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Physical Review A

Nonadiabatic theory of fine-structure branching cross sections for Na-He, Na-Ne, and Na-Ar optical collisions

Linda L. Vahala, Paul S. Julienne, Mark D. Havey

Published Sep 1, 1986• 41 citations
Publisher

Abstract

The nonadiabatic close-coupled theory of atomic collisions in a radiation field is generalized to include electron spin and is used to consider the weak-field Na--rare-gas (RG) optical collision Na${(}^{2}$${S}_{1/2}$)+RG+nh\ensuremath{\nu} \ensuremath{\mu}Na${(}^{2}$${\mathrm{P}}_{\mathrm{j}}$)+RG+(n-1)h\ensuremath{\nu}. The effects of detuning and incident energy on the branching into the atomic Na 3${p}^{2}$${P}_{3/2}$ and 3p $^{2}P_{1/2}$ states are examined. The cross sections \ensuremath{\sigma}(j) are found to have a strong asymmetry between red and blue detuning as well as a complex threshold and resonance structure dependence on energy. A partial cross-section analysis of \ensuremath{\sigma}(j) shows a significant difference between contributions from states of e and f molecular parity. The theoretically calculated detuning dependence of the branching ratio into each fine-structure state is in good agreement with available experimental data for Na-Ar, Na-Ne, and Na-He, as well as the total absorption coefficient for the production of Na 3p atoms. The fine-structure branching ratio for thermal energy collisions shows considerable variation with a rare-gas collision partner, due to the different interaction potentials. For sufficiently high collision energy, the branching approaches a recoil limit which is independent of collision partner.

DOI
10.1103/physreva.34.1856

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Experimental fine-structure branching ratios for Na–rare-gas optical collisions

Mark D. Havey, F. T. Delahanty, Linda L. Vahala +1 more

Experimental ratios for branching into the fine-structure levels of the Na 3p multiplet, as a consequence of an optical collision with He, Ne, Ar, Kr, or Xe, are reported. The process studied is Na(3s $^{2}S_{1/2}$)+scrR+nh\ensuremath{\nu}\ensuremath{\rightarrow} Na(3p $^{2}P_{j}$)+scrR+(n-1)h\ensuremath{\nu} , where scrR represents a rare-gas atom and where the laser frequency \ensuremath{\nu} is tuned in the wings of the Na resonance transitions. The branching ratios are defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Na D1 and D2 lines. The ratios are determined for detunings ranging from about 650 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the blue wing to 170 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the red wing of the Na 3p multiplet. The branching is found to be strongly detuning dependent in the vicinity of the NaAr, NaKr, and NaXe near-red-wing satellites. The blue-wing branching ratios show a detuning-dependent approach to a recoil, or sudden statistical, limit of 0.5, irrespective of the rare gas. Fine-structure changing cross sections have also been measured for resonant excitation of the Na 3p $^{2}P_{j}$ state; the results are consistent with cross sections obtained from wing excitation.

Physical Review A•Oct 1, 1986•21 citations

Experimental fine-structure branching ratios for Na-rare gas optical collisions

Mark D. Havey, F. T. Delahanty, Linda L. Vahala +1 more

Experimental ratios for branching into the fine‐structure levels of the Na 3p multiplet, as a consequence of an optical collision with He, Ne, Ar, Kr, or Xe, are reported. The process studied is Na(3s2S1/2) +RG+nhν → Na(3p2 Pj)+RG+(n−1)hν, where RG represents a rare gas atom and where the laser frequency ν is tuned in the wings of the Na resonance transitions. The branching ratios are defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Na D1 and D2 lines. The ratios are determined for detunings ranging from about 650 cm−1 blue to 170 cm−1 red of the Na 3p multiplet. The branching is found to be strongly detuning dependent in the vicinity of the NaKr and NaXe near red‐wing satellites. The blue wing branching ratios show a detuning‐dependent approach to a recoil or sudden statistical limit of 0.5, irrespective of the rare gas.

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Radiative scattering close-coupled calculations for isotope dependence of fine-structure branching in 3He-Na and 4He-Na optical collisions

Linda L. Vahala, Paul S. Julienne

Assume that collisional redistribution occurs in a collision of two atoms in scattering state i by absorption of a photon through an isolated molecular state a to an isolated molecular state b, followed by separation to excited product scattering state f. If the separation velocity of the two atoms is sufficiently large, the final state can be approximated by the same recoil limit which has been developed for photofragmentation.1 Our close coupling calculations on Na + He systems show how the recoil limit for fine-structure branching rations is approached for both red and blue detuning as product separation velocity increases. Comparisons are made between the lighter Na-He system at thermal energies and the heavier Na-He system.

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Nonadiabatic theory of atomic line broadening: Final-state distributions and the polarization of redistributed radiation

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Sodium 3P fine-structure excitation transfer induced by collisions with rubidium and caesium atoms

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The cross sections for the excitation energy transfer in the collisional processes Na*(3P 1 2/)+M(nS 1 2/) to or from Na*(3p 3 2/)+m(Ns 3 2/), m being ground-state Rb (n=5) or Cs (n=6) atom, have been measured by laser fluorescence method. With either of the two sodium 3P fine-structure states optically excited, the intensity ratio of the sensitized to direct fluorescence was measured. The polarization effects due to partially polarized and anisotropic direct fluorescence were investigated. The measured cross sections (T=530 K) for the sodium 3P fine-structure excitation transfer induced by collisions with Rb are: sigma ( 1 / 2 to 3 / 2 )=170 AA 2 , with an overall accuracy of 20%. The corresponding values in the Cs case are: sigma ( 1 / 2 to 3 / 2 )=140 AA 2 , sigma ( 3 / 2 to 1 / 2 )=83 AA 2 . The theoretical calculations reveal the decisive role of the dipole-quadrupole interaction. The obtained values are in satisfactory agreement with the experiment only if both the dipole-dipole and dipole-quadrupole interactions are taken into account, while the calculations involving the dipole-dipole term alone yield the cross section values which are as much as one order of magnitude lower than the experimentally observed ones.

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[Measurement of fine-structure branching ratios for Rb-He optical collisions].

Lei Lü, Lin Li, Yu-Hua Deng +3 more

Experimental ratios of branching in the fine-structure levels of the Rb5P multiplet, as a consequence of an optical collision with He, are reported. The process studied is Rb(5S1/2 )+ He + hrv --> Rb(5P(J)) +He, where the pulsed laser frequency v is tuned in the wings of the Rb resonance transitions. The authors defined the detuning delta to be v-v (D2 )(delta > 0) for laser frequency v highter than that of RbD2 transition and to be v-v (D1)(delta < 0) for v lower than the RbD1 transition. As RbHe molecular states are correlated to the two 5 2P(J) states, there is some likelihood that the molecule will dissociate into 5 2P1/2 or 5P3/2 state. The dissociation results in a nonuniform distribution of atomic Rb5P(J) states. The branching ratios are defined as n1/n2, where n1 and n2 are densities of the 5P1/2 and 5P3/2 states dissociated. To determine experimentally the relative cross section for scattering into the two fine-structure states, the relative time-intergrated intensities of the resulting Rb emission lines, I(5P3/2 --> 5P1/2 )[I(D2)] and I(5P1/2 --> 5P3/2) ) [I(D1)], were measured. The ratios are determined by detunings from about 200 cm(-1) in the blue wing to -180 cm(-1) in the red wing of the Rb5P multiplet. A rate equation analysis of the pressure dependence was yielded. The branching ratios and cross sections for collisional 5P1/2 --> 5P3/2 transition were obtained from the slope and intercept. The blue-wing branching ratios show a detuning-dependent approach to limit of 0. 2. The branching was found to be very large (-40) in the red wing, irrespective of the detuning. Fine structure changing cross section (1.1 +/- 0.3) x 10(-17) cm2 was measured from wing excitation, and the result is consistent with the cross section obtained from resonant excitation of the Rb5P(J) state. The measurements show a strong sensitivity to interatomic potentials and to nonadiabatic effects in dissociation dynamics.

•Jul 1, 2009•0 citations
The nonadiabatic close-coupled theory of atomic collisions in a radiation field is generalized to include electron spin and is used to consider the weak-field Na--rare-gas (RG) optical collision Na{(}^{2}$${S}_{1/2})+RG+nh\ensuremath{\nu} \ensuremath{\mu}Na{(}^{2}$${\mathrm{P}}_{\mathrm{j}})+RG+(n-1)h\ensuremath{\nu}. The effects of detuning and incident energy on the branching into the atomic Na 3{p}^{2}$${P}_{3/2} and 3p 2P1/2^{2}P_{1/2}2P1/2​ states are examined. The cross sections \ensuremath{\sigma}(j) are found to have a strong asymmetry between red and blue detuning as well as a complex threshold and resonance structure dependence on energy. A partial cross-section analysis of \ensuremath{\sigma}(j) shows a significant difference between contributions from states of e and f molecular parity. The theoretically calculated detuning dependence of the branching ratio into each fine-structure state is in good agreement with available experimental data for Na-Ar, Na-Ne, and Na-He, as well as the total absorption coefficient for the production of Na 3p atoms. The fine-structure branching ratio for thermal energy collisions shows considerable variation with a rare-gas collision partner, due to the different interaction potentials. For sufficiently high collision energy, the branching approaches a recoil limit which is independent of collision partner.
Experimental ratios for branching into the fine-structure levels of the Na 3p multiplet, as a consequence of an optical collision with He, Ne, Ar, Kr, or Xe, are reported. The process studied is Na(3s 2S1/2^{2}S_{1/2}2S1/2​)+scrR+nh\ensuremath{\nu}\ensuremath{\rightarrow} Na(3p 2Pj^{2}P_{j}2Pj​)+scrR+(n-1)h\ensuremath{\nu} , where scrR represents a rare-gas atom and where the laser frequency \ensuremath{\nu} is tuned in the wings of the Na resonance transitions. The branching ratios are defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Na D1 and D2 lines. The ratios are determined for detunings ranging from about 650 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the blue wing to 170 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the red wing of the Na 3p multiplet. The branching is found to be strongly detuning dependent in the vicinity of the NaAr, NaKr, and NaXe near-red-wing satellites. The blue-wing branching ratios show a detuning-dependent approach to a recoil, or sudden statistical, limit of 0.5, irrespective of the rare gas. Fine-structure changing cross sections have also been measured for resonant excitation of the Na 3p 2Pj^{2}P_{j}2Pj​ state; the results are consistent with cross sections obtained from wing excitation.
Experimental ratios for branching into the fine‐structure levels of the Na 3p multiplet, as a consequence of an optical collision with He, Ne, Ar, Kr, or Xe, are reported. The process studied is Na(3s2S1/2) +RG+nhν → Na(3p2 Pj)+RG+(n−1)hν, where RG represents a rare gas atom and where the laser frequency ν is tuned in the wings of the Na resonance transitions. The branching ratios are defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Na D1 and D2 lines. The ratios are determined for detunings ranging from about 650 cm−1 blue to 170 cm−1 red of the Na 3p multiplet. The branching is found to be strongly detuning dependent in the vicinity of the NaKr and NaXe near red‐wing satellites. The blue wing branching ratios show a detuning‐dependent approach to a recoil or sudden statistical limit of 0.5, irrespective of the rare gas.
Assume that collisional redistribution occurs in a collision of two atoms in scattering state i by absorption of a photon through an isolated molecular state a to an isolated molecular state b, followed by separation to excited product scattering state f. If the separation velocity of the two atoms is sufficiently large, the final state can be approximated by the same recoil limit which has been developed for photofragmentation.1 Our close coupling calculations on Na + He systems show how the recoil limit for fine-structure branching rations is approached for both red and blue detuning as product separation velocity increases. Comparisons are made between the lighter Na-He system at thermal energies and the heavier Na-He system.
The close-coupled theory of atomic collisions in the presence of a radiation field may be used to calculate the distribution of final atomic states which results from absorption of polarized light during a collision. The theory applies equally well to optical collisions (line broadening) and to radiative collisions (laser-induced collisional energy transfer). For an optical collision the detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\infty}}$ is restricted to be larger than either the Rabi frequency or the widths due to natural, Doppler, or pressure broadening. The radiation field is assumed to be weak enough that the transition probabilities are linear in field intensity. The molecular picture is emphasized in which the wave function is expanded in a basis of field-free molecular states and the Hamiltonian is blocked in accordance with molecular quantum numbers. The quantities needed to predict experimental observables are reduced radiative scattering SSS-matrix elements ${s}_{\ensuremath{\omega}}$ in the asymptotic Hund's case-(e) representation. The theory of product orientation and alignment is equivalent to that which has been developed for molecular photodissociation. It requires coherent sums of ${s}_{\ensuremath{\omega}}$ matrix elements from different transition branches, that is, for PPP-, QQQ-, and RRR-type transitions corresponding to changes of -1, 0, and +1 in total molecular angular momentum. On the other hand, the total absorption coefficient and the branching ratio to different final fine-structure states irrespective of orientation or alignment depend on incoherent sums of the same matrix elements.
The cross sections for the excitation energy transfer in the collisional processes Na*(3P 1 2/)+M(nS 1 2/) to or from Na*(3p 3 2/)+m(Ns 3 2/), m being ground-state Rb (n=5) or Cs (n=6) atom, have been measured by laser fluorescence method. With either of the two sodium 3P fine-structure states optically excited, the intensity ratio of the sensitized to direct fluorescence was measured. The polarization effects due to partially polarized and anisotropic direct fluorescence were investigated. The measured cross sections (T=530 K) for the sodium 3P fine-structure excitation transfer induced by collisions with Rb are: sigma ( 1 / 2 to 3 / 2 )=170 AA 2 , with an overall accuracy of 20%. The corresponding values in the Cs case are: sigma ( 1 / 2 to 3 / 2 )=140 AA 2 , sigma ( 3 / 2 to 1 / 2 )=83 AA 2 . The theoretical calculations reveal the decisive role of the dipole-quadrupole interaction. The obtained values are in satisfactory agreement with the experiment only if both the dipole-dipole and dipole-quadrupole interactions are taken into account, while the calculations involving the dipole-dipole term alone yield the cross section values which are as much as one order of magnitude lower than the experimentally observed ones.
Experimental ratios of branching in the fine-structure levels of the Rb5P multiplet, as a consequence of an optical collision with He, are reported. The process studied is Rb(5S1/2 )+ He + hrv --> Rb(5P(J)) +He, where the pulsed laser frequency v is tuned in the wings of the Rb resonance transitions. The authors defined the detuning delta to be v-v (D2 )(delta > 0) for laser frequency v highter than that of RbD2 transition and to be v-v (D1)(delta < 0) for v lower than the RbD1 transition. As RbHe molecular states are correlated to the two 5 2P(J) states, there is some likelihood that the molecule will dissociate into 5 2P1/2 or 5P3/2 state. The dissociation results in a nonuniform distribution of atomic Rb5P(J) states. The branching ratios are defined as n1/n2, where n1 and n2 are densities of the 5P1/2 and 5P3/2 states dissociated. To determine experimentally the relative cross section for scattering into the two fine-structure states, the relative time-intergrated intensities of the resulting Rb emission lines, I(5P3/2 --> 5P1/2 )[I(D2)] and I(5P1/2 --> 5P3/2) ) [I(D1)], were measured. The ratios are determined by detunings from about 200 cm(-1) in the blue wing to -180 cm(-1) in the red wing of the Rb5P multiplet. A rate equation analysis of the pressure dependence was yielded. The branching ratios and cross sections for collisional 5P1/2 --> 5P3/2 transition were obtained from the slope and intercept. The blue-wing branching ratios show a detuning-dependent approach to limit of 0. 2. The branching was found to be very large (-40) in the red wing, irrespective of the detuning. Fine structure changing cross section (1.1 +/- 0.3) x 10(-17) cm2 was measured from wing excitation, and the result is consistent with the cross section obtained from resonant excitation of the Rb5P(J) state. The measurements show a strong sensitivity to interatomic potentials and to nonadiabatic effects in dissociation dynamics.