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

Second-Order Nonradiative Processes in Ca F2 : Sm2+

R. Orbach

Published Jan 6, 1964• 17 citations
Publisher

Abstract

It was first shown by Axe and Sorokin that nonradiative decay of the terminal optical maser level ($^{7}F_{1}$) Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ is forbidden to first order even though many phonon states are available with the proper energy for the transition. At first sight this would indicate the $^{7}F_{1}$ level to be metastable. It is shown that a second-order two-phonon emission transition can alleviate this bottleneck, and the decay process rate is computed. This process, involving virtual transitions to a higher level ($^{7}F_{2}$), is shown to be very effective and to lead to a nonradiative lifetime of \ensuremath{\sim}${10}^{\ensuremath{-}6}$ sec, in accord with the necessary conditions for the existence of optical maser action in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$.

DOI
10.1103/physrev.133.a34

Related papers

Spectroscopy and Optical Maser Action in Sr F2 : Sm2+

P. P. Sorokin, M. J. Stevenson, J. R. Lankard +1 more

A crystal of Sr${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ was operated as a pulsed optical maser at temperatures close to 4.2\ifmmode^\circ\else\textdegree\fi{}K. The 6969 \AA{} output corresponds to the wavelength of an exceedingly sharp line ($\ensuremath{\Delta}\ensuremath{\nu}<0.6$ ${\mathrm{cm}}^{\ensuremath{-}1}$) in which almost all of the low-temperature fluorescence is concentrated. In contrast to what prevails in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{+2}$ masers, the output is characterized by strong relaxation oscillations. This may be explained by the large difference in the fluorescent lifetimes in the two systems. While in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ the value of $\ensuremath{\tau}$ is approximately 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec, in Sr${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ it has a value of 15 msec. The reason for the large difference in $\ensuremath{\tau}$ values, in turn, depends upon the relative proximity of the long-wavelength edge of the red band to the position of the metastable $^{5}D_{0}$ level from which fluorescence occurs. Absorption measurements taken at helium temperatures on Sr${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ show that the lowest vibrational level of the lowest lying $4f\ensuremath{-}5d$ band lies \ensuremath{\sim}600 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the position of the $^{5}D_{0}$ level while in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ there is near coincidence of the corresponding levels and consequently strong configurational mixing. Crystals of Sr${\mathrm{Cl}}_{2}$: ${\mathrm{Sm}}^{2+}$ were also studied in this regard and display an expected close similarity in spectral characteristics to Sr${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$. The vibrational structure on the $4f\ensuremath{-}5d$ bands is much more pronounced, however, than in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$ and Sr${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{2+}$, indicating weaker coupling to the lattice in the excited $5d$ state. A tentative interpretation for the splitting of the red band seen in the absorption spectra of ${\mathrm{Sm}}^{2+}$ ions is given.

Physical Review•Jul 15, 1962•66 citations

Fluorescence and Optical Maser Effects in Ca F2 : Sm++

W. Kaiser, C. G. B. Garrett, Darwin L. Wood

Measurements are reported of absorption, emission, and activation spectra in Ca${\mathrm{F}}_{2}$: ${\mathrm{Sm}}^{++}$, and also of fluorescence lifetime. A revised level scheme is proposed. Observations of optical maser effects were made at liquid hydrogen and liquid helium temperatures over a wide range of pumping intensities. For illumination in the 6400-A band, the threshold intensity of illumination was about 20 w ${\mathrm{cm}}^{\ensuremath{-}2}$. Observations are reported of the dependence of the intensity of the maser beam on the pumping intensity. Photographic observations, made both with or without a Fabry-Perot etalon, show that on one particular sample five distinct frequencies were present in the maser signal, and that the number of modes excited was of the order of 1000.

Physical Review•Aug 1, 1961•162 citations

Excitation, Relaxation, and Continuous Maser Action in the 2.613-Micron Transition of Ca F2 : U3+

Gary D. Boyd, R. J. Collins, Sergio P. S. Porto +2 more

This letter describes an investigation of the 2.613 micron fluorescence of trivalent uranium in CaF2 (CaF2:U3+) and the operation of a continuous solid-state maser using this transition.

Physical Review Letters•Apr 1, 1962•80 citations

Laser and Two-Photon Processes

David A. Kleinman

The possibility of observing two-photon processes using the intense beam of the ruby optical maser is considered theoretically for two general types of experiment. The essential approximation in the theory is the hypothesis that excited states exist which connect both the initial and final states by electric dipole transitions having a total oscillator strength $f\ensuremath{\sim}1$. Simple formulas are obtained for the two-photon absorption which do not depend on the details of the electronic structure. Recent experiments on the Ca${\mathrm{F}}_{2}$: ${\mathrm{Eu}}^{++}$ system are in quantitative agreement with the predictions of the theory.

Physical Review•Jan 1, 1962•102 citations

Evidence of Phonon Annihilation Processes in the Excited States of BaClF: Sm2+

A. S. M. Mahbub'ul Alam, Baldassare Di Bartolo

We have found direct evidence of upward, phonon annihilation, processes in the decay patterns of two metastable states $^{5}D_{0}(14542 {\mathrm{cm}}^{\ensuremath{-}1})$ and $^{5}D_{1}(15878 {\mathrm{cm}}^{\ensuremath{-}1})$ of BaClF: ${\mathrm{Sm}}^{2+}$. Under pulse excitation, the decay curve of the $^{5}D_{1}$ fluorescence includes a long tail, with a time constant equal to the lifetime of $^{5}D_{0}$, which appears at \ensuremath{\sim}280\ifmmode^\circ\else\textdegree\fi{}K and grows in intensity with temperature; finally at \ensuremath{\sim}400\ifmmode^\circ\else\textdegree\fi{}K both states decay with the same time constant. This finding is consistent with the thermal dependence of the ratio of the intensities of the $^{5}D_{1}$ to the $^{5}D_{0}$ flourescence.

Physical Review Letters•Oct 30, 1967•16 citations

Lifetime, collisional-quenching, andj-mixing measurements of the metastable 3Dlevels of Ca+

Martina Knoop, M. Vedel, F. Vedel

The metastable ${3}^{2}$${\mathit{D}}_{3/2,5/2}$ doublet of ${\mathrm{Ca}}^{+}$ ions stored in a Paul trap was investigated in the presence of different neutral gases, in the pressure range ${10}^{\mathrm{\ensuremath{-}}9}$--${10}^{\mathrm{\ensuremath{-}}6}$ mbar. The natural lifetimes were determined to be \ensuremath{\tau}(${\mathit{D}}_{3/2}$)=1111\ifmmode\pm\else\textpm\fi{}46 ms and \ensuremath{\tau}(${\mathit{D}}_{5/2}$)=994\ifmmode\pm\else\textpm\fi{}38 ms, which agree very well with previous experiments. The estimation of the quenching rates of ${\mathrm{Ca}}^{+}$-He [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}$=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], ${\mathrm{Ca}}^{+}$-Ne [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{}\mathrm{Ne}}$=(0.9\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], and ${\mathrm{Ca}}^{+}$-${\mathrm{N}}_{2}$ [${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{N}}_{2}}$=(1.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] was carried out for collisions in the energy range 0.3--1.3 eV. In addition, rate constants for the mixing of the fine-structure states were measured in the presence of helium and nitrogen for the j=3/2\ensuremath{\rightarrow}j=5/2 case [${\ensuremath{\gamma}}_{35}$(He)=(2.24\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{35}$(${\mathrm{N}}_{2}$)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] and for the j=5/2\ensuremath{\rightarrow}j=3/2 case [${\ensuremath{\gamma}}_{53}$(He)=(1.2\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{53}$(${\mathrm{N}}_{2}$)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.

Physical Review A•Nov 1, 1995•50 citations
It was first shown by Axe and Sorokin that nonradiative decay of the terminal optical maser level (7F1^{7}F_{1}7F1​) CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ is forbidden to first order even though many phonon states are available with the proper energy for the transition. At first sight this would indicate the 7F1^{7}F_{1}7F1​ level to be metastable. It is shown that a second-order two-phonon emission transition can alleviate this bottleneck, and the decay process rate is computed. This process, involving virtual transitions to a higher level (7F2^{7}F_{2}7F2​), is shown to be very effective and to lead to a nonradiative lifetime of \ensuremath{\sim}10\ensuremath−6{10}^{\ensuremath{-}6}10\ensuremath−6 sec, in accord with the necessary conditions for the existence of optical maser action in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+.
A crystal of SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ was operated as a pulsed optical maser at temperatures close to 4.2\ifmmode^\circ\else\textdegree\fi{}K. The 6969 \AA{} output corresponds to the wavelength of an exceedingly sharp line ($\ensuremath{\Delta}\ensuremath{\nu}<0.6$ ${\mathrm{cm}}^{\ensuremath{-}1}$) in which almost all of the low-temperature fluorescence is concentrated. In contrast to what prevails in CaF2{\mathrm{F}}_{2}F2​: Sm+2{\mathrm{Sm}}^{+2}Sm+2 masers, the output is characterized by strong relaxation oscillations. This may be explained by the large difference in the fluorescent lifetimes in the two systems. While in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ the value of $\ensuremath{\tau}$ is approximately 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec, in SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ it has a value of 15 msec. The reason for the large difference in $\ensuremath{\tau}$ values, in turn, depends upon the relative proximity of the long-wavelength edge of the red band to the position of the metastable 5D0^{5}D_{0}5D0​ level from which fluorescence occurs. Absorption measurements taken at helium temperatures on SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ show that the lowest vibrational level of the lowest lying $4f\ensuremath{-}5d$ band lies \ensuremath{\sim}600 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the position of the 5D0^{5}D_{0}5D0​ level while in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ there is near coincidence of the corresponding levels and consequently strong configurational mixing. Crystals of SrCl2{\mathrm{Cl}}_{2}Cl2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ were also studied in this regard and display an expected close similarity in spectral characteristics to SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+. The vibrational structure on the $4f\ensuremath{-}5d$ bands is much more pronounced, however, than in CaF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+ and SrF2{\mathrm{F}}_{2}F2​: Sm2+{\mathrm{Sm}}^{2+}Sm2+, indicating weaker coupling to the lattice in the excited 5d5d5d state. A tentative interpretation for the splitting of the red band seen in the absorption spectra of Sm2+{\mathrm{Sm}}^{2+}Sm2+ ions is given.
Measurements are reported of absorption, emission, and activation spectra in CaF2{\mathrm{F}}_{2}F2​: Sm++{\mathrm{Sm}}^{++}Sm++, and also of fluorescence lifetime. A revised level scheme is proposed. Observations of optical maser effects were made at liquid hydrogen and liquid helium temperatures over a wide range of pumping intensities. For illumination in the 6400-A band, the threshold intensity of illumination was about 20 w ${\mathrm{cm}}^{\ensuremath{-}2}$. Observations are reported of the dependence of the intensity of the maser beam on the pumping intensity. Photographic observations, made both with or without a Fabry-Perot etalon, show that on one particular sample five distinct frequencies were present in the maser signal, and that the number of modes excited was of the order of 1000.
The possibility of observing two-photon processes using the intense beam of the ruby optical maser is considered theoretically for two general types of experiment. The essential approximation in the theory is the hypothesis that excited states exist which connect both the initial and final states by electric dipole transitions having a total oscillator strength $f\ensuremath{\sim}1$. Simple formulas are obtained for the two-photon absorption which do not depend on the details of the electronic structure. Recent experiments on the CaF2{\mathrm{F}}_{2}F2​: Eu++{\mathrm{Eu}}^{++}Eu++ system are in quantitative agreement with the predictions of the theory.
We have found direct evidence of upward, phonon annihilation, processes in the decay patterns of two metastable states $^{5}D_{0}(14542 {\mathrm{cm}}^{\ensuremath{-}1})$ and $^{5}D_{1}(15878 {\mathrm{cm}}^{\ensuremath{-}1})$ of BaClF: Sm2+{\mathrm{Sm}}^{2+}Sm2+. Under pulse excitation, the decay curve of the 5D1^{5}D_{1}5D1​ fluorescence includes a long tail, with a time constant equal to the lifetime of 5D0^{5}D_{0}5D0​, which appears at \ensuremath{\sim}280\ifmmode^\circ\else\textdegree\fi{}K and grows in intensity with temperature; finally at \ensuremath{\sim}400\ifmmode^\circ\else\textdegree\fi{}K both states decay with the same time constant. This finding is consistent with the thermal dependence of the ratio of the intensities of the 5D1^{5}D_{1}5D1​ to the 5D0^{5}D_{0}5D0​ flourescence.
The metastable 32{3}^{2}32D3/2,5/2{\mathit{D}}_{3/2,5/2}D3/2,5/2​ doublet of Ca+{\mathrm{Ca}}^{+}Ca+ ions stored in a Paul trap was investigated in the presence of different neutral gases, in the pressure range ${10}^{\mathrm{\ensuremath{-}}9}$--${10}^{\mathrm{\ensuremath{-}}6}$ mbar. The natural lifetimes were determined to be \ensuremath{\tau}(D3/2{\mathit{D}}_{3/2}D3/2​)=1111\ifmmode\pm\else\textpm\fi{}46 ms and \ensuremath{\tau}(D5/2{\mathit{D}}_{5/2}D5/2​)=994\ifmmode\pm\else\textpm\fi{}38 ms, which agree very well with previous experiments. The estimation of the quenching rates of Ca+{\mathrm{Ca}}^{+}Ca+-He [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}$=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], Ca+{\mathrm{Ca}}^{+}Ca+-Ne [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{}\mathrm{Ne}}$=(0.9\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], and Ca+{\mathrm{Ca}}^{+}Ca+-N2{\mathrm{N}}_{2}N2​ [${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{N}}_{2}}$=(1.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] was carried out for collisions in the energy range 0.3--1.3 eV. In addition, rate constants for the mixing of the fine-structure states were measured in the presence of helium and nitrogen for the j=3/2\ensuremath{\rightarrow}j=5/2 case [${\ensuremath{\gamma}}_{35}$(He)=(2.24\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{35}$(N2{\mathrm{N}}_{2}N2​)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] and for the j=5/2\ensuremath{\rightarrow}j=3/2 case [${\ensuremath{\gamma}}_{53}$(He)=(1.2\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{53}$(N2{\mathrm{N}}_{2}N2​)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.