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Physical Review A

Effects of alignment on strontium energy pooling collisions

Jonathan Andrew Neuman, Alan Gallagher

Published Mar 1, 1998• 2 citations
Publisher

Abstract

The dependence of energy pooling cross sections on the alignment of atomic angular momentum with respect to the collision axis is investigated. In a vapor cell, excitation with counter-propagating polarized laser beams that define the collision axis prepares aligned strontium atoms in the $5s5p{}^{3}{P}_{1}$ level. Excited-state energy pooling collision products from the endothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s6s{}^{1}{S}_{0}{+5s}^{2}{}^{1}{S}_{0}$ reaction and the exothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s5p{}^{1}{P}_{1}{+5s}^{2}{}^{1}{S}_{0}$ reaction are studied. Alignment effects are studied as a function of collision energy, using pulsed laser excitation followed by delayed fluorescence detection to lower the transverse collision velocity and laser detuning to vary the collision velocity in the laser-beam direction. The rate coefficient for energy transfer to the $6{}^{1}{S}_{0}$ state is enhanced by $38\ifmmode\pm\else\textpm\fi{}13%$ when the ${M}_{J}$ alignment of the collision partners is perpendicular to the collision axis and parallel to each other compared to when there is no alignment of the collision partners. No alignment dependence is observed for energy transfer to the $5{}^{1}{P}_{1}$ state. This experiment offers the unique capability of simultaneously and independently controlling collision velocity and angular momentum alignment.

DOI
10.1103/physreva.57.2231

Related papers

Velocity dependence of energy pooling collisions in strontium

Jonathan Andrew Neuman, J. Cooper, Alan C. Gallagher

The threshold behavior of the cross section of an endothermic energy pooling reaction is investigated. In a vapor cell experiment, pulsed excitation followed by delayed fluorescence detection narrows the transverse velocity distribution of colliding pairs of laser-excited strontium atoms in the ${5s5p}^{3}{P}_{1}$ level, and laser detuning establishes the collision velocity in the direction of counterpropagating laser beams. A probe laser detects the excited-state collision product of the endothermic ${5s5p}^{3}{P}_{1}{+5s5p}^{3}{P}_{1}\ensuremath{\rightarrow}{5s6s}^{1}{S}_{0}{+5s}^{21}{S}_{0}$ reaction. The cross section rises steeply at threshold and is nearly flat for 1.2--2 times the threshold energy. This behavior can be partly explained by the shape of the molecular potential curve of the collisionally produced state. From the measured $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{3}{\mathrm{}\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ thermally averaged rate coefficient, the above-threshold cross section is found to be approximately $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}.$ The thermally averaged rate coefficient for the highly exothermic energy pooling reaction ${5s5p}^{3}{P}_{1}{+5s5p}^{3}{P}_{1}\ensuremath{\rightarrow}{5s5p}^{1}{P}_{1}{+5s}^{21}{S}_{0}$ is also reported and measured to be $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{\mathrm{cm}}^{3}{\mathrm{}\mathrm{s}}^{\mathrm{\ensuremath{-}}1}.$ The cross section for this exothermic reaction is found to be nearly independent of collision velocity.

Physical Review A•Jul 1, 1997•5 citations

Initial- and final-state alignment and orientation effects in Ca energy pooling

Harold Parks, Stephen R. Leone

An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial $\mathrm{Ca}(4s4p{}^{3}{P}_{1})$ state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.

Physical Review A•Oct 1, 1999•5 citations

Experimental investigation of the initial-state alignment dependence in the energy pooling process: Ca(4s4p3P1)+Ca(4s4p3P1)→Ca(4s4p1P1)+Ca(4s2)

Harold Parks, Eileen M. Spain, John E. Smedley +1 more

A pulsed laser investigation is performed to study the detailed effects of electronic angular-momentum alignment on the cross section for the energy-transfer process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ A uniform magnetic field imposed by a set of Helmholtz coils is used to systematically precess the initial state orbitals with a well-defined period, allowing different alignments to be sampled at different time delays after the pulsed laser excites and aligns the $\mathrm{Ca}(4s4p{}^{3}{P}_{1})$ states. The polarization effects in this collision process are striking. For example, the cross section for two atoms both in the ${m}_{j}=0$ magnetic substrate is 13 times larger than the cross section for two atoms that are both in the ${m}_{j}=1$ (or -1) substrate, where the quantization axis is taken to be along the relative velocity vector of the collision. The initial m-sublevel dependence of this three-vector correlation process can be completely described with eight fundamental parameters, five of which are accurately obtained. In addition, the coarse energy dependence of these parameters is deduced.

Physical Review A•Sep 1, 1998•7 citations

Alignment and Orientation Effects in Sr Energy Pooling

Harold Parks, Stephen R. Leone

Alignment and orientation effects in the energy pooling process, Sr(5s5p 3 P 1 ) + Sr(5s5p 3 P 1 ) → Sr(5s5p 1 P 1 ) + Sr(5s 2 1 S 0 ), are studied in a single atomic beam. The Sr atoms are prepared in an aligned initial state with a polarized laser, and alignment information is extracted by observing the fluorescence from the final Sr(5s5p 1 P 1 ) state as the atoms precess in an applied magnetic field. This allows the dependence of the total energy pooling cross section (integrated over the final state alignment) on the initial state alignment to be almost completely described. A prominent alignment effect is observed. If m j represents the component of total electronic angular momentum of a Sr(5s5p 3 P 1 ) atom along the relative velocity vector of the collision, then the total energy transfer cross section for a particular initial state alignment can be expressed as a sum of the so-called fundamental cross sections, σ m 1 m 2 and σ m 1 m 2; m 1 ‘ m 2 ‘, that describe collisions between the various m j states. Here σ m 1 m 2 represents the cross section for energy transfer when an atom in state m 1 collides with an atom in state m 2 . The cross section σ m 1 m 2; m 1 ‘ m 2 ‘ represents the contribution to the total cross section from interference when the colliding system is in a superposition of the state m 1 colliding with m 2 and the state m 1 ‘ colliding with m 2 ‘. It is found that the cross sections σ 1-1, σ 00, and σ 10 as well as the interference terms Re( σ 00;1-1 ) and σ 01;10 have relatively large values while σ 11 and σ 1-1;-11 are small. Coupled with future theoretical work, these results may provide new insights into the dynamics of the curve crossings that lead to energy transfer.

The Journal of Physical Chemistry A•Aug 21, 1999•1 citation

Collisional energy transfer between excited Sr atoms

H. G. C. Werij, Martin A. Harris, J. Cooper +2 more

The following energy-transfer reactions have been observed in a Sr vapor following pulsed excitation of the 5 $^{1}$${\mathit{P}}_{1}$ state: ${\mathrm{Sr}}^{\mathrm{*}}$(5 $^{1}$${\mathit{P}}_{1}$)+${\mathrm{Sr}}^{\mathrm{*}}$(5 $^{1}$${\mathit{P}}_{1}$)\ensuremath{\rightarrow}Sr(5 $^{1}$${\mathit{S}}_{0}$)+${\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}$(${\mathit{n}}^{2\mathit{S}+1}$L)-\ensuremath{\Delta}E, ${\mathrm{Sr}}^{\mathrm{*}}$(4 $^{1}$${\mathit{D}}_{2}$) +${\mathrm{Sr}}^{\mathrm{*}}$(4 $^{1}$${\mathit{D}}_{2}$)\ensuremath{\rightarrow}Sr(5 $^{1}$${\mathit{S}}_{0}$)+${\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}$(${\mathit{n}}^{2\mathit{S}+1}$L)-\ensuremath{\Delta}E. The 4 $^{1}$${\mathit{D}}_{2}$ state was populated by a nonlinear stimulated process. By measuring the rate coefficients for these reactions for over 40 final states ${\mathit{n}}^{2\mathit{S}+1}$L, we look for insight into how these reactions depend on energy defect, spin, and angular momentum. It is found that there is not a very strong dependence on the energy defect, and that singlet and triplet final states are produced in comparable amounts. The final states tend to be populated more effectively as their angular momentum increases. Total rate coefficients are of the order of gas-kinetic rates.

Physical Review A•Mar 1, 1991•21 citations

Collision energy pooling for Sr(5 3 PJ )+Sr(5 J’3 ) → Sr(6 3,1 S)+Sr(5 1 S)

James Floyd Kelly, Martin A. Harris, Alan C. Gallagher

Energy pooling (EP) has been observed in Sr vapor following pulsed optical excitation to the 5${}^{3}$${P}_{1}$ state. From the time-dependent radiative decay of 6${}^{3}$${S}_{1}$ and of ${6}^{1}$${\mathit{S}}_{0}$ via the cascade resonance line, the EP rate coefficients have been investigated for the following: Sr(5 $^{3}P_{J}$)+Sr(5${}^{3}$${\mathit{P}}_{\mathit{J}\mathcal{'}}$) ${(5}^{1}$${S}_{0}$) +Sr(6 $^{3}S_{1}$ or ${6}^{1}$${S}_{0}$). The values of ${k}_{11}$ have been measured, as well as ${k}_{\mathrm{JJ}\mathcal{'}}$ averaged over a thermal distribution of 5 $^{3}P_{J}$ populations. The time-dependent Sr(${5}^{3}$${P}_{J}$) densities were measured by absorption of lines from a Sr lamp crossing the excitation region. The rate coefficients are surprisingly large; in spite of the small statistical weights of these product states, they are nearly gas-kinetic. The dependence of the rates upon spin, J, and energy defect \ensuremath{\Delta}E has also been examined.

Physical Review A•Aug 1, 1988•36 citations
The dependence of energy pooling cross sections on the alignment of atomic angular momentum with respect to the collision axis is investigated. In a vapor cell, excitation with counter-propagating polarized laser beams that define the collision axis prepares aligned strontium atoms in the 5s5p3P15s5p{}^{3}{P}_{1}5s5p3P1​ level. Excited-state energy pooling collision products from the endothermic 5s5p3P1+5s5p3P1\ensuremath→5s6s1S0+5s21S05s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s6s{}^{1}{S}_{0}{+5s}^{2}{}^{1}{S}_{0}5s5p3P1​+5s5p3P1​\ensuremath→5s6s1S0​+5s21S0​ reaction and the exothermic 5s5p3P1+5s5p3P1\ensuremath→5s5p1P1+5s21S05s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s5p{}^{1}{P}_{1}{+5s}^{2}{}^{1}{S}_{0}5s5p3P1​+5s5p3P1​\ensuremath→5s5p1P1​+5s21S0​ reaction are studied. Alignment effects are studied as a function of collision energy, using pulsed laser excitation followed by delayed fluorescence detection to lower the transverse collision velocity and laser detuning to vary the collision velocity in the laser-beam direction. The rate coefficient for energy transfer to the 61S06{}^{1}{S}_{0}61S0​ state is enhanced by 38\ifmmode±\else\textpm\fi1338\ifmmode\pm\else\textpm\fi{}13%38\ifmmode±\else\textpm\fi13 when the MJ{M}_{J}MJ​ alignment of the collision partners is perpendicular to the collision axis and parallel to each other compared to when there is no alignment of the collision partners. No alignment dependence is observed for energy transfer to the 51P15{}^{1}{P}_{1}51P1​ state. This experiment offers the unique capability of simultaneously and independently controlling collision velocity and angular momentum alignment.
The threshold behavior of the cross section of an endothermic energy pooling reaction is investigated. In a vapor cell experiment, pulsed excitation followed by delayed fluorescence detection narrows the transverse velocity distribution of colliding pairs of laser-excited strontium atoms in the 5s5p3P1{5s5p}^{3}{P}_{1}5s5p3P1​ level, and laser detuning establishes the collision velocity in the direction of counterpropagating laser beams. A probe laser detects the excited-state collision product of the endothermic ${5s5p}^{3}{P}_{1}{+5s5p}^{3}{P}_{1}\ensuremath{\rightarrow}{5s6s}^{1}{S}_{0}{+5s}^{21}{S}_{0}$ reaction. The cross section rises steeply at threshold and is nearly flat for 1.2--2 times the threshold energy. This behavior can be partly explained by the shape of the molecular potential curve of the collisionally produced state. From the measured $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{3}{\mathrm{}\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ thermally averaged rate coefficient, the above-threshold cross section is found to be approximately $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}.$ The thermally averaged rate coefficient for the highly exothermic energy pooling reaction ${5s5p}^{3}{P}_{1}{+5s5p}^{3}{P}_{1}\ensuremath{\rightarrow}{5s5p}^{1}{P}_{1}{+5s}^{21}{S}_{0}$ is also reported and measured to be $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{\mathrm{cm}}^{3}{\mathrm{}\mathrm{s}}^{\mathrm{\ensuremath{-}}1}.$ The cross section for this exothermic reaction is found to be nearly independent of collision velocity.
An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial Ca(4s4p3P1)\mathrm{Ca}(4s4p{}^{3}{P}_{1})Ca(4s4p3P1​) state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.
A pulsed laser investigation is performed to study the detailed effects of electronic angular-momentum alignment on the cross section for the energy-transfer process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ A uniform magnetic field imposed by a set of Helmholtz coils is used to systematically precess the initial state orbitals with a well-defined period, allowing different alignments to be sampled at different time delays after the pulsed laser excites and aligns the Ca(4s4p3P1)\mathrm{Ca}(4s4p{}^{3}{P}_{1})Ca(4s4p3P1​) states. The polarization effects in this collision process are striking. For example, the cross section for two atoms both in the mj=0{m}_{j}=0mj​=0 magnetic substrate is 13 times larger than the cross section for two atoms that are both in the mj=1{m}_{j}=1mj​=1 (or -1) substrate, where the quantization axis is taken to be along the relative velocity vector of the collision. The initial m-sublevel dependence of this three-vector correlation process can be completely described with eight fundamental parameters, five of which are accurately obtained. In addition, the coarse energy dependence of these parameters is deduced.
Alignment and orientation effects in the energy pooling process, Sr(5s5p 3 P 1 ) + Sr(5s5p 3 P 1 ) → Sr(5s5p 1 P 1 ) + Sr(5s 2 1 S 0 ), are studied in a single atomic beam. The Sr atoms are prepared in an aligned initial state with a polarized laser, and alignment information is extracted by observing the fluorescence from the final Sr(5s5p 1 P 1 ) state as the atoms precess in an applied magnetic field. This allows the dependence of the total energy pooling cross section (integrated over the final state alignment) on the initial state alignment to be almost completely described. A prominent alignment effect is observed. If m j represents the component of total electronic angular momentum of a Sr(5s5p 3 P 1 ) atom along the relative velocity vector of the collision, then the total energy transfer cross section for a particular initial state alignment can be expressed as a sum of the so-called fundamental cross sections, σ m 1 m 2 and σ m 1 m 2; m 1 ‘ m 2 ‘, that describe collisions between the various m j states. Here σ m 1 m 2 represents the cross section for energy transfer when an atom in state m 1 collides with an atom in state m 2 . The cross section σ m 1 m 2; m 1 ‘ m 2 ‘ represents the contribution to the total cross section from interference when the colliding system is in a superposition of the state m 1 colliding with m 2 and the state m 1 ‘ colliding with m 2 ‘. It is found that the cross sections σ 1-1, σ 00, and σ 10 as well as the interference terms Re( σ 00;1-1 ) and σ 01;10 have relatively large values while σ 11 and σ 1-1;-11 are small. Coupled with future theoretical work, these results may provide new insights into the dynamics of the curve crossings that lead to energy transfer.
The following energy-transfer reactions have been observed in a Sr vapor following pulsed excitation of the 5 1^{1}1P1{\mathit{P}}_{1}P1​ state: Sr∗{\mathrm{Sr}}^{\mathrm{*}}Sr∗(5 1^{1}1P1{\mathit{P}}_{1}P1​)+Sr∗{\mathrm{Sr}}^{\mathrm{*}}Sr∗(5 1^{1}1P1{\mathit{P}}_{1}P1​)\ensuremath{\rightarrow}Sr(5 1^{1}1S0{\mathit{S}}_{0}S0​)+Sr∗∗{\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}Sr∗∗(n2S+1{\mathit{n}}^{2\mathit{S}+1}n2S+1L)-\ensuremath{\Delta}E, Sr∗{\mathrm{Sr}}^{\mathrm{*}}Sr∗(4 1^{1}1D2{\mathit{D}}_{2}D2​) +Sr∗{\mathrm{Sr}}^{\mathrm{*}}Sr∗(4 1^{1}1D2{\mathit{D}}_{2}D2​)\ensuremath{\rightarrow}Sr(5 1^{1}1S0{\mathit{S}}_{0}S0​)+Sr∗∗{\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}Sr∗∗(n2S+1{\mathit{n}}^{2\mathit{S}+1}n2S+1L)-\ensuremath{\Delta}E. The 4 1^{1}1D2{\mathit{D}}_{2}D2​ state was populated by a nonlinear stimulated process. By measuring the rate coefficients for these reactions for over 40 final states n2S+1{\mathit{n}}^{2\mathit{S}+1}n2S+1L, we look for insight into how these reactions depend on energy defect, spin, and angular momentum. It is found that there is not a very strong dependence on the energy defect, and that singlet and triplet final states are produced in comparable amounts. The final states tend to be populated more effectively as their angular momentum increases. Total rate coefficients are of the order of gas-kinetic rates.
Energy pooling (EP) has been observed in Sr vapor following pulsed optical excitation to the 53{}^{3}3P1{P}_{1}P1​ state. From the time-dependent radiative decay of 63{}^{3}3S1{S}_{1}S1​ and of 61{6}^{1}61S0{\mathit{S}}_{0}S0​ via the cascade resonance line, the EP rate coefficients have been investigated for the following: Sr(5 3PJ^{3}P_{J}3PJ​)+Sr(53{}^{3}3PJ′{\mathit{P}}_{\mathit{J}\mathcal{'}}PJ′​) (51{(5}^{1}(51S0{S}_{0}S0​) +Sr(6 3S1^{3}S_{1}3S1​ or 61{6}^{1}61S0{S}_{0}S0​). The values of k11{k}_{11}k11​ have been measured, as well as kJJ′{k}_{\mathrm{JJ}\mathcal{'}}kJJ′​ averaged over a thermal distribution of 5 3PJ^{3}P_{J}3PJ​ populations. The time-dependent Sr(53{5}^{3}53PJ{P}_{J}PJ​) densities were measured by absorption of lines from a Sr lamp crossing the excitation region. The rate coefficients are surprisingly large; in spite of the small statistical weights of these product states, they are nearly gas-kinetic. The dependence of the rates upon spin, J, and energy defect \ensuremath{\Delta}E has also been examined.