Vol. 18, No. 2 (1962)
The energies of the first ten atoms in the periodic table are calculated with a set of new variational wave functions. The form of the wave functions used is as follows: 1s:ψ1(r)=N1e-μαr[1+(μbr)2], 2s:ψ2(r)=N2[(μr)e-μr-Ne-μcr], 2p:ψ3(r)=N3(μdr)cosθe-μdr, ψ4(r)=N4(μdr)sinθeiφ-μdr, ψ5(r)=N5(μdr)sinθe-iφ-μdr. There are five parameters in all, two for the ls function, two for the 2s and one for the 2p functions. The parameter μ is a scale factor, the best value of which can be determined analytically, leaving but four parameters to be determined numerically. N1,N2,N3,N4 and N5 are normalization factors. The constant N is fixed so that ψ2 is orthogonal to ψ1. The energies and the parameters of the various states are determined by the variational method. The results of this calculation are better than that calculated by Morse, Young and Haurwitz with their wave functions containing four parameters. If we put c=1 in our wave functions, then there are four parameters only in all and it will be found that the results are still better than that found by Morse et al.
1962, 82 (2): 81-90. doi: 10.7498/aps.18.81
In this paper the influence of the scattering between spin waves on the ferromagnetic resonance absorption curves is discussed. The first order approximation of absorption curves and an exact expression for its 1-th moment are obtained.
A short review on recent works on the analytic properties of perturbation expansions including those of Tarski, Eden is given. In the appendix, a number of related problems are discussed. In appendix 1, it is explicitly shown that for N-π, N-N scattering, the critical α for all points on the surface of singularities for the simplest 4-pt diagram lies entirely outside the interval (01) of the real axis, except those α corresponding to points on the curve of singularities as required by the Mandelstamm's theory. In appendix 2, a heuristic proof of the single dispersive relation independent of the momentum trausfer is provided. The proof rests on averaging over the azimuthal augle of meson momentum while the unclear momentum is oriented along the polar axis (here Breit system is emple-yed). In appendix 3, it is shown that hermiticity of certain variables leads to unitarity condition and thus one may hope to formulate the unitarity condition without encoanlering quadratic terms in the scattering amplitudes.