Stuart Allen Wallace, M. D.: 1898-1965

Powell, W. N.; Grossman, Marshall; Lind, Carla

doi:10.1093/ajcp/46.1.122

Cited by 20 publications

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“…(11) is easier to satisfy than the two-electron cusp conditions of Eqs. (12) and (13). For our wave functions, the largest deviation of C, " from unity is only 7.…”

Section: Introductionmentioning

confidence: 67%

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Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

1992

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states, with n (7, of the two-electron ions from He through Ne +. The variational energies are the best available for 180 of the 261 states. Electron-nuclear and electron-electron cusp checks are used to test the wave functions. For each ion, dipole oscillator strengths are calculated for 55 S-P and 40 P-D transitions. Our oscillator strengths are more accurate than previous values for 739 of the 855 transitions considered. Some coefficients for the 1/Z expansions of the energies and oscillator strengths have been estimated as an aid to extrapolating our results to higher nuclear charges.PACS number(s): 32.70.Cs, 31. 20.Tz X k( -12) I e P(~krl~kr2 Ykr12) k=1 X YL 0( 0 ] ) Yo o ( Q~) in which Xis the number of terms, P]p is the permutation operator, the plus and minus signs refer to the singlet and triplet states, respectively, L is the total orbital angular in which r;=(r;, Q;) is the position vector of electron i for i = 1,2, r, z is the interelectronic distance, and Z is the nuclear charge. Schiff, Pekeris, and Accad [l], Kono and Hattori [2,3), and Sanders and Knight [4] all used Hylleraas-type [5] wave functions containing several hundred and, in some cases, a few thousand terms. We have previously [6 -8] shown that use of exponential correlation factors [5,9] can lead to compact wave functions of similar accuracy. Although our original work was restricted to low-lying states [6,7], the success of our ansatz for obtaining pseudospectra [8] encouraged us to expect that it would do well for more highly excited states as well. Thus, for the S and P states, we use spin free wave functions of the form [6 -8] 46 5397

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“…(11) is easier to satisfy than the two-electron cusp conditions of Eqs. (12) and (13). For our wave functions, the largest deviation of C, " from unity is only 7.…”

Section: Introductionmentioning

confidence: 67%

“…(5) -(7), for each of the 29 states of each ion using Powell s conjugate direction algorithm [13]. All optimization methods are plagued by local minima; hence it was not surprising that different initial estimates of the parameters often led to substantially different "optimized" values.…”

Section: Introductionmentioning

confidence: 99%

Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

1992

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“…These results do not differ significantly from those obtained by Becker & Coppens using our formalism. However, we have used a computer program (TAILS) which minimizes an agreement factor based on the intensities rather than F or F 2 (see Cooper & Rouse, 1971) and uses the search algorithm of Powell (1965) rather than a conventional least-squares algorithm. These factors presumably account for small differences in the final values of the refined parameters.…”

Section: Becker-coppens Theorymentioning

confidence: 99%

The wavelength dependence of secondary extinction effects

Cooper¹,

Rouse²

1976

Acta Cryst Sect A

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The wavelength dependence of extinction effects in X-ray and neutron diffraction predicted by recent theories is considered and compared with the results obtained for recent accurate diffraction measurements. It is shown that it is not usually possible to determine reliable values of the domain radius and mosaic spread parameters separately from data measured at only one or two conventional wavelengths. The most significant experimental test of the wavelength dependence is at present that for secondary extinction in a spherical crystal arising from neutron diffraction measurements for SrFz at three different wavelengths. These have been analysed on both the Cooper-Rouse and the Becker-Coppens formalisms, both of which predict a simple form for the wavelength dependence. Although both these formalisms give excellent agreement with the data when those for different wavelengths are analysed separately the results indicate, in both cases, that the wavelength dependence is not accounted for adequately by the theory.

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“…where Ioi is the observed background corrected intensity of the ith reflexion, Ici is the computed intensity and w~ is the weight given to the observation. Minimization of $2 is effected by the search algorithm of Powell (1965), which does not necessitate the computation of partial derivatives.…”

Section: Data Analysis (A) Methods Of Analysismentioning

confidence: 99%

A neutron diffraction study of anharmonic temperature factors in SrF₂

Mair¹,

Barnea²,

Cooper³

et al. 1974

Acta Cryst Sect A

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Accurate integrated intensities for the Bragg reflexion of neutrons from two single crystals of SrF2 have been measured at temperatures between 295 and 1043 °K. Corrections for extinction and thermal diffuse scattering were applied and the experimental data were analysed in terms of a model which includes both harmonic and anharmonic components in the thermal vibrations of the atoms. Significant contributions from the third-order anharmonic term, flF, in the one-particle potential of the fluorine atoms, consistent with their tetrahedral site symmetry, were observed at all temperatures. At 773 °K significant anisotropic fourth-order components, Jsr and JF, became apparent in the thermal vibration of both the strontium and the fluorine atoms. At this temperature flF was refined to -3.45 ( + 0.11) x 10 -12 erg/1,-3, with fist = 1"30 (+_ 0.75) x 10-12 erg A -4 and JF = 0.84 (+_ 0"29) x 10 -12 erg A -4. The positive signs of the parameters fist and JF result from the influence of Coulombic forces on the atomic vibrations. IntroductionIn almost all cases determination of crystal structures is carried out with models which assume harmonic thermal vibrations for all constituent atoms. The thermal vibration of each atom is then constrained such that the time-averaged probability function for the position of an atom is a Gaussian function of the displacement from its equilibrium position and contours of equal probability are ellipsoids. However, in a crystal the neighbours of an atom will of necessity be arranged with a particular symmetry which one would expect to influence the thermal vibration of that atom. This thermal motion will then be modified in such a way that the atom will spend more of its time in the regions of low potential. For an ionic crystal these are determined mainly by the relative influences of the Coulombic and repulsive forces. Such anharmonic components in the thermal vibration will contribute to the Bragg intensities and their effect can be readily recognized in such structures as the fluorite structure. Careful diffraction measurements can thus provide valuable information about the thermal vibration of the atoms and, in particular, about the way in which this is affected by the atomic environment.In an earlier experiment accurate integrated intensity measurements for the Bragg reflexion of neutrons were made for single crystals of SrF2 at room temperature (Cooper & Rouse, 1971). The experimental data were analysed to obtain a third-order parameter, fiE, in the potential of the fluorine ions, appropriate to their noncentrosymmetric site symmetry. In this paper we report the results of two further neutron experiments on SrF2. The first of these (Experiment A) was conducted at the A.A.E.C. Research Establishment, Lucas Heights, Australia and resulted in the determination of a value for flF, referred to 273°K, as reported previously (Mair & Barnea, 1971), as well as the temperature variation of the Debye-Waller factors, BF and Bsr, between 295 and 893°K. The second (Experiment B), carried out at A....

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Stuart Allen Wallace, M. D.: 1898-1965

Cited by 20 publications

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Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

The wavelength dependence of secondary extinction effects

A neutron diffraction study of anharmonic temperature factors in SrF₂

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Stuart Allen Wallace, M. D.: 1898-1965

Cited by 20 publications

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Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

The wavelength dependence of secondary extinction effects

A neutron diffraction study of anharmonic temperature factors in SrF2

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A neutron diffraction study of anharmonic temperature factors in SrF₂