Physical Review A

Approximate scaling formula for collisional angular-momentum mixing of Rydberg atoms

A. P. Hickman

Published Jan 1, 1981• 50 citations

Abstract

An approximate scaling formula has been determined that permits the rapid estimation of cross sections for angular-momentum-changing collisions of Rydberg atoms with a variety of targets, using information about low-energy-electron scattering from the target. The formula is obtained by fitting the results of coupled-channel and Born-approximation calculations to functions of reduced parameters. Application to $\mathrm{Na}(\mathrm{nd})$ + He, Ne, Ar, ${\mathrm{N}}_{2}$, C${\mathrm{H}}_{4}$, ${\mathrm{C}}_{3}$${\mathrm{H}}_{8}$; $\mathrm{Rb}(\mathrm{nf})$ + He, Ar, Xe; and $\mathrm{Xe}(\mathrm{nf})$ + C${\mathrm{O}}_{2}$, suggests that the accuracy is about a factor of 2.

DOI: 10.1103/physreva.23.87

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Relation between low-energy-electron scattering and l -changing collisions of Rydberg atoms

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Physical Review AOct 1, 197865 citations

Collisional angular-momentum mixing of Rydberg states of Na by He, Ne, and Ar

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Physical Review A

Approximate scaling formula for collisional angular-momentum mixing of Rydberg atoms

A. P. Hickman

Published Jan 1, 1981• 50 citations

Publisher

Abstract

\mathrm{Na}(\mathrm{nd})

+ He, Ne, Ar,

{\mathrm{N}}_{2}

, C

{\mathrm{H}}_{4}

{\mathrm{C}}_{3}$${\mathrm{H}}_{8}

;

\mathrm{Rb}(\mathrm{nf})

+ He, Ar, Xe; and

\mathrm{Xe}(\mathrm{nf})

+ C

{\mathrm{O}}_{2}

, suggests that the accuracy is about a factor of 2.

DOI: 10.1103/physreva.23.87

Related papers

Relation between low-energy-electron scattering and l -changing collisions of Rydberg atoms

A. P. Hickman

Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the $s$ -wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the $l$ -mixing cross section at a particular $n$ is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on $n$ . The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of $\mathrm{Na}(\mathrm{nd})+\mathrm{He}$ , Ne, and Ar are treated as specific examples.Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the $s$-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the $l$-mixing cross section at a particular $n$ is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on $n$. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of $\mathrm{Na}(\mathrm{nd})+\mathrm{He}$, Ne, and Ar are treated as specific examples.

Physical Review AMar 1, 197955 citations

Theory of angular momentum mixing in Rydberg-atom-rare-gas collisions

A. P. Hickman

A coupled-channel approach based on the Arthurs and Dalgarno formalism is presented to describe the scattering of a Rydberg atom and a rare-gas atom. The method permits the calculation of cross sections for changes in the electronic orbital angular momentum of the Rydberg atom. The theory explicitly relates the scattering behavior of the Rydberg state to the electron-rare-gas scattering length. Preliminary results for ${\mathrm{Na}}^{*}(\mathrm{nd})$ +He and ${\mathrm{Na}}^{*}(\mathrm{nf})$ +He are in good agreement with experiment.A coupled-channel approach based on the Arthurs and Dalgarno formalism is presented to describe the scattering of a Rydberg atom and a rare-gas atom. The method permits the calculation of cross sections for changes in the electronic orbital angular momentum of the Rydberg atom. The theory explicitly relates the scattering behavior of the Rydberg state to the electron-rare-gas scattering length. Preliminary results for ${\mathrm{Na}}^{*}(\mathrm{nd})$+He and ${\mathrm{Na}}^{*}(\mathrm{nf})$+He are in good agreement with experiment.

Physical Review AOct 1, 197865 citations

Collisional angular-momentum mixing of Rydberg states of Na by He, Ne, and Ar

Thomas F. Gallagher, S. A. Edelstein, R. M. Hill

The collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na $d$ states with the $l>2$ states of the same $n$ has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same $n$ . Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each $n$ and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for $l$ mixing by each of the gases is found to increase sharply from $n=5 \mathrm{to} 10$ and decrease above $n=10$ . The magnitudes of the $l$ -mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.The collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na $d$ states with the $l>2$ states of the same $n$ has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same $n$. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each $n$ and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for $l$ mixing by each of the gases is found to increase sharply from $n=5 \mathrm{to} 10$ and decrease above $n=10$. The magnitudes of the $l$-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.

Physical Review AMay 1, 1977144 citations

Collision Cross Sections for Angular Momentum Mixing of High Rydberg States of Na by He, Ar, and Ne

Thomas F. Gallagher, S. A. Edelstein, Robert M. Hill

peacJan 1, 19750 citations

Quasielastic state-changing collisions of high-Rydberg atoms with rare-gas atoms

Kunitaka Sasano, Yutaka S. Sato, Michio Matsuzawa

For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) $l$ -changing and (ii) $n$ -and $l$ -changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and $V$ is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the $n$ - and $l$ -changing collision of ${\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}$ . This is in contrast with the uniform distribution over the final angular-momentum states for the usual $l$ -changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) $l$-changing and (ii) $n$-and $l$-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and $V$ is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the $n$- and $l$-changing collision of ${\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}$. This is in contrast with the uniform distribution over the final angular-momentum states for the usual $l$-changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.

Physical Review AMay 1, 198317 citations

Energy and angular momentum transfer to Rydberg atoms in collisions with electrons

M. I. Syrkin

The analytical formulae for the cross-sections with arbitrary change {triangle}n=n{prime}-n and {triangle}1=1{prime}-1 has been obtained in the Born limit. No spin exchange {triangle}S=0: although the total cross-sections n->n are dominated by dipole transitions, the non-dipole transitions {triangle}1>1 can contribute up to 30-50%ER for large {triangle}n>>1. Intercombination transitions {triangle}S=1: the large transfer transitions {triangle}1>>1 are of major importance, as opposed to the previous case.The analytical formulae for the cross-sections with arbitrary change {triangle}n=n{prime}-n and {triangle}1=1{prime}-1 has been obtained in the Born limit. No spin exchange {triangle}S=0: although the total cross-sections n->n are dominated by dipole transitions, the non-dipole transitions {triangle}1>1 can contribute up to 30-50%ER for large {triangle}n>>1. Intercombination transitions {triangle}S=1: the large transfer transitions {triangle}1>>1 are of major importance, as opposed to the previous case.

Bulletin of the American Physical SocietyMay 1, 19930 citations

\mathrm{Na}(\mathrm{nd})

+ He, Ne, Ar,

{\mathrm{N}}_{2}

, C

{\mathrm{H}}_{4}

{\mathrm{C}}_{3}$${\mathrm{H}}_{8}

;

\mathrm{Rb}(\mathrm{nf})

+ He, Ar, Xe; and

\mathrm{Xe}(\mathrm{nf})

+ C

{\mathrm{O}}_{2}

, suggests that the accuracy is about a factor of 2.

s

-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the

l

-mixing cross section at a particular

n

is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on

n

. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of

\mathrm{Na}(\mathrm{nd})+\mathrm{He}

, Ne, and Ar are treated as specific examples.

{\mathrm{Na}}^{*}(\mathrm{nd})

+He and

{\mathrm{Na}}^{*}(\mathrm{nf})

+He are in good agreement with experiment.

The collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na

d

states with the

l>2

states of the same

n

has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same

n

. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each

n

and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for

l

mixing by each of the gases is found to increase sharply from

n=5 \mathrm{to} 10

and decrease above

n=10

. The magnitudes of the

l

-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.

For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i)

l

-changing and (ii)

n

-and

l

-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and

V

is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the

n

- and

l

-changing collision of

{\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}

. This is in contrast with the uniform distribution over the final angular-momentum states for the usual

l

-changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.