Resonance Quasi-Projection Operators: Calculation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>Autoionization State of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow

Temkin, A.; Bhatia, A. K.; Bardsley, J. N.

doi:10.1103/physreva.5.1663

Cited by 74 publications

(5 citation statements)

References 31 publications

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“…In order to test our procedures, we have investigated the (1s2s 2 ) 2 S resonances of Li and He Ϫ , two three-electron atomic systems that closely resemble the collisional complex under consideration here: the He Ϫ resonance involves the same open shell 1s He orbital, and Li represents the united atom limit of He*(2s 3 S) ϩ H. Both cases have been treated previously by various theoretical methods [39][40][41][42][43][44][45] and comparison can be made with precise measurements of the resonance energies [46][47][48][49][50][51][52] and, in the case of He Ϫ , also with experimental data for the width. [46][47][48][49] As pointed out by Davis and Chung, 45 the proper account of electron correlation is essential for accurate results for the widths of these 2 S atomic resonances.…”

Section: Application To Atomic Resonancesmentioning

confidence: 99%

Theoretical investigation of the autoionization process in molecular collision complexes: Computational methods and applications to He*(23S)+H(12S)

Movre

Meyer

1997

The Journal of Chemical Physics

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The first complete ab initio treatment is applied to the autoionization process in the He*(2s 3 S) ϩ H(1s) collisional complex. The autoionizing resonance state is defined through Feshbach projection based on orbital occupancy, and the corresponding potential is determined from multireference-configuration interaction ͑MR-CI͒ calculations with an accuracy of about 10 meV. The energy-dependent coupling with the continuum is derived from a compact (L 2) molecular orbital ͑MO͒ without any phase information being lost. This ''Penning MO'' is projected onto the states of the continuum electron for energies that comply with the resonance condition thus providing the l-dependent coupling elements in local approximation. The continuum electron functions are calculated within the static-exchange approximation for up to 25 coupled angular momentum channels. The nuclear dynamics calculation is based on a complex Numerov algorithm and uses a converged set of seven complex coupling matrix elements. Weighting with experimental collision energy distributions finally gives the angle-dependent, as well as the angle-integrated, electron spectra for Penning and associative ionization processes. The results are discussed with respect to previous, either partial or model studies, and are compared with the recent most detailed experimental study of the angular-dependent Penning ionization electron spectra. The close agreement of theory and experiment demonstrates the adequacy of the local complex potential approach, as well as the importance of electron angular momentum transfer so far neglected in theoretical treatments.

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Section: Application To Atomic Resonancesmentioning

confidence: 99%

Theoretical investigation of the autoionization process in molecular collision complexes: Computational methods and applications to He*(23S)+H(12S)

Movre

Meyer

1997

The Journal of Chemical Physics

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“…Although in principle Ere, could, and maybe should, be stabilized with respect to each nonlinear parameter in the wavefunction, we restricted the optimization to the parameters associated with the unbound particle in \kp. This is because the nonlinear parameters in \ k~ had been optimized previously in the quasiprojection calculation [9], while those in the target function had been obtained from a variational calculation on the ground state of helium. Since the first five orbitals in Table I were primarily associated with \ k~, they were also not varied.…”

Section: Trial Wavefunction For the (1s 2s2) 2s He-resonancementioning

confidence: 99%

The complex stabilization method: Application to atomic resonances

Junker

2009

Int. J. Quantum Chem.

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The complex stabilization method is used to compute the position and width of the (1s 2 9 ) zS He-resonance using a number of different basis sets. All of the results converge to the same eigenvalue we obtained earlier in a so-called complex coordinate calculation. This calculation uses the unrotated real Hamiltonian with a square-integrable basis without explicitly imposing any boundary condition. Calculations are reported in which the bases contained one and two complex basis functions. It is shown that the resonant eigenvalue is easily distinguished from all other eigenvalues.

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“…The actual wave functions employed in the calculations are given in detail elsewhere [4]. The "Q-space" part of the wave function consists basically of the 28 configuration wave function used in a previous quasi-Feshbach calculation [6] of this resonance with r replaced by p exp (ia) in the Slater orbital basis. Four configurations of the form 1s ns ns were added to this wave function.…”

Section: Lowest *S Resonance In He-mentioning

confidence: 99%

Complex coordinate calculations of resonances in N‐electron atoms

Junker

1978

Int J of Quantum Chemistry

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We present a discussion of the functional dependences of the wave functions for bound, resonant, and scattering states on the radial coordinate p and the rotation angle a in the complex coordinate method. We conclude that for bound states and resonances, p and a are constrained to appear in the wave functions only in the form p exp (ia). On the other hand, this constraint is not obtained for the scattering states since the energy of the scattering states depends on a. In addition we suggest a partitioning of the resonant wave function into two parts-a boundlike or "Qspace" part and a scattering like or "P-space" part. With these concepts one can incorporate physical insight into the choice of configurations as one does in other methods and can apply the complex coordinate method to many electron systems with an expected rate of convergence similar to other techniques. Its advantages are that a single calculation yields the position and width of the resonance, only square integrable functions are used, only a solution of a straightforward eigenvalue problem is required unlike some methods, arbitrarily accurate target states are easily incorporated, and polarization terms can easily be explicitly included. Variational calculations for the position and width of the lowest *S resonance in the negative helium ion are reported using trial wave functions containing 39, 43, 55, 24, and 32 "P-space" configurations, respectively. Values of 19.387 eV and 12.13 meV are obtained for the position and width, respectively, for the resonance over a range in the rotation angle of almost two orders of magnitude. One also finds that inclusion of free-particle-like basis functions improves the representation of the scattering states.

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Resonance Quasi-Projection Operators: Calculation of theS2Autoionization State ofHe

Cited by 74 publications

References 31 publications

Theoretical investigation of the autoionization process in molecular collision complexes: Computational methods and applications to He*(23S)+H(12S)

Theoretical investigation of the autoionization process in molecular collision complexes: Computational methods and applications to He*(23S)+H(12S)

The complex stabilization method: Application to atomic resonances

Complex coordinate calculations of resonances in N‐electron atoms

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