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The paper reports on experimental vibrational intensity distributions for continuum photoionization of oxygen using both 584 and 304 A helium lines. A cylindrical mirror energy analyzer with known transmission properties was used to record photoelectron spectra at a resolution of 45 meV with dispersed He radiation. At each wavelength the vibrational intensity distribution were corrected for the transmission of the analyzer and normalized to 100 at the strongest level. A table lists the results with calculated Franck-Condon factors.

The lower‐bounds method presented by Löwdin in the preceding paper has been applied to oscillators perturbed by third‐ and fourth‐power terms in the potential‐energy expression. For favorable cases agreement between upper and lower bounds is easily carried to many more figures than are likely to be physically significant. In many cases the lower bounds agreed more closely to the true eigenvalue than did the corresponding upper bounds. For a given basis set, this method gives closer bounds than that of Bazley and Fox, except for energy levels too high to be satisfactorily treated in the given basis. The only disadvantage found was that for close bounds double precision proved necessary, indicating more than ordinary loss of computational accuracy.

The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.

Many recent studies of solid-state phenomena, particularly in the area of crystal imperfections, have involved the use of melt-grown NaCl single crystals. Quite often trace impurities in these materials have had a prominent effect on these phenomena. Trace amounts of hydroxide ion have been found in melt-grown NaCl crystals. This paper describes a nondestructive method of neutralizing the hydroxide ion in such crystals. Crystals of similar hydroxide content are maintained at an elevated temperature below the melting point of NaCl in a flowing atmosphere containing. dry hydrogen chloride. Heat treatment is continued until an analysis of the test specimens shows no excess hydroxide ion. A colorimetric method previously described4 is used for this analysis.