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Phys. Rev. 154, 40 (1967). 43J. M. Peck, Phys. Rev. 154,~" . (1967). 44At 1000'K, the Boltzmann factor for the seventh vibrational state of H2' is 5x10, compared with 5xl0 for the state v =2. Hence, if the electronic-coupling crossing-point mechanism introduced by Bates were significant in the DR of H2'+e, the mean cross section for the process would have to be at least six orders of magnitude larger than that of the noncrossing vibronic mechanism discussed here. As the results will show, this would imply that the cross section for the Bates mechanism wouldhaveto be at least 10 cm, for states with v~7, or that the rate coefficient for DR of H2' in high vibrational states would be of order 4 x 10 . This is between one and two orders of magnitude larger than any rate coefficient previously attributed to DR by the Bates mechanism.f values have been computed for the transitions m S-n P, m = 1-5, n= 2-5 and m S-n P, m, n= 2-5 for members of the helium isoelectronic sequence up to Z=10. The agreement between the results obtained using the dipole length, and velocity formulas, together with the convergence of the results as an increasing number of terms are included in the expansions of the wave functions, indicate that the values obtained are accurate to within 1% or better for the large majority of the transitions. Various authors have computed f values for transitions between S and P states of helium and of heliumlike atoms using different types of approximate wave functions. ' The wide variation between the results of the different calculations show the computed f values to be particularly sensitive to the wave function employed. Thus in order to ob-tain reasonably reliable f values it is necessary to employ wave functions of high accuracy. %e have previously' obtained accurate wave functions for the states 1'S and n S, n S, n'P, n P, n=2-5, for members of the helium isoelectronic sequence up to Z =10, and have therefore been able to carry out a systematic calculation of the f values for 886 SCHIF F, P EKERIS, AND AC CAD transitions between these states. The methods used to obtain the wave functions have been described elsewhere, ' ' and we shall only give a brief outline here. The nonrelativistic Schrodinger wave equation for a two-electron atomwith an infinitely heavy nucleus is solved by assuming a solution i.n the form of a series expansion possessing the appropriate symmetry. Each solution then gives an approximation to the nonrelativistic wave function for one of the states with the given symmetry, while the corresponding eigenvalue E gives an approximation to the energy of this state. To obtain the total energy, the contributions from the relativistic effects and a correction for the finite mass of the nucleus have to be added. The nonrelativistic wave function obtained is, however, accurate enough for computing the f values. The dependence of the wave function on the angular coordinates of the two electrons is determined by considerations of symmetry.Thus it remains to determine the dependence on the thre...

The Sand P-state helium wave functions recently obtained by the authors have been used to make an accurate calculation of the f values for transitions between the 1'S, 2'S, and 2'S states and the 2'P, 2'P, 3'P, and 33P states in this atom. The accuracy of the results has been estimated by evaluating the dipole length, velocity, and acceleration forms of the matrix element for the transition, and by the inclusion of differing numbers of terms in the expansions of the wave functions. Wave functions containing up to 220 terms have been used, and the least accurate f value is estimated to be correct to within +0.0002, an accuracy sufficient for all practical applications.