The Theory of Cyclical Transitions.

Abstract

view Abstract Citations (3) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Theory of Cyclical Transitions. Henyey, L. G. Abstract The general theory of cyclical transitions in the absence of coffisions is discussed, first for a finite number of discrete states. It is found that the rigorous treatment of the radiation field can be carried conveniently to a fairly advanced state, short of the com- plete solution of the problem. It is found that there exist a number of first integrals of the differential equations, some of which are generalizations of the constancy of the net flux and of the linear dependence of the radiation pressure on the optical depth in the simple scattering problem. The remaining integrals are simple relationships among the optical depths in the various frequencies. The second part of the discussion is devoted to a study of the properties of the radia- tion field when the exciting radiation is highly diluted. The approximation appropriate to a high dilution is introduced, and it is found that the problem can be completely solved to within the Milne-Eddington approximation to the directional dependence of the specific intensity. The boundary conditions for a planetary nebula are introduced, and the values of the emergent fluxes are obtained. Physically the approximation for a high dilution is equivalent to neglecting the transitions corresponding to stimulated emissions and those corresponding to absorption when the lower state is not the ground state. However, these facts do not constitute the basis for the approximation; it is in- troduced from more fundamental considerations. The last part of the theoretical discussion pertains to the generalization of the theory to an infinite number of discrete states together with a continuum. This formal exten- sion follows in a natural way and depends on no new physical concepts. Finally there is a section devoted to some computations on the four-state problem for a planetary nebula. One interesting result is the weakness of the (i, ~) radiation (Ly f3 for hydrogen) when the fourth state is identified with the continuum Publication: The Astrophysical Journal Pub Date: September 1938 DOI: 10.1086/143966 Bibcode: 1938ApJ....88..133H full text sources ADS |