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Relativistic calculations of quasi-one-electron atoms and ions using Laguerre and Slater spinors
Atomic Physics · Submitted 17 May 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed.
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A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr$^+$. The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. | contribution 0.96 | 0.91 | 0.20 | asserted 1.00 |
| s1 | The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. | method 1.00 | 0.85 | 0.04 | asserted 1.00 |
| s2 | The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. | method 1.00 | 0.86 | 0.07 | asserted 1.00 |
| s3 | The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. | result 0.61 | 0.93 | 0.11 | asserted 1.00 |
| s4 | The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr$^+$. | contribution 0.81 | 0.94 | 0.11 | asserted 1.00 |
| s5 | The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. | result 0.82 | 0.90 | 0.15 | asserted 0.99 |
| s6 | Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions. | interpretation 0.76 | 0.32 | 0.21 | hedged possibility 0.89 |
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Original abstract
A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr$^+$. The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions.
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