Function Of R1 Research Articles

On the analytic solution of the first-order perturbed wave function of the two-electron atom

It is shown that the first-order perturbation equation for the ground state of the helium atom, with r−112 as the perturbation, may be solved by an infinite power series in r12. The coefficients, which are functions of r1 and r2, satisfy two-term differential recursion relations which can be integrated analytically to give the higher coefficients in terms of the lower. In this preliminary communication, the first coefficient, which describes short-range correlation, is given explicitly. The extensions of the technique are discussed.

Raman microscopy of a small uniaxial crystal: Tetragonal aspartame

AbstractA general method is presented for determining the shape and orientation of the Raman tensor of a molecule in a uniaxial crystal using a Raman microscope. First, equations are derived to connect the Raman tensor components (αxx, αyy, etc.) of a molecule to the Raman tensor components (αaa, αcc, etc.) of a crystal that is composed of molecules in a uniaxial arrangement, with an orientation specified by the two angles χ and θ. Next, a method is presented to obtain a correct set of values of the intensity ratios Iac/Iaa and Icc/Iaa from observed values of the intensity ratios measured with a Raman microscope. To augment the experimental data, the depolarization ratio ρ (for a completely random molecular orientation) is plotted as a function of r1 = αxx/αzz and r2 = αyy/αzz, so that a possible set of r1 and r2 values can be found from an observed value of ρ. The method has been applied to an aspartame IIA crystal (P41). A set of values of r1, r2, χ and θ has been determined for each of the following Raman fundamentals: 1741 cm−1 (ester CO stretch), 1667 cm−1 (amide I), 1275 cm−1 (amide III) and 1204 cm−1 (CCphenyl stretch), excited at 488.0 nm.

Correlation energy in the ground state of He I.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Correlation energy in the ground state of He I. Green, Louis C. ; Mulder, Marjorie M. Abstract for the computation of atomic transition probabilities. It is generally recognized that configuration interaction can play an important role in the determination of both wave functions and energies for the various atomic states. With a view to examining the effects of configuration interaction in a simple case, use has been made of expansions of the three- and six-term expressions, given by Hylleraas, for the ground state wave function of Hei in series of Legendre functions of the cosine of the angle between the two radii vectores. The coefficients in these expansions are functions of r1 and r2, the distances of the two electrons from the nucleus. The contributions of the various components to the total energy are presented. A discussion is given of the method of estimating the magnitude of the correlation, or configuration interaction, energy. Evidence is presented that the total correlation energy is at least -0.129 R~ehG and may be even more negative. Of this amount -0.056 RHehG is associated with the radial part of the correlation energy and -0.073 R~ehC with the angular part. I.L. C. Green etal., A. J. 57, II, 1952. Strawbridge Observatory, Haverford College, Haverford, Pa. Publication: The Astronomical Journal Pub Date: March 1953 DOI: 10.1086/106811 Bibcode: 1953AJ.....58...40G full text sources ADS |