Analysis of the data on spontaneous emission probabilities and collisional broadening cross sections of 00⁰1-10⁰0 lines of the CO₂molecule

Abstract

We critically examine a model that attempts to explain the emergence of power laws (e.g., Zipf's law) in human language. The model is based on the principle of least effort in communications-specifically, the overall effort is balanced between the speaker effort and listener effort, with some trade-off. It has been shown that an information-theoretic interpretation of this principle is sufficiently rich to explain the emergence of Zipf's law in the vicinity of the transition between referentially useless systems (one signal for all referable objects) and indexical reference systems (one signal per object). The phase transition is defined in the space of communication accuracy (information content) expressed in terms of the trade-off parameter. Our study explicitly solves the continuous optimization problem, subsuming a recent, more specific result obtained within a discrete space. The obtained results contrast Zipf's law found by heuristic search (that attained only local minima) in the vicinity of the transition between referentially useless systems and indexical reference systems, with an inverse-factorial (sub-logarithmic) law found at the transition that corresponds to global minima. The inverse-factorial law is observed to be the most representative frequency distribution among optimal solutions.

Study of the parameters of the collisionally broadened R22 absorption line of the 1000-0001 transition in CO2 molecules: I. Experiment

“…An exception is the spontaneous emission probabilities A mn ; the corre sponding data in the literature are rather ambiguous [2,3,[14][15][16]. In view of the aforesaid, one must either measure A mn with a high accuracy or apply techniques that do not involve A mn in order to reduce the error in determining .…”

Parameters of the collisionally broadened R22 absorption line of the 1000–0001 transition of the CO2 molecule

“…(2) have been measured for CO 2 with fairly high accuracy. The exception is the spontaneous emission probability A mn , for which the published values have a rather large uncertainty [2,[11][12][13]. Given this, in order to increase the accuracy of the determination of γ CO 2 −CO 2 , it is either necessary to measure A mn or to propose a method that does not use A mn .…”

Gasdynamic problems for optically inverse media

“…Based on the analysis of nine independent measurements of the Einstein coefficient A 21 for P20 line of the transition 1000 ~ 0001, the authors of [57] have recommended the value of A21 = 0.187 s-1. This magnitude is a mean value of three most accurate measurements, while the experimental results from [57] give the arithmetic mean of A21 = 0.189 s-1, which practically fits the recommended magnitude.…”

“…Based on the analysis of nine independent measurements of the Einstein coefficient A 21 for P20 line of the transition 1000 ~ 0001, the authors of [57] have recommended the value of A21 = 0.187 s-1. This magnitude is a mean value of three most accurate measurements, while the experimental results from [57] give the arithmetic mean of A21 = 0.189 s-1, which practically fits the recommended magnitude. The dependence of the Einstein coefficient on the quantum number, J, can be defined by expressing A 21 through the square of the matrix element of the vibrational transition dipole moment (Rv'v")2 [58] :…”

“…where S( J) is Hanley-London's factor equal to J, with a good accuracy, for the P-branch and (J + 1), for the R-branch [58], and g l is the degeneracy factor of the lower state. The tabular data for the optical cross-sections collisional broadening are also presented in [57].…”