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Physical Review A

Fine-structure-changing collisions in atomic titanium

Mei-Ju Lu, Kyle S. Hardman, Jonathan D. Weinstein, Bernard Zygelman

Published Jun 10, 2008• 30 citations
Publisher

Abstract

We have measured cold titanium-helium collisions that cause transitions between the fine-structure levels of the $[3{d}^{2}4{s}^{2}]\phantom{\rule{0.3em}{0ex}}^{3}F_{J}$ electronic ground state of atomic titanium, over a temperature range from 5 to $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{He}$ inelastic collision cross section is significantly smaller than cross sections measured for collisions of non-transition-metal atoms with noble gas atoms. Our theoretical calculations of the inelastic cross sections reproduce the magnitude and temperature dependence of the measurements, and attribute the suppression of inelastic collisions to titanium's ``submerged'' $d$-shell valence electrons.

DOI
10.1103/physreva.77.060701

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We have measured cold titanium-helium collisions that cause transitions between the fine-structure levels of the [3d24s2]3FJ[3{d}^{2}4{s}^{2}]\phantom{\rule{0.3em}{0ex}}^{3}F_{J}[3d24s2]3FJ​ electronic ground state of atomic titanium, over a temperature range from 5 to 20K20\phantom{\rule{0.3em}{0ex}}\mathrm{K}20K. The Ti\ensuremath-He\mathrm{Ti}\text{\ensuremath{-}}\mathrm{He}Ti\ensuremath-He inelastic collision cross section is significantly smaller than cross sections measured for collisions of non-transition-metal atoms with noble gas atoms. Our theoretical calculations of the inelastic cross sections reproduce the magnitude and temperature dependence of the measurements, and attribute the suppression of inelastic collisions to titanium's ``submerged'' ddd-shell valence electrons.
We have measured cold inelastic collisions between neutral ground-state titanium atoms: collisions that cause transitions between the different magnetic sublevels of the [3d24s2]3F2[3{d}^{2}4{s}^{2}]{^{3}F}_{2}[3d24s2]3F2​ ground state of 50Ti^{50}\text{T}\text{i}50Ti, as well as collisions that cause transitions between the fine-structure levels of the [3d24s2]3FJ[3{d}^{2}4{s}^{2}]{^{3}F}_{J}[3d24s2]3FJ​ electronic ground state. Both processes occur with large rate coefficients, as would be expected from titanium's anisotropic electronic potential.
Inelastic-collision processes in fine-structure-changing collisions have been studied by selective stepwise excitation and observation of the resulting fluorescence. Hereby, the effect of ground-state rubidium atoms colliding with excited-state rubidium atoms was investigated. The ground-state density was changed by three orders of magnitude by performing the measurements over the temperature range of 75 to 200 \ifmmode^\circ\else\textdegree\fi{}C. The cross section for fine-structure-changing collisions [i.e., $\mathrm{Rb}({6}^{2}{D}_{\frac{5}{2}})+\mathrm{Rb}({5}^{2}{S}_{\frac{1}{2}})\ensuremath{\rightarrow}\mathrm{Rb}({6}^{2}{D}_{\frac{3}{2}})+\mathrm{Rb}({5}^{2}{S}_{\frac{1}{2}})$] is ${\ensuremath{\sigma}}_{\mathrm{fs}}=(1.0\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2. The cross sections for transfer out of the fine-structure doublet [i.e., $\mathrm{Rb}({6}^{2}D)+\mathrm{Rb}({5}^{2}{S}_{\frac{1}{2}})\ensuremath{\rightarrow}\mathrm{states}\mathrm{other}\mathrm{than}\mathrm{Rb}({6}^{2}D)$] is ${\ensuremath{\sigma}}_{\mathrm{tr}}=(3.8\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2. It is demonstrated that for the intermediate excited rubidium states, both the fine-structure-changing and transfer cross sections are of the order of the geometrical cross section of the excited rubidium states.
We report on the results of a multichannel calculation of fine-structure transition cross sections for collisions of ground-state Ti with He. We find significant suppression of fine-structure level quenching over a wide range of collision energies. We show that the suppression is due to a mechanism proposed by [Hancox et al., Nature (London) 431, 281 (2004)] to explain similar suppression of Zeeman relaxation in collisions of magnetically trapped rare-earth-metal atoms with cold He atoms. We find that the quenching rates are sensitive to the value of the Born-Oppenheimer adiabatic potential surfaces of the Ti-He system in the region of the inner repulsive wall. Adjusting the ab initio potentials for TiHe, available in the literature, we find good agreement with laboratory measurements.
Inelastic collisional processes in fine-structure-state mixing have been studied by selective stepwise excitation and observation of the resulting fluorescence during collisions of excited rubidium 62D526^{2}D_{\frac{5}{2}}62D25​​ state atoms with various noble-gas atoms. It is shown that for intermediately excited rubidium atoms the fine-structure-state mixing cross sections are generally increasing from helium to xexon. The cross sections for the process $\mathrm{Rb}(6^{2}D_{\frac{5}{2}})+A(n^{1}S_{0})\ensuremath{\rightarrow}\mathrm{Rb}(6^{2}D_{\frac{3}{2}})+A(n^{1}S_{0})+\ensuremath{\Delta}E$ have the values ${\ensuremath{\sigma}}_{\mathrm{fs}}^{*}=2.4\ifmmode\pm\else\textpm\fi{}0.9, 3.1\ifmmode\pm\else\textpm\fi{}1.2, 2.6\ifmmode\pm\else\textpm\fi{}1.0, 5.8\ifmmode\pm\else\textpm\fi{}2.2, \mathrm{and} 9.3\ifmmode\pm\else\textpm\fi{}5.6$ in units of ${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2, where AAA denotes in sequence any one of the noble gas atoms He, Ne, Ar, Kr, and Xe, respectively. Transfer cross sections for the transfer of excited Rb62D6^{2}D62D-state atoms out of the doublet were also determined and are about an order of magnitude smaller than the fine-structure-mixing cross sections.
The thermal cross sections for inelastic transfer of excited rubidium atoms from the n2D52n^{2}D_{\frac{5}{2}}n2D25​​ to the n2D32n^{2}D_{\frac{3}{2}}n2D23​​ fine-structure state caused by fine-structure-changing collisions with ground-state rubidium atoms have been measured by selective stepwise excitation of the rubidium atoms and observation of the resulting fluorescence. The cross sections (in units of ${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2) for nnn being 5-9 are 2.9\ifmmode\pm\else\textpm\fi{}0.6, 6.9\ifmmode\pm\else\textpm\fi{}1.4, 11.5\ifmmode\pm\else\textpm\fi{}2.3, 17.1\ifmmode\pm\else\textpm\fi{}3.0, and 26.0\ifmmode\pm\else\textpm\fi{}5.0, respectively. The fine-structure-changing cross sections are of the order of the geometrical cross sections and increase slightly less than (n∗)4{({n}^{*})}^{4}(n∗)4 for the low-lying n2Dn^{2}Dn2D states studied.