On the Closure of Certain Assemblages of Trigonometrical by Wiener N.

By Wiener N.

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When the Boltzmanndistributionis valid, Eq. •(j'j") = const $(J'J")e-•{J')•,/•a'. 86) For singletbandsthe strengthsare relatedto J' and J" by the HOnlLondonformulae(Herzberg [1950a, p. 208]), which may also be used as a guide for transitionswith higher multiplicity, when spin splitting is not resolved,by replacingJ with the quantumnumbereK. Theoretical line strengthshave also been calculatedfor the detailed structureof some transitions and for certain forbidden transitions. Rotationaltemperaturesfor forbiddenband systems(when the molecules are in the excited level long enoughfor the relative rotational populationsto reach equilibrium with the gas through collisions)may be directlyindicativeof the kinetictemperaturein the upperatmosphere.

42)], whichdependson the quantumnumbersL, S, J, and the I for the jumping electron. For relativestrengths withina singletransitionarrayit is not necessary to knowthe radialcomponent of the matrix dement,whichinvolvesa knowledge of the radialwavefunctionandis moredifficultto evaluate. Of course,in any evaluationof absolutetransitionprobabilitiesthe entirewavefunctionmustbe considered. Aller [1953a,p. 134] gives samples of the White and Goldbergtables,with examples on their use for particularproblems.

EXCITATION AND IONIZATION PROCESSES 33 2. Assumethat continuousradiation with monochromaticflux •r• normalto the beam(where•r• = constant with v overthe frequency rangeof interest) fallsonanassembly of N oxygen atomsin theground term. What is the numberof upwardtransitionsto the XDterm (in the groundconfiguration) if theatomsaredistributed overthevarious levels of the aP term accordingto the statisticalweights? (SeeBatesandDalgarno Chapter2. 1. , the troposphere). Further,certainairglowemissions, suchas the resonance D linesof sodium,mayinvolveappreciable multiplescatterings beforethe light leavesthe emittinglayers.

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