Calculation of two-photon decay rates of hydrogen-like ions by using B-polynomials

Amaro, Pedro; Surzhykov, A.; Parente, F.; Indelicato, P.; Santos, J. P.

doi:10.1088/1751-8113/44/24/245302

Cited by 15 publications

(23 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results with a Coulomb potential perfectly agree with the benchmark values presented in Refs. [8], [9], and [24]. They are even more accurate, providing for some partial rates up to five more significant digits than in Refs.…”

Section: Discussionmentioning

confidence: 84%

“…The Gauss-Legendre quadrature over ω 1 is performed with N ω 1 = 15 mesh points, in order to be consistent with the choice made in Ref. [8]. The Lagrange-mesh results are in excellent agreement with the B-polynomial values.…”

Section: S 1/2 → 1s 1/2 Transitionmentioning

confidence: 86%

“…[8], leads to a difference in the sixth digit of the results. Besides, using 15 mesh points for the Gauss-Legendre quadrature over ω 1 may be insufficient to reach the convergence of all the displayed figures.…”

Section: S 1/2 → 1s 1/2 Transitionmentioning

confidence: 98%

“…From the general requirement of gauge invariance, the final results must be independent of G. The gauge invariance of the two-photon relativistic calculations was studied by Goldman and Drake [7], Santos et al [6], and Amaro et al [8].…”

Section: Relativistic Formulationmentioning

confidence: 99%

“…This calculation involves an infinite number of intermediate virtual states. However, excellent results can be obtained with a finite number of pseudostates, built on complete basis sets such as Dirac Green's functions [7], B splines [6], B polynomials [8], and Sturmians [9]. This calculation is simplified by the Lagrange-mesh method, which is an approximate variational method involving a basis of Lagrange functions related to a set of mesh points associated with a Gauss quadrature [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Relativistic two-photon decay rates with the Lagrange-mesh method

2016

View full text Add to dashboard Cite

Relativistic two-photon decay rates of the 2s 1/2 and 2p 1/2 states towards the 1s 1/2 ground state of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. Highly accurate values are obtained by a simple calculation involving different meshes for the initial, final, and intermediate wave functions and for the calculation of matrix elements. The accuracy of the results with a Coulomb potential is improved by several orders of magnitude in comparison with benchmark values from the literature. The general requirement of gauge invariance is also successfully tested, down to rounding errors. The method provides high accuracies for two-photon decay rates of a particle in other potentials and is applied to a hydrogen atom embedded in a Debye plasma simulated by a Yukawa potential.

show abstract

Section: Discussionmentioning

confidence: 84%

Section: S 1/2 → 1s 1/2 Transitionmentioning

confidence: 86%

Section: S 1/2 → 1s 1/2 Transitionmentioning

confidence: 98%

Section: Relativistic Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Relativistic two-photon decay rates with the Lagrange-mesh method

2016

View full text Add to dashboard Cite

show abstract

Electromagnetic Transitions in the Spectrum of a Confined Hydrogen Atom

Baye

2022

Few-Body Syst

View full text Add to dashboard Cite

Transition probabilities per time unit in the spectrum of the hydrogen atom conned in a spherical cavity are studied with the Dirac equation. The calculations are performed with simple and accurate expansions of the Dirac components provided by the Lagrange-mesh method with small numbers of scaled Jacobi mesh points. The initial and nal states as well as intermediate states occurring in two-photon transitions are described with a single Lagrange mesh. With this simplication, accurate matrix elements are easily computed with the Gauss quadrature associated with the Lagrange-Jacobi mesh. One-photon transitions are considered from the n = 2 and 3 levels. Most transition probabilities increase as a negative power of the connement radius when it becomes small. The two-photon 2s 1/2 − 1s 1/2 transition stops being the main deexcitation channel of the 2s 1/2 level when the connement radius decreases below about 15 atomic units. The 2p 1/2 and 2p 3/2 levels come below the 2s 1/2 level and allow a faster one-photon deexcitation.Keywords Conned hydrogen atom • Electromagnetic transition probabilities • Dirac equation • Lagrange-mesh method

show abstract