Lowest-order relativistic corrections of helium computed using Monte Carlo methods

Alexander, S. A.; Datta, Saiti; Coldwell, R. L.

doi:10.1103/physreva.81.032519

Cited by 19 publications

(7 citation statements)

References 71 publications

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“…Our values for the excited-state energies agree to five digits with the measured energies, while we reproduce the measured ground-state energy to three digits. We note that the experimental energies quoted in Table I also agree slightly better with both relativistic and nonrelativistic calculations by Alexander et al [46] for the excited states than the ground state. 12 W/cm 2 , τ IR = 2.6 fs (1 IR optical cycle), respectively.…”

Section: Comparison Of the "Poisson Equation" And "Direct Integratsupporting

confidence: 73%

Laser-assisted XUV few-photon double ionization of helium: Joint angular distributions

Liu

Thumm

2014

Phys. Rev. A

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We investigate few-photon extreme ultraviolet (XUV) double ionization of helium atoms without and in the presence of an assisting infrared (IR) laser field by numerically solving the time-dependent Schrödinger equation in full dimensionality within a finite-element discrete-variable-representation scheme. We discuss joint energy distributions for coplanar emission where the emitted electron momenta and polarization axis of the linearly polarized XUV and IR pulses lie in a plane. Our analysis focuses on joint angular distributions for highly correlated equal-energy-sharing double ionization by absorption of one, two, or three XUV photons and IR-laser-assisted single-photon XUV double ionization.

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Section: Comparison Of the "Poisson Equation" And "Direct Integratsupporting

confidence: 73%

Laser-assisted XUV few-photon double ionization of helium: Joint angular distributions

Liu

Thumm

2014

Phys. Rev. A

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“…So far, we are unable to find accurately the wavefunction for the 2 (spin-orbit, spin-spin interactions, radiative effects) to energy of the lowest states ( 14), (15) should not be more than ∼ 10 −4 a.u. similarly to ones for Helium [22] Note that conceptually the prediction ( 14) is in agreement with D.R. Yafaev's rigorous mathematical statement [23] about the finite number of bound states at Z = 1 but in contradiction to the widely-known theoretical statement by R.N.…”

Section: For Illustration) Then Taking Into Account the Points From T...supporting

confidence: 71%

Three-body quantum Coulomb problem: Analytic continuation

2016

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The second (unphysical) critical charge in the 3-body quantum Coulomb system of a nucleus of positive charge Z and mass m p , and two electrons, predicted by F Stillinger has been calculated to be equal to Z ∞ B = 0.904854 and Z mp B = 0.905138 for infinite and finite (proton) mass m p , respectively. It is shown that in both cases, the ground state energy E(Z) (analytically continued beyond the first critical charge Z c , for which the ionization energy vanishes, to ReZ < Z c ) has a square-root branch point with exponent 3/2 at Z = Z B in the complex Z-plane. Based on analytic continuation, the second, excited, spin-singlet bound state of negative hydrogen ion H − is predicted to be at -0.51554 a.u. (-0.51531 a.u. for the finite proton mass m p ). The first critical charge Z c is found accurately for a finite proton mass m p in the Lagrange mesh method, Z mp c = 0.911 069 724 655.

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“…( 24)) and spin-other-orbit (Eq. ( 25)) matrix elements for some lowest P and D states are presented in Table II and are in a good agreement with the previous calculations [26], [25]. Nonrelativistic variational energies of bound states obtained and used in this work are presented in Table III.…”

Section: Technical Details and Resultssupporting

confidence: 87%

Spin-statistic selection rules for multiphoton transitions: Application to helium atoms

2016

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A theoretical investigation of the three-photon transition rates 2 1 P1 → 2 1 S0 , 1 1 S0 and 2 3 P2 → 2 1 S0 , 1 1 S0 for the helium atom is presented. Photon energy distributions and precise values of the nonrelativistic transition rates are obtained with employment of correlated wave functions of the Hylleraas type. The possible experiments for the tests of the Bose-Einstein statistics for multiphoton systems are discussed.

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Lowest-order relativistic corrections of helium computed using Monte Carlo methods

Cited by 19 publications

References 71 publications

Laser-assisted XUV few-photon double ionization of helium: Joint angular distributions

Laser-assisted XUV few-photon double ionization of helium: Joint angular distributions

Three-body quantum Coulomb problem: Analytic continuation

Spin-statistic selection rules for multiphoton transitions: Application to helium atoms

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