Physical Review A

Lifetimes of alkali-metal—atom Rydberg states

Constantine E. Theodosiou

Published Dec 1, 1984• 316 citations

Abstract

We report a comprehensive set of calculations of the lifetimes of Rydberg states in alkali-metal atoms, using realistic potentials to represent the atomic core. The effects due to core polarizability, spin-orbit interaction, and blackbody radiation are explicitly included. A complete cross reference listing of all available experimental lifetimes is also attempted. The results compare well with experiment for all principal quantum numbers $n$ examined and should provide guidance for future experimental investigations. The relation of the present approach to other works is discussed.

DOI: 10.1103/physreva.30.2881

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Physical Review A

Lifetimes of alkali-metal—atom Rydberg states

Constantine E. Theodosiou

Published Dec 1, 1984• 316 citations

Publisher

Abstract

n

examined and should provide guidance for future experimental investigations. The relation of the present approach to other works is discussed.

DOI: 10.1103/physreva.30.2881

Related papers

Model-potential calculation of lifetimes of Rydberg states of alkali atoms

Xinghong He, Baiwen Li, Aiqiu Chen +1 more

A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.

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General properties were determined and asymptotic approximation formulas for probabilities of spontaneous decay and photoionization cross-sections were derived on the basis of numerically calculated amplitudes of bound-bound and bound-free radiation transitions from Rydberg nS -, nP - and nD -states of alkali atoms with high principal quantum numbers, up to n = 1000. The departure of data from the asymptotic formulas for states with principal quantum numbers in the range between n = 10 and n = 2000 from originally calculated data does not exceed 0.1–1%, and may be useful for estimations of natural radiation widths for arbitrary high Rydberg levels.General properties were determined and asymptotic approximation formulas for probabilities of spontaneous decay and photoionization cross-sections were derived on the basis of numerically calculated amplitudes of bound-bound and bound-free radiation transitions from Rydberg nS -, nP - and nD -states of alkali atoms with high principal quantum numbers, up to n = 1000. The departure of data from the asymptotic formulas for states with principal quantum numbers in the range between n = 10 and n = 2000 from originally calculated data does not exceed 0.1–1%, and may be useful for estimations of natural radiation widths for arbitrary high Rydberg levels.

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Polarizabilities of Rydberg states of Rb atoms with n up to 140

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Up to the present, although experimental studies about the polarizabilities of alkali-metal Rydberg atoms have involved the states with principal quantum numbers $n\ensuremath{\le}80$, theoretical calculations are limited to the states with $n\ensuremath{\le}50$. In this work, we calculate the scalar and tensor polarizabilities of the $n{S}_{1/2}$ , $n{P}_{1/2,3/2}$ , and $n{D}_{3/2,5/2}$ Rydberg states of Rb with principal quantum number $n$ up to 140 employing a model potential and the $B$ -spline expansion technique. We obtain the polarizabilities that are in good agreement with the existing theoretical and experimental data.Up to the present, although experimental studies about the polarizabilities of alkali-metal Rydberg atoms have involved the states with principal quantum numbers $n\ensuremath{\le}80$, theoretical calculations are limited to the states with $n\ensuremath{\le}50$. In this work, we calculate the scalar and tensor polarizabilities of the $n{S}_{1/2}$, $n{P}_{1/2,3/2}$, and $n{D}_{3/2,5/2}$ Rydberg states of Rb with principal quantum number $n$ up to 140 employing a model potential and the $B$-spline expansion technique. We obtain the polarizabilities that are in good agreement with the existing theoretical and experimental data.

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Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal $nS$ , $nP$ , and $nD$ Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal $nS$, $nP$, and $nD$ Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.

arXiv:0810.0339Physical Review AMay 8, 2009392 citations

Calculation of Lifetimes of Rydberg States for Na Atom

He Li

Huadong Li-Gong Daxue xuebaoJan 1, 20030 citations

n

examined and should provide guidance for future experimental investigations. The relation of the present approach to other works is discussed.

n{D}_{3/2,\phantom{\rule{0.16em}{0ex}}5/2}

states with large principal quantum numbers up to

n=50

. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.

n{S}_{1/2}

n{P}_{1/2,3/2}

, and

n{D}_{3/2,5/2}

Rydberg states of Rb with principal quantum number

n

up to 140 employing a model potential and the

B

-spline expansion technique. We obtain the polarizabilities that are in good agreement with the existing theoretical and experimental data.

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal

nS

nP

, and

nD

Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.