Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Dynamical contributions to the quantum defects of calcium

A. Ganesh Vaidyanathan, Philip Shorer

Published Jun 1, 1982• 14 citations
Publisher

Abstract

Nonadiabatic effects on the structure of Rydberg states of alkaline-earth atoms are examined and found to be large in many cases. Calculations for the quantum defects of the singlet $F$ and $G$ series in calcium, including dynamical contributions, are shown to be in good agreement with recent experimental data. This is in contrast to predictions based on the adiabatic core-polarization model, which significantly overestimates the quantum defects. Values for quantum defects of Ca for $l\ensuremath{\ge}4$ are presented.

DOI
10.1103/physreva.25.3108

Related papers

Ab InitioCalculations of Quantum-Defect Parameters for Alkaline Earths

K. C. Pandey, Sudhanshu Shekhar Jha, John A. Armstrong

Within the framework of the close-coupling method, ab initio calculations of parameters of multichannel quantum-defect theory have been carried out for several Rydberg series of Ca, Sr, and Ba. A local-density approximation, commonly used in solid-state calculations, including self-consistent, self-energy corrections, was made to the exchange-correlation potential. Good agreement with experimental values of multichannel quantum-defect theory parameters is obtained, permitting accurate prediction of highly excited-state binding energies.

Physical Review Letters•Jun 16, 1980•20 citations

Core polarization and quantum defects in high-angular-momentum states of alkali atoms

Richard R. Freeman, Daniel Kleppner

We discuss the systematics of energy levels of high-angular-momentum Rydberg states of alkali-metal atoms, and show that they are well described by a quantum-defect model. Polarization of the core electrons by the valence electron is shown to be the dominant contribution to the quantum defect. As an example, recently observed splittings between the $l=3,4,\mathrm{and} 5$ levels in various Rydberg states of sodium are analyzed to yield values for the core polarizabilities. Effective values of the dipole and quadrupole polarizability of 1.0015(15) and 0.48(15) a.u., respectively, are obtained. Implications for the precise determination of the structure of highly excited Rydberg states in alkali atoms are discussed.

Physical Review A•Nov 1, 1976•190 citations

Study on ionic Rydberg states of calcium

C. B. Xu, Xiu-Ping Xie, R. C. Zhao +5 more

Using five-laser resonance excitation, we observe the p Rydberg series with n from 39 to 92. The energy levels calculated using the self-consistent-field method and quantum defect theory are in good agreement with the experimental results.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 28, 1998•7 citations

Interaction of Rydberg atoms in circular states with the alkaline-earth Ca(4s 2) and Sr(5s 2) atoms

E. S. Mironchuk, Alexander A. Narits, Владимир Сергеевич Лебедев

The resonant mechanism of interaction of alkaline-earth atoms having a low electron affinity to Rydberg atoms in circular (l = |m| = n–1) and near-circular states has been studied. To describe the dynamics of resonant processes accompanied by nonadiabatic transitions between ionic and Rydberg covalent terms of a quasimolecule, an approach based on the integration of coupled equations for the probability amplitudes has been developed taking into account the possibility of the decay of an anion in the Coulomb field of the positive ionic core of a highly excited atom. The approach involves the specific features of the problem associated with the structure of the wavefunction of a Rydberg electron in states with high orbital angular momenta l ~ n–1. This approach provides a much more accurate description of the dynamics of electronic transitions at collisions between atoms than that within the modified semiclassical Landau–Zener model. In addition, this approach makes it possible to effectively take into account many channels of the problem. The cross sections for resonant quenching of Rydberg states of the Li(nlm) atom with given principal n, orbital l = n–1, and magnetic m quantum numbers at thermal collisions with the Ca(4s 2) and Sr(5s 2) atoms have been calculated. The dependences of the results on n, m, and angle α between the relative velocity of the atoms and the normal to the plane of the orbit of the Rydberg electron have been obtained. The influence of orientational effects on the efficiency of the collisional destruction of circular and near-circular states has been studied. The results indicate a higher stability of such states to their perturbations by neutral particles as compared to usually studied nl states with low values of l (l ≪ n).

Journal of Experimental and Theoretical Physics•Nov 1, 2015•1 citation

Stark structure of the Rydberg states of alkaline-earth atoms

Zhi Miao-chan, Dai Chang-Jian, Shiben Li

The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg ( n = 16, M = 0), Ca ( n = 10, M = 0), Sr ( n = 12, M = 0) and Ba ( n = 13, | M | = 0, 1) are presented. Topics such as the general methods of calculation, the treatment of fine structure and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.

Chinese Physics•Sep 25, 2001•19 citations

Van der Waals Interaction of Alkaline Earth Atoms in Singlet Rydberg States

Igor L. Glukhov, Aleksandr A. Kamenski, A. S. Kornev +3 more

Abstract The numerical values of the van der Waals interaction constant C6 are determined between alkaline earth atoms in singlet Rydberg |n1S0〉 states with large principal quantum numbers, n > 20. The results of calculations using the semiempirical quantum defect theory (QDT) method are approximated by quadratic polynomials. The polynomial coefficients are tabulated and can be used for simplified quantitative estimates of interatomic interaction-induced energy shifts, determination of the Rydberg state excitation blockade radius, and limitations on the wavelengths of radiation forming Rydberg lattices for group IIA atoms. The numerical values of the contributions of various diatomic states to the constant C6 are calculated. States providing the main contribution, analogous to that of the Förster resonance, are identified.

Bulletin of the Lebedev Physics Institute•Dec 1, 2025•1 citation
Nonadiabatic effects on the structure of Rydberg states of alkaline-earth atoms are examined and found to be large in many cases. Calculations for the quantum defects of the singlet FFF and GGG series in calcium, including dynamical contributions, are shown to be in good agreement with recent experimental data. This is in contrast to predictions based on the adiabatic core-polarization model, which significantly overestimates the quantum defects. Values for quantum defects of Ca for l\ensuremath≥4l\ensuremath{\ge}4l\ensuremath≥4 are presented.
Within the framework of the close-coupling method, ab initio calculations of parameters of multichannel quantum-defect theory have been carried out for several Rydberg series of Ca, Sr, and Ba. A local-density approximation, commonly used in solid-state calculations, including self-consistent, self-energy corrections, was made to the exchange-correlation potential. Good agreement with experimental values of multichannel quantum-defect theory parameters is obtained, permitting accurate prediction of highly excited-state binding energies.
We discuss the systematics of energy levels of high-angular-momentum Rydberg states of alkali-metal atoms, and show that they are well described by a quantum-defect model. Polarization of the core electrons by the valence electron is shown to be the dominant contribution to the quantum defect. As an example, recently observed splittings between the l=3,4,and5l=3,4,\mathrm{and} 5l=3,4,and5 levels in various Rydberg states of sodium are analyzed to yield values for the core polarizabilities. Effective values of the dipole and quadrupole polarizability of 1.0015(15) and 0.48(15) a.u., respectively, are obtained. Implications for the precise determination of the structure of highly excited Rydberg states in alkali atoms are discussed.
The resonant mechanism of interaction of alkaline-earth atoms having a low electron affinity to Rydberg atoms in circular (l = |m| = n–1) and near-circular states has been studied. To describe the dynamics of resonant processes accompanied by nonadiabatic transitions between ionic and Rydberg covalent terms of a quasimolecule, an approach based on the integration of coupled equations for the probability amplitudes has been developed taking into account the possibility of the decay of an anion in the Coulomb field of the positive ionic core of a highly excited atom. The approach involves the specific features of the problem associated with the structure of the wavefunction of a Rydberg electron in states with high orbital angular momenta l ~ n–1. This approach provides a much more accurate description of the dynamics of electronic transitions at collisions between atoms than that within the modified semiclassical Landau–Zener model. In addition, this approach makes it possible to effectively take into account many channels of the problem. The cross sections for resonant quenching of Rydberg states of the Li(nlm) atom with given principal n, orbital l = n–1, and magnetic m quantum numbers at thermal collisions with the Ca(4s 2) and Sr(5s 2) atoms have been calculated. The dependences of the results on n, m, and angle α between the relative velocity of the atoms and the normal to the plane of the orbit of the Rydberg electron have been obtained. The influence of orientational effects on the efficiency of the collisional destruction of circular and near-circular states has been studied. The results indicate a higher stability of such states to their perturbations by neutral particles as compared to usually studied nl states with low values of l (l ≪ n).
The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg ( n = 16, M = 0), Ca ( n = 10, M = 0), Sr ( n = 12, M = 0) and Ba ( n = 13, | M | = 0, 1) are presented. Topics such as the general methods of calculation, the treatment of fine structure and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.
Abstract The numerical values of the van der Waals interaction constant C6 are determined between alkaline earth atoms in singlet Rydberg |n1S0〉 states with large principal quantum numbers, n > 20. The results of calculations using the semiempirical quantum defect theory (QDT) method are approximated by quadratic polynomials. The polynomial coefficients are tabulated and can be used for simplified quantitative estimates of interatomic interaction-induced energy shifts, determination of the Rydberg state excitation blockade radius, and limitations on the wavelengths of radiation forming Rydberg lattices for group IIA atoms. The numerical values of the contributions of various diatomic states to the constant C6 are calculated. States providing the main contribution, analogous to that of the Förster resonance, are identified.