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Acta Physica Sinica

A new expression for photoionization cross sections and its application in high density system

Xiao‐Guang Ma, Sun Weiguo, Cheng Yan-Song, 四川大学原子与分子物理研究所，成都 610065

Published Jan 1, 2005• 8 citations
Publisher

Abstract

A new expression for photoionization cross section has been proposed based on the Beer_Lambert's law and Maxwell equations for a material.And we also proposed a function varying with the number density of the system,which includes the local field effect and the higher_order dielectric correction to the famous formula for photoionization cross section of isolated atoms,proposed by Fano and Cooper in 1968The photoionization cross sections of solid xenon have been studied by using this alternative expression which couples the macroproperty and the quantum quantity of the photoionization system,and which makes it possible for one to study the influence of induced dipoles on the photoionization.The dielectric behaviors of the matter in condensed state under several physical conditions (given the complex dielectric constants or the model of electric susceptibility of the system) are considered using our new expression for photoionization cross sections.The results show that it is reasonable in physics to calculate the cross sections of atoms in a real system by using the accurate expression.Furthermore,the more correct the model of electric susceptibility for the real system,the more accurate the cross section obtained from our formula will be.

DOI
10.7498/aps.54.1149

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A new expression for photoionization cross section has been proposed based on the Beer_Lambert's law and Maxwell equations for a material.And we also proposed a function varying with the number density of the system,which includes the local field effect and the higher_order dielectric correction to the famous formula for photoionization cross section of isolated atoms,proposed by Fano and Cooper in 1968The photoionization cross sections of solid xenon have been studied by using this alternative expression which couples the macroproperty and the quantum quantity of the photoionization system,and which makes it possible for one to study the influence of induced dipoles on the photoionization.The dielectric behaviors of the matter in condensed state under several physical conditions (given the complex dielectric constants or the model of electric susceptibility of the system) are considered using our new expression for photoionization cross sections.The results show that it is reasonable in physics to calculate the cross sections of atoms in a real system by using the accurate expression.Furthermore,the more correct the model of electric susceptibility for the real system,the more accurate the cross section obtained from our formula will be.
The evolution of the photoabsorption cross sections of atomic xenon with number densities varying from ideal gas to condensed matter has been studied by an alternative view in the present work. The alternative expressions of the photoabsorption cross sections presented by Sun et al recently were used with the local field models that has proven to be generalized easily to multiatomic systems including molecules and condensed phase systems. The present results show that the variation of the photoabsorption cross sections of atomic xenon in the giant resonance region from the isolated to the condensed conditions is very small, which agrees well with the variation law of the solid and gas experiments.
The influence of the local-field on the photoabsorption cross section of the atomic silver is studied in detail by using the Clausius–Mossotti (CM) model and the Onsager model separately. The variations of the photoabsorption cross section of atomic silver with number density and radius of the environmental interaction cavity are studied systematically by using more general expressions for the photoabsorption cross sections, proposed by Sun et al recently. It has proved to be reasonable to model the optical response properties of bulky material by coupling the property of isolated atom with the environmental effects in the present work.
Exact calculations of the photoionization cross sections of ground-state H in the presence of an external electric field are presented. The oscillations obtained above the zero-field ionization limit for $\ensuremath{\pi}$ polarization do not arise from specific properties of m=0m=0m=0 states, but from cancellation effects in the oscillator strengths due to the symmetry properties of the wave functions and of the light. The dependence of the cross section upon the light polarization is thoroughly explained and agrees with recent experiments on Rb.
We describe a new technique for accurate measurement of absolute photoionization cross sections. By measuring the loss rateof atoms from a laser trap in the presence of ionizing light, we directly measure the photoionization rate. The only quantities requiring absolute calibration are the ionizing laser intensity and the fractional population in the relevant state. Our technique is capable of detecting extremely small ionization rates, which means that low-power cw sources can be used. We have applied this method to photoionization from the 5P(3/2) state of rubidium at wavelengths of 413 and 407 nm.The cross sections are 1.36(12) x 10(-17) and 1.25(11) x 10(-17) cm(2) , respectively.
A theory is developed for the resonant dielectric susceptibility of a high density gas which consists of two level atoms interacting through the dipole–dipole potential. A many body collision model, which includes the binary as well as the shielding effects, is investigated. The linear response of the dielectric is given by a generalized transport equation. Self-consistent coupled equations are derived for the various collision operators, using the propagator techniques. In the two limiting cases, the results of the binary collision model and those of the shielded interaction model, respectively, are recovered. The equations are simplified by neglecting the nonresonant contributions. Finally, a solution is obtained in the resonance broadening approximation. The resulting expression for the dielectric susceptibility includes the two body collision as well as the many body shielding effects. In particular, it includes the important collective excitation transfer effects. The proposed many body collision model should be appropriate for the resonant, linear response of high density gases.
Approximation formulae in the form of quadratic polynomials in combination with Planck's distribution are proposed for the thermal ionization rates of Rydberg states in helium and alkali atoms. The coefficients of the polynomials were determined by fitting the data for the rates calculated by integrating the photoionization cross sections obtained in the model potential approach for the S, P and D states with the principal quantum number ranging from n = 10 to n = 45, in product with Planck's frequency distribution for the flux of blackbody photons at temperatures from 100 K to 2000 K. Tables of the polynomial coefficients are presented for the atoms indicated. The deviations of the data given by the approximation formula from that of the straightforward integration of cross sections is less than 7% for states with n from 20 up to 55 in the temperature range from 70 K to about 1000 K, not exceeding 40–50% for states with n = 20–100 in the temperature range extending up to 10 000 K, thus providing rather simple and accurate estimates for experiments and for practical applications.