the perturbers are extracted from the shifts using Fermi theory in which the polarization term is that of Alekseev and Sobel’man. These scattering lengths are compared with those from swarm and time-of-flight experiments. It is found that the uncorrected shift scattering lengths correspond to the zero energy or near-zero energy scattering lengths obtained from extrapolated swarm and time-of-flight data. It is found that plots of scattering length vs polarizability α (ᾱ for molecules) define two linearities, one for the rare gases and one for molecules, CO2 being an exception to the latter linearity (presumably because of its large quadrupole moment). For a given polarizability, it is also found that molecules exhibit a larger scattering length than the rare gases. These results are discussed and consequences for scattering cross sections are elaborated.

Relation between the electron scattering length and the van der Waals approximation to the equation of state

“…This empirical relation is based on experimental electron scattering lengths derived from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe. It was also noted that for molecular Rydberg levels n ) 10, the measured energy shifts are not dependent on n, within experimental error [2].…”

“…The effect of the hard sphere can be accounted as follows: for 1=0 and r & R, Ro(r) can be replaced by go(r -R) where the pp is the exact solution for the wave equation, with the potential V(r+R). Thus the phase shift for Ro is prefor r (R ae /2r for r &R, (2) where R is the radius of the scatterer and ae /2r accounts for the polarization of the rare-gas atom by the scattered electron (electron-dipole interaction). The potential applied for the van der Waals approximation for equation of state is analogous with the potential describ-where m, is the electron mass, k is the wave number of the electron, Rt is the radial function of the electron (note that in this notation [5], a global phase of 5& is attached to Rt ), and Ji is the Bessel function.…”

Photoionization spectra of CH3I perturbed by SF6: electron scattering in SF6 gas

“…The experimental method employed in this paper provides an excellent means for the precise determination of the electron scattering length in gaseous perturbers [1][2][3][4][5][6][7][8]. Recently, Al-Omari, Reininger and Huber [13] have called into question the use of Eq.…”

“…(At high perturber number densities, however, photoabsorption measurements can become limited if both the perturber and the dopant absorb in the same spectral region.) Thus, pressure effects have been analyzed for discrete and autoionizing dopant Rydberg states [1][2][3][4][5][6][7] and for subthreshold photoionization structure [5,6], and a synopsis of data pertaining to electron scattering lengths has been given [8].…”

“…The extraction [1][2][3][4][5][6][7][8] of the electron scattering length in a perturber medium from the densitydependent energy shift of dopant Rydberg states follows the theory by Fermi [9], as modified by Alekseev and Sobel'man [10]. According to these authors [9,10], the total energy shift ) may be written as a sum of contributions where ) sc , the "scattering shift," is due to the interaction of the Rydberg electron with the perturber molecule, while ) p , the "polarization shift," results from the interaction of the positive core of the Rydberg molecule with the perturber molecule. )…”