Application of the Hylleraas-
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>B</mml:mi></mml:math>
-spline basis set: Static dipole polarizabilities of helium

We study static-field ionization of He-like ions with nuclear charge number in the range of 2 ≤ Z ≤ 36. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of 1/Z, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30% for He and 2% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as 1/Z.

show abstract

“…The ionization potential is calculated as where α He = 1.3832 a.u. is the polarizability of He [63].…”

Section: Discussionmentioning

confidence: 99%

“…( 17), we employ the value η = 4.8713 for He (Z = 2), so that twice the polarizability α SAE of the active electron equals the polarizability of He, α He = 1.3832 a.u. [63]. The numerical calculation of the SAE rates and the calculation of the SAE polarizability are described in Appendix E.…”

Section: Comparison Of Sae Approximation Rates and Mctdhf Ratesmentioning

confidence: 99%

Static-field ionization model of He-like ions for diagnostics of light-field intensity

2020

View full text Add to dashboard Cite

show abstract

“…A solution to improve the ground state result is modifying the basis of equation ( 11) with r 12 being included, similarly as done in the correlated Hylleraas basis. This termed Hylleraas-B-splines basis have been successfully used to calculate the static dipole polarizabilities of He [39]. And there is reason to believe that the ground state BL also can be given with good precision by using this modified B-splines basis [40].…”

Section: The Helium Atom Blmentioning

confidence: 99%

Calculations of Bethe logarithm for hydrogen and helium using B-splines in different gauges

Zhang¹,

Shen²,

Xiao³

et al. 2020

J. Phys. B: At. Mol. Opt. Phys.

Self Cite

View full text Add to dashboard Cite

The efficient and simple B-splines variational method is successfully used to calculate Bethe logarithm for the hydrogen atom in the velocity and length gauges. The ground state Bethe logarithm of hydrogen with fourteen accurate figures is obtained in the velocity gauge, and in the length gauge the ground state value has eleven accurate figures. Present velocity-and length-gauge results for the ns, np, nd, and nf states up to n = 200 of hydrogen are at the 10 −10 level of accuracy, which represent the successful variational attempt to calculate Bethe logarithm of hydrogen in the velocity and length gauges. In addition, the B-splines variational method is successfully extended to calculate Bethe logarithm for the helium atom combined with configuration interaction. Results of numerical calculations for n 1,3 S up to n = 8 states are presented in the acceleration gauge, the velocity gauge, and a hybrid of the velocity and acceleration gauges(also called pa-gauge). For the 2 3 S state, the acceleration-gauge value of 4.364 036 7(2) a.u. and the pa-gauge value of 4.364 036 4(2) a.u. both have eight significant digits. For other triplet S states, present results in three different gauges all have five to seven accurate figures. While for the singlet S states, the best convergent values are obtained in the pa-gauge, of which the numerical precision is at the 10 −5 to 10 −7 level of accuracy as well.

show abstract

“…Recently, Yang et al introduced a convenient basis set, called the H-B-spline basis, by integrating the r 12 = |𝑟 1 −𝑟 2 | factor in the B-spline basis. [21] This basis inherits the virtue of traditional B-spline basis, the high localization of each spline, and also has the ability of describing the behavior of wavefunctions at two-electron coalescences, which improves greatly the rate of convergence in partial-wave expansion. The H-B-spline basis was successfully applied to calculation on polarizabilities, magic wavelengths and Bethe logarithm of helium.…”

Section: Introductionmentioning

confidence: 99%

“…The H-B-spline basis was successfully applied to calculation on polarizabilities, magic wavelengths and Bethe logarithm of helium. [21][22][23] Here we will use this basis to calculate DESs, 2pnp 1 P e (3 ≤ n ≤ 5), 2pnp 3 P e (2 ≤ n ≤ 5) and 2pnd 1,3 D o (3 ≤ n ≤ 5), of helium.…”

Section: Introductionmentioning

confidence: 99%

Geometric quantities of lower doubly excited bound states of helium

Zhou

Yang

et al. 2022

Chinese Phys. B

View full text Add to dashboard Cite

Expectation values of single electron and interelectronic geometric quantities such as 〈r〉, 〈r 12〉, 〈r <〉, 〈r >〉, 〈cosθ 12〉 and 〈θ 12〉 are calculated for doubly excited 2pn p1 P e (3 ≤ n ≤ 5), 2pn p3 P e (2 ≤ n ≤ 5) and 2pnd1,3 D° (3 ≤ n ≤ 5) states of helium using Hylleraas-B-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for 〈θ 12〉 reach 10 significant digits as well; 〈θ 12〉 reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.

show abstract

Application of the Hylleraas- B -spline basis set: Static dipole polarizabilities of helium

Cited by 12 publications

References 29 publications

Static-field ionization model of He-like ions for diagnostics of light-field intensity

Static-field ionization model of He-like ions for diagnostics of light-field intensity

Calculations of Bethe logarithm for hydrogen and helium using B-splines in different gauges

Geometric quantities of lower doubly excited bound states of helium

Contact Info

Product

Resources

About