Theoretical formulas for the length, velocity, and acceleration forms of the electric-dipole matrix element within the adiabatic hyperspherical coordinate representation are presented. The length and acceleration formulas are used to calculate the photoionization cross section for He up to 1.0 a.u. above threshold and the photodetachment cross section for H up to 0.35 a.u. above threshold.Lengthand acceleration-form results for the dipole oscillator strengths for the discrete He transitions, 1sns('S') -+1smp('P'), where n =1, 2, and 3 and m =2, 3, and 4, are also presented. The accuracy of the length-and acceleration-form adiabatic hyperspherical coordinate approximation results is discussed.
In this paper, we discuss a rigorous treatment of the refractive scintillation caused by a two-component interstellar scattering medium and a Kolmogorov form of density spectrum. It is assumed that the interstellar scattering medium is composed of a thin-screen interstellar medium (ISM) and an extended interstellar medium. We consider the case that the scattering of the thin screen concentrates in a thin layer represented by a δ function distribution and that the scattering density of the extended irregular medium satisfies the Gaussian distribution. We investigate and develop equations for the flux density structure function corresponding to this two-component ISM geometry in the scattering density distribution and compare our result with the observations. We conclude that the refractive scintillation caused by this two-component ISM scattering gives a more satisfactory explanation for the observed flux density variation than does the single extended medium model. The level of refractive scintillation is strongly sensitive to the distribution of scattering material along the line of sight (LOS). The theoretical modulation indices are comparatively less sensitive to the scattering strength of the thin-screen medium, but they critically depend on the distance from the observer to the thin screen. The logarithmic slope of the structure function is sensitive to the scattering strength of the thin-screen medium, but is relatively insensitive to the thin-screen location. Therefore, the proposed model can be applied to interpret the structure functions of flux density observed in pulsar PSR B2111 + 46 and PSR B0136 + 57. The result suggests that the medium consists of a discontinuous distribution of plasma turbulence embedded in the interstellar medium. Thus our work provides some insight into the distribution of the scattering along the LOS to the pulsar PSR B2111 + 46 and PSR B0136 + 57.
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