The Influence Of Matter And Black-Body Radiation Photons On The Dipole Polarizabilities A And γ Of Atoms

Abstract

The influence of the surroundings on the linear dipole polarizability a and second hyperpolarizability 7 is discussed in terms of the density om of isotropically distributed matter as well as the density qp of thermal black-body radiation photons, a and 7 of the rare gas atoms are studied as examples. At standard conditions, both effects are of comparable size for the rare gases. Possible consequences for ion-molecule reaction rate constants in astronomical environments are suggested.Apart from a few exceptions theoretical calculations of molecular properties ^ pertain to single, noninteracting particles (see e.g. [1]). In experiments, however, the properties of single particles are more or less influenced by interaction with the surrounding matter and black-body radiation photons [2 -6], This is the case even for gases at ambient temperature and pressure.Concerning the dipole polarizabilities a and 7, the first effect is well-known. Perturbation of a and 7 by electric fields produced by the surrounding isotropically distributed matter is usually formulated in a virial expansion of these properties in powers of the molar density £>m = (N/V)m/N A of the matter,In the case of the static linear dipole polarizability <P = a, (1) is obtained from the ClausiusMossotti-function [7]. In this case the expansion coefficients B a and C Q are related to the dielectric virial coefficients via B e = a(0).B Q iV A /(3£o) and C e = a(0)C Q A r A /(3£o)-Be is known from experiment to within a few percent for a limited number of atoms and small molecules. Concerning the second hyperpolarizability $ = 7 of the rare gases, there are only a few sets of experiments which confirm the density dependence of this property unambiguously [8,9]. The experimental results are also expressed in Reprint requests to Priv.-Doz. Dr. U. Hohm. a virial expansion similar to (1). In both cases, a and 7, is directly related to the radial pair distribution function g(R) and the collision induced incremental pair polarizability A<& = <P ]2 -2$, where <P\2 is the polarizability of a colliding pair.In what follows it is helpful to remember the frequency dependence of a and 7 outside absorbtion bands. a(-uj\u)) is usually represented by a(-cü-,UJ) = a(0;0)(l + a\^aco 2 + a 2 , Q uj 4 + ...). (2) The expansion coefficients are related to the wellknown dipole sums S(k) via a(0; 0) = 4tt£qOqS(-2), 0|,a = S(-4)/S(-2) and a 2 , a = S(-6)/S(-2), where 47re 0 ao = 1.648 x 10 _4I C 2 m 2 J" ! is the atomic unit of the dipole polarizability. These coefficients are precisely known for about 50 atoms and small molecules (see the work of Meath and co-workers, e.g. [10,11]). In the case of 7, the situation becomes somewhat more complicated because the frequency dependence of 7 depends on the type of the non-linear process considered. However, Shelton has shown [12-14| that an expansion similar to (2) can be used to describe the frequency dependence of 7 as

Electric Dipole Polarizability of As4, a Challenging Problem for Both Experiment and Theory

“…At moderate temperatures T electronic excitations can be neglected, and R changes due to temperature-dependent vibration-rotation 17 and black-body radiation effects. 18,19 The latter leads to an increase of the measured dipole polarizability 〈R(0)〉 T of 0.16 e 2 a 0 2 E h -1 at 870 K compared to the 0 K value.…”

“…In order to compare the static polarizability obtained in the calculations and in the experiments, it is essential to adapt both results to the same temperature. At moderate temperatures T electronic excitations can be neglected, and α changes due to temperature-dependent vibration−rotation 17 and black-body radiation effects. , The latter leads to an increase of the measured dipole polarizability 〈α(0)〉 T of 0.16 e 2 a 0 2 E h -1 at 870 K compared to the 0 K value.…”