Towards accurate wave functions and oscillator strengths

2000 ◽  
Author(s):  
Alan Hibbert
Keyword(s):  
Wave Functions ◽  
Oscillator Strengths ◽  
Accurate Wave

Inelastic Scattering of High Energy Electrons by Helium

1973 ◽  
Vol 51 (3) ◽  
pp. 311-315 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Ground State ◽  
High Energy ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
High Energy Electrons ◽  
Approximate Wave ◽  
Accurate Wave

Generalized oscillator strengths and the cross section for excitation of helium by electron impact have been calculated in the Born approximation. Transitions from the ground state to the n1P (n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and "configuration–interaction" type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiment.

Relativistic corrections to He I transition ratesThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

2011 ◽  
Vol 89 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Donald C. Morton ◽  
Paul Moffatt ◽  
G. W.F. Drake
Keyword(s):  
Nuclear Charge ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Nuclear Mass ◽  
Atomic Systems ◽  
Relativistic Corrections ◽  
Doubly Excited ◽  
Accurate Wave ◽  
The Continuum

The relativistic corrections to the theoretical oscillator strengths of light elements such as helium are typically less than 0.1% and usually are ignored. However, they can be important for comparisons with the most accurate experiments, and they rapidly increase in magnitude with increasing nuclear charge. We have begun with the spin-forbidden electric-dipole transitions of neutral helium, using calculations consisting of (1) extremely accurate wave functions without relativistic corrections for both infinite and finite nuclear mass, (2) spin-changing matrix elements through the perturbations of the wave functions by the spin-orbit and spin-other-orbit Breit operators, (3) the use of pseudostates in the sums over all the intermediate states including the continuum, and (4) the inclusion as perturbers of the 1S0 and 3S1 states the pseudostates corresponding to the doubly excited npn′p 3P 0e and npn′p 1P 1e terms, respectively. As examples of these calculations, we present oscillator strengths for the transitions 1 1S0–2 3P1, 2 1S0–2 3P1, 2 3S1–2 1P1, 2 1P1–3 3D1,2, and 2 3P1,2–3 1D2.

scholarly journals Accurate wave functions in the presence of long-ranged potentials

2016 ◽  
Vol 113 ◽  
pp. 08015
Author(s):  
George Rawitscher
Keyword(s):  
Wave Functions ◽  
Accurate Wave

Theoretical ionization energies and oscillator strengths for the sodium isoelectronic sequence

1969 ◽  
Vol 47 (8) ◽  
pp. 835-838 ◽  
Author(s):  
R. P. McEachran ◽  
C. E. Tull ◽  
M. Cohen
Keyword(s):  
Matrix Element ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Ionization Energies ◽  
Core Approximation

Orbital wave functions for a number of 2S, 2P0, 2D, and 2F0 states of Na, Mg+, and Al2+ have been calculated by means of the frozen core approximation. The oscillator strengths of all allowed dipole transitions have been determined using both length and velocity formulations for the transition matrix element; these results agree with each other to within a few percent.

Electric Quadrupole Transitions in Na I, Mg II and Al III

1972 ◽  
Vol 50 (11) ◽  
pp. 1169-1174 ◽  
Author(s):  
C. E. Tull ◽  
M. Jackson ◽  
R. P. McEachran ◽  
M. Cohen
Keyword(s):  
Electric Quadrupole ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Hartree Fock ◽  
Good Agreement

Theoretical multiplet strengths for electric quadrupole transitions between 2S, 2P0, 2D, and 2F0 levels of Na I, Mg II, and Al III have been calculated using Hartree–Fock wave functions of frozen-core type. The resulting 2S–2D oscillator strengths for Na I are in good agreement with calculations by Bogaard and Orr, Boyle and Murray, and Warner; however, for Mg II there is a discrepancy of a factor of 2 between our results and those of Warner.

Cancellation in the transition integrals for some dipole transitions: He isoelectronic series

1980 ◽  
Vol 58 (4) ◽  
pp. 546-548 ◽  
Author(s):  
Swadesh Kumar Ghoshal ◽  
Sankar Sengupta
Keyword(s):  
Confidence Level ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Isoelectronic Series

The amount of cancellation in the transition integrals for some np–n′d and nd–n′f singlet and triplet transitions for some members of helium isoelectronic sequence is estimated with Hartree–Fock wave functions. The results may act as a measure of the confidence level that can be attributed to the values of oscillator strengths of the respective cases.

Relativistic oscillator strengths for np2 → np(n + 1)s transition array of SnI and PbI spectra in jj and intermediate coupling

1979 ◽  
Vol 57 (2) ◽  
pp. 147-151 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Transition Probabilities ◽  
Theoretical Data ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Intermediate Coupling ◽  
Hartree Fock ◽  
Semiempirical Approach ◽  
Exchange Effects ◽  
Relativistic Oscillator ◽  
Transition Array

The relativistic oscillator strengths for the np2 → np(n + 1)s transition array as well as the lifetimes of levels of the np(n + 1)s configuration in SnI and PbI spectra were calculated in jj and intermediate coupling. The relativistic radial integrals were computed employing the wave functions obtained by a semiempirical approach which allowed for exchange effects. The results obtained are compared with existing experimental and theoretical data. The significance of intermediate coupling for oscillator strengths computations is discussed. The agreement with experiment is for the present semiempirical results generally better (particularly for the PbI spectrum) than for oscillator strength deduced from 'Optimized Hartree–Fock–Slater' transition probabilities, which were published previously.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

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