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

Determination of cross sections for collisionally induced multipole relaxation in alkali-metal atoms from Zeeman fluorescence intensities

R. W. Berends, W. Kedzierski, W. E. Baylis, L. Krause

Published Feb 1, 1989• 3 citations
Publisher

Abstract

The determination of cross sections for the relaxation of atomic multipole moments from the intensities of the components of a resolved Zeeman fluorescence spectrum may be carried out using the density-matrix formalism. However, the spherical-tensor basis is not well adapted to state-selected measurements and can allow a significant propagation of error. We can reduce the error by determining the Q(j,m\ensuremath{\rightarrow}j',m') cross sections directly from the data taken at the lowest pressures. A comparison is given between recent experimental and theoretical relaxation cross sections for collisions of 5 $^{2}P$ potassium atoms with ground-state He, Ne, and Ar atoms.

DOI
10.1103/physreva.39.1526

Related papers

Collisional mJ mixing and multipole relaxation in 4P2 potassium atoms

P. Skalinski, L. Krause

${m}_{J}$ mixing in $4^{2}P_{\frac{1}{2}}$ and $4^{2}P_{\frac{3}{2}}$ potassium atoms as well as atomic multipole relaxation induced in K-K and K-Ar collisions were investigated by methods of atomic fluorescence spectroscopy. K vapor, pure or mixed with Ar, was placed in a kG magnetic field and irradiated with a single Zeeman component of 7665- or 7699-\AA{} resonance radiation, causing the selective excitation of the $^{2}P_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$ or $^{2}P_{\frac{3}{2},\ensuremath{-}\frac{3}{2}}$ substate. Collisions of the excited atoms with ground-state K or Ar atoms caused ${m}_{J}$ mixing which was monitored by analysis of the resulting fluorescent spectrum with a scanning Fabry-Perot interferometer. Intensity measurements on the fluorescent Zeeman components in relation to ground-state atomic densities yielded the following multipole relaxation cross sections ${\ensuremath{\Lambda}}_{J}^{(L)}$: K-K (${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$): ${\ensuremath{\Lambda}}_{\frac{1}{2}}^{(1)}=5.7\ifmmode\pm\else\textpm\fi{}0.9$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(1)}=8.1\ifmmode\pm\else\textpm\fi{}1.4$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(2)}=11.4\ifmmode\pm\else\textpm\fi{}2.0$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(3)}=9.8\ifmmode\pm\else\textpm\fi{}1.5$; K-Ar (${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$): ${\ensuremath{\Lambda}}_{\frac{1}{2}}^{(1)}=65\ifmmode\pm\else\textpm\fi{}10$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(1)}=175\ifmmode\pm\else\textpm\fi{}25$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(2)}=230\ifmmode\pm\else\textpm\fi{}35$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(3)}=190\ifmmode\pm\else\textpm\fi{}30$. The ${Q}_{J}(m\ensuremath{\leftrightarrow}{m}^{\ensuremath{'}})$ cross sections for ${m}_{J}$ mixing were derived from the ${\ensuremath{\Lambda}}_{J}^{(L)}$ as well as the cross sections for multipole decay ${\ensuremath{\sigma}}_{J}^{(L)}={\ensuremath{\Lambda}}_{J}^{(L)}+{\ensuremath{\sigma}}_{J}^{(0)}$. The experimental results are in good agreement with theoretical calculations.

Physical Review A•Dec 1, 1982•12 citations

Multipole relaxation in 52 P potassium atoms by collisions with He, Ne, and Ar

R. W. Berends, W. Kedzierski, L. Krause

Potassium vapor, contained together with a buffer gas in a fluorescence cell located in a 7-T magnetic field, was irradiated with light from a pulsed dye laser producing selective excitation of the ${5}^{2}$${P}_{1/2}$,-1/2 or the ${5}^{2}$${P}_{3/2}$,-3/2 Zeeman substate. Collisions of the excited and polarized atoms and the resulting Zeeman mixing produced a population of the whole Zeeman manifold and resulted in the emission of a fluorescent Zeeman spectrum which was resolved with a Fabry-Perot interferometer and registered with a photomultiplier and multichannel scaler. Measurements of the relative intensities of the fluorescence components yielded the absolute (thermally averaged) multipole-relaxation cross sections and cross sections for Zeeman mixing by collisions with He, Ne, and Ar atoms.

Physical Review A•Jan 1, 1988•5 citations

mJ mixing and multipole relaxation in 6 2 Prubidium atoms induced by He, Ne, and Ar collisions

W. Kedzierski, R. B. Middleton, L. Krause

Rubidium vapor, contained together with a buffer gas in a quartz cell located in a 4.75-T magnetic field, was irradiated with light from a pulsed dye laser producing selective excitation of each 6 $^{2}$P Zeeman substate in turn. Collisions of the excited and polarized atoms with the ground-state He, Ne, or Ar atoms and the resulting Zeeman mixing produced a population of the whole Zeeman manifold and resulted in the emission of a Zeeman fluorescence spectrum that was resolved with a scanning Fabry-P\'erot interferometer and recorded with a photomultiplier and a multichannel scaler. Measurements of the relative intensities of the fluorescence components in relation to the buffer-gas pressures yielded the absolute (thermally averaged) cross sections for Zeeman mixing and cross sections for relaxation of the atomic multipole moments for collisions with He, Ne, and Ar.

Physical Review A•Jan 1, 1991•9 citations

Multipole relaxation in 42P potassium atoms by collisions with N2and H2

R. W. Berends, P. Skalinski, L. Krause

Techniques of atomic fluorescence were used to determine cross sections for relaxation and decay of atomic multipole moments associated with the 4 2 P 1/2 and 4 2 P 3/2 states in potassium. 4 2 P 1/2-1/2 or 2 P 3/2-3/2 Zeeman substates were selectively populated by irradiating potassium vapour, mixed with N 2 or H 2 and located in a kilogauss magnetic field, with monochromatic and circularly polarised radiation. Collisions with the buffer gas molecules caused the population of the other Zeeman substates and the emission of a Zeeman fluorescent spectrum, the sigma components of which were resolved with a piezoelectrically scanned Fabry-Perot interferometer. Measurements of the intensities of the Zeeman fluorescent components yielded cross sections for relaxation and decay of the dipole, quadrupole and octupole moments.

Journal of Physics B Atomic and Molecular Physics•Feb 28, 1984•3 citations

Collisional relaxation in 5(2)P potassium atoms.

R. W. Berends

Collisional excitation transfer and relaxation of K 5$\\sp2$P atoms in collisions with noble gases, as well as the radiative lifetimes of the K 5P, 6P and 7P fine-structure states have been investigated by methods of atomic fluorescence spectroscopy. Potassium vapour was mixed in a cell with a noble gas and selectively excited by pulsed dye-laser radiation to the 5$\\sp2$P$\\sb{1\\over2}$ or the 5$\\sp2$P$\\sb{3\\over 2}$ state in zero magnetic field and to the 5$\\sp2$P$\\sb{{1\\over 2}-{1\\over 2}}$ or the 5$\\sp2$P$\\sb{{3\\over 2}-{3\\over 2}}$ Zeeman substate in a field of 70 kG. Interferometric analysis of the fluorescence emitted from the directly (optically) excited state and that emitted from the collisionally populated states allowed the determination of the fine-structure mixing cross sections for collisions with He, Ne, Ar, Kr and Xe in zero magnetic field. Excitation transfer between Zeeman substates was investigated for collisions between the selectively excited 5P atoms and He, Ne and Ar atoms, allowing the determination of the multipole relaxation (depolarization) cross sections for dipole, quadrupole and octupole decay, as well as the Zeeman and fine-structure mixing cross sections and orientation transfer cross sections. A comparison of theoretical calculations with the experimental data has been made and the rate equations governing multipole relaxation and including effects due to strong fine-structure mixing on the multipole relaxation, have been described in detail. The radiative lifetimes of the individual fine-structure components of the K 5P, 6P and 7P states have been determined experimentally by means of time-resolved laser-induced fluorescence techniques. These data are compared with numerous theoretical calculations and the available experimental values.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1988 .B474. Source: Dissertation Abstracts International, Volume: 49-04, Section: B, page: 1223. Thesis (Ph.D.)--University of Windsor (Canada), 1988.

•Jan 1, 1988•0 citations

Collision-Induced Mixing in the First Excited States of Sodium and Potassium

J. A. Jordan, P. A. Franken

The cross sections for the collision-induced transfer of excitation from the $^{2}P_{\frac{3}{2}}$ level to the $^{2}P_{\frac{1}{2}}$ level of the first excited states of the alkali atoms have been measured for several alkali-noble gas systems. The cross sections were determined with a conventional resonance fluorescence technique in which the radiation from a spectral source was absorbed and re-emitted by an alkali vapor at low pressure (\ensuremath{\sim}${10}^{\ensuremath{-}6}$ Torr), and the scattered light analyzed with a scanning spectrometer. Provision was made for the introduction of various noble gases at controlled pressures into the alkali vapor. The determined cross sections are (in units of ${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$): Na-He, 41.1\ifmmode\pm\else\textpm\fi{}2.9; Na-Ne, 36.1\ifmmode\pm\else\textpm\fi{}2.5; Na-Ar, 64.6\ifmmode\pm\else\textpm\fi{}5.2; Na-Kr, 68.2\ifmmode\pm\else\textpm\fi{}5.5; Na-Xe, 61.8\ifmmode\pm\else\textpm\fi{}4.9; K-He, 52.8\ifmmode\pm\else\textpm\fi{}5.8; K-Ne, 14.0\ifmmode\pm\else\textpm\fi{}1.2; K-Ar, 34.0\ifmmode\pm\else\textpm\fi{}3.1. The quoted errors are estimated 70% confidence intervals. The measurements are compared with other experimental results and with various estimated cross sections.

Physical Review•Feb 4, 1966•39 citations
The determination of cross sections for the relaxation of atomic multipole moments from the intensities of the components of a resolved Zeeman fluorescence spectrum may be carried out using the density-matrix formalism. However, the spherical-tensor basis is not well adapted to state-selected measurements and can allow a significant propagation of error. We can reduce the error by determining the Q(j,m\ensuremath{\rightarrow}j',m') cross sections directly from the data taken at the lowest pressures. A comparison is given between recent experimental and theoretical relaxation cross sections for collisions of 5 2P^{2}P2P potassium atoms with ground-state He, Ne, and Ar atoms.
mJ{m}_{J}mJ​ mixing in 42P124^{2}P_{\frac{1}{2}}42P21​​ and 42P324^{2}P_{\frac{3}{2}}42P23​​ potassium atoms as well as atomic multipole relaxation induced in K-K and K-Ar collisions were investigated by methods of atomic fluorescence spectroscopy. K vapor, pure or mixed with Ar, was placed in a kG magnetic field and irradiated with a single Zeeman component of 7665- or 7699-\AA{} resonance radiation, causing the selective excitation of the $^{2}P_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$ or $^{2}P_{\frac{3}{2},\ensuremath{-}\frac{3}{2}}$ substate. Collisions of the excited atoms with ground-state K or Ar atoms caused mJ{m}_{J}mJ​ mixing which was monitored by analysis of the resulting fluorescent spectrum with a scanning Fabry-Perot interferometer. Intensity measurements on the fluorescent Zeeman components in relation to ground-state atomic densities yielded the following multipole relaxation cross sections ${\ensuremath{\Lambda}}_{J}^{(L)}$: K-K (${10}^{\ensuremath{-}12}$ cm2{\mathrm{cm}}^{2}cm2): ${\ensuremath{\Lambda}}_{\frac{1}{2}}^{(1)}=5.7\ifmmode\pm\else\textpm\fi{}0.9$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(1)}=8.1\ifmmode\pm\else\textpm\fi{}1.4$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(2)}=11.4\ifmmode\pm\else\textpm\fi{}2.0$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(3)}=9.8\ifmmode\pm\else\textpm\fi{}1.5$; K-Ar (${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2): ${\ensuremath{\Lambda}}_{\frac{1}{2}}^{(1)}=65\ifmmode\pm\else\textpm\fi{}10$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(1)}=175\ifmmode\pm\else\textpm\fi{}25$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(2)}=230\ifmmode\pm\else\textpm\fi{}35$, ${\ensuremath{\Lambda}}_{\frac{3}{2}}^{(3)}=190\ifmmode\pm\else\textpm\fi{}30$. The ${Q}_{J}(m\ensuremath{\leftrightarrow}{m}^{\ensuremath{'}})$ cross sections for mJ{m}_{J}mJ​ mixing were derived from the ${\ensuremath{\Lambda}}_{J}^{(L)}$ as well as the cross sections for multipole decay ${\ensuremath{\sigma}}_{J}^{(L)}={\ensuremath{\Lambda}}_{J}^{(L)}+{\ensuremath{\sigma}}_{J}^{(0)}$. The experimental results are in good agreement with theoretical calculations.
Potassium vapor, contained together with a buffer gas in a fluorescence cell located in a 7-T magnetic field, was irradiated with light from a pulsed dye laser producing selective excitation of the 52{5}^{2}52P1/2{P}_{1/2}P1/2​,-1/2 or the 52{5}^{2}52P3/2{P}_{3/2}P3/2​,-3/2 Zeeman substate. Collisions of the excited and polarized atoms and the resulting Zeeman mixing produced a population of the whole Zeeman manifold and resulted in the emission of a fluorescent Zeeman spectrum which was resolved with a Fabry-Perot interferometer and registered with a photomultiplier and multichannel scaler. Measurements of the relative intensities of the fluorescence components yielded the absolute (thermally averaged) multipole-relaxation cross sections and cross sections for Zeeman mixing by collisions with He, Ne, and Ar atoms.
Rubidium vapor, contained together with a buffer gas in a quartz cell located in a 4.75-T magnetic field, was irradiated with light from a pulsed dye laser producing selective excitation of each 6 2^{2}2P Zeeman substate in turn. Collisions of the excited and polarized atoms with the ground-state He, Ne, or Ar atoms and the resulting Zeeman mixing produced a population of the whole Zeeman manifold and resulted in the emission of a Zeeman fluorescence spectrum that was resolved with a scanning Fabry-P\'erot interferometer and recorded with a photomultiplier and a multichannel scaler. Measurements of the relative intensities of the fluorescence components in relation to the buffer-gas pressures yielded the absolute (thermally averaged) cross sections for Zeeman mixing and cross sections for relaxation of the atomic multipole moments for collisions with He, Ne, and Ar.
Techniques of atomic fluorescence were used to determine cross sections for relaxation and decay of atomic multipole moments associated with the 4 2 P 1/2 and 4 2 P 3/2 states in potassium. 4 2 P 1/2-1/2 or 2 P 3/2-3/2 Zeeman substates were selectively populated by irradiating potassium vapour, mixed with N 2 or H 2 and located in a kilogauss magnetic field, with monochromatic and circularly polarised radiation. Collisions with the buffer gas molecules caused the population of the other Zeeman substates and the emission of a Zeeman fluorescent spectrum, the sigma components of which were resolved with a piezoelectrically scanned Fabry-Perot interferometer. Measurements of the intensities of the Zeeman fluorescent components yielded cross sections for relaxation and decay of the dipole, quadrupole and octupole moments.
Collisional excitation transfer and relaxation of K 5sp2\\sp2sp2P atoms in collisions with noble gases, as well as the radiative lifetimes of the K 5P, 6P and 7P fine-structure states have been investigated by methods of atomic fluorescence spectroscopy. Potassium vapour was mixed in a cell with a noble gas and selectively excited by pulsed dye-laser radiation to the 5sp2\\sp2sp2Psb1over2\\sb{1\\over2}sb1over2 or the 5sp2\\sp2sp2Psb3over2\\sb{3\\over 2}sb3over2 state in zero magnetic field and to the 5sp2\\sp2sp2Psb1over2−1over2\\sb{{1\\over 2}-{1\\over 2}}sb1over2−1over2 or the 5sp2\\sp2sp2Psb3over2−3over2\\sb{{3\\over 2}-{3\\over 2}}sb3over2−3over2 Zeeman substate in a field of 70 kG. Interferometric analysis of the fluorescence emitted from the directly (optically) excited state and that emitted from the collisionally populated states allowed the determination of the fine-structure mixing cross sections for collisions with He, Ne, Ar, Kr and Xe in zero magnetic field. Excitation transfer between Zeeman substates was investigated for collisions between the selectively excited 5P atoms and He, Ne and Ar atoms, allowing the determination of the multipole relaxation (depolarization) cross sections for dipole, quadrupole and octupole decay, as well as the Zeeman and fine-structure mixing cross sections and orientation transfer cross sections. A comparison of theoretical calculations with the experimental data has been made and the rate equations governing multipole relaxation and including effects due to strong fine-structure mixing on the multipole relaxation, have been described in detail. The radiative lifetimes of the individual fine-structure components of the K 5P, 6P and 7P states have been determined experimentally by means of time-resolved laser-induced fluorescence techniques. These data are compared with numerous theoretical calculations and the available experimental values.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1988 .B474. Source: Dissertation Abstracts International, Volume: 49-04, Section: B, page: 1223. Thesis (Ph.D.)--University of Windsor (Canada), 1988.
The cross sections for the collision-induced transfer of excitation from the 2P32^{2}P_{\frac{3}{2}}2P23​​ level to the 2P12^{2}P_{\frac{1}{2}}2P21​​ level of the first excited states of the alkali atoms have been measured for several alkali-noble gas systems. The cross sections were determined with a conventional resonance fluorescence technique in which the radiation from a spectral source was absorbed and re-emitted by an alkali vapor at low pressure (\ensuremath{\sim}${10}^{\ensuremath{-}6}$ Torr), and the scattered light analyzed with a scanning spectrometer. Provision was made for the introduction of various noble gases at controlled pressures into the alkali vapor. The determined cross sections are (in units of ${10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2): Na-He, 41.1\ifmmode\pm\else\textpm\fi{}2.9; Na-Ne, 36.1\ifmmode\pm\else\textpm\fi{}2.5; Na-Ar, 64.6\ifmmode\pm\else\textpm\fi{}5.2; Na-Kr, 68.2\ifmmode\pm\else\textpm\fi{}5.5; Na-Xe, 61.8\ifmmode\pm\else\textpm\fi{}4.9; K-He, 52.8\ifmmode\pm\else\textpm\fi{}5.8; K-Ne, 14.0\ifmmode\pm\else\textpm\fi{}1.2; K-Ar, 34.0\ifmmode\pm\else\textpm\fi{}3.1. The quoted errors are estimated 70% confidence intervals. The measurements are compared with other experimental results and with various estimated cross sections.