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Physical Review A

Electron-impact widths and shifts of Sr II lines in ultracold neutral plasmas

Bin Duan, Muhammad Abbas Bari, Zhifeng Wu, Jun Feng Yan, Y. M. Li

Published Mar 11, 2013• 4 citations
Publisher

Abstract

In this paper, we report on relativistic quantum-mechanical calculations of electron-impact linewidths and line shifts in singly ionized strontium ions in ultracold neutral plasmas. We have used the Dirac $R$-matrix methods to solve ($N+1$)-electron colliding systems and to generate the required scattering matrices. Calculated linewidths and line shifts at an electron density ${10}^{17}\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}3}$ and electron temperatures (several electronvolts) agree well with other theoretical calculations and are closer to the experimental observations. Our theoretical findings of linewidths and line shifts are almost twice as large as the earlier calculations for the particular selected plasma conditions. This work develops these quantum-mechanical procedures and applies them to the emission from ultracold neutral plasmas.

DOI
10.1103/physreva.87.032505

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In this paper, we report on relativistic quantum-mechanical calculations of electron-impact linewidths and line shifts in singly ionized strontium ions in ultracold neutral plasmas. We have used the Dirac RRR-matrix methods to solve (N+1N+1N+1)-electron colliding systems and to generate the required scattering matrices. Calculated linewidths and line shifts at an electron density 1017cm\ensuremath−3{10}^{17}\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}3}1017cm\ensuremath−3 and electron temperatures (several electronvolts) agree well with other theoretical calculations and are closer to the experimental observations. Our theoretical findings of linewidths and line shifts are almost twice as large as the earlier calculations for the particular selected plasma conditions. This work develops these quantum-mechanical procedures and applies them to the emission from ultracold neutral plasmas.
Ultracold neutral plasmas are formed by photoionizing laser-cooled atoms near the ionization threshold. Through the application of atomic physics techniques and diagnostics, these experiments stretch the boundaries of traditional neutral plasma physics. The electron temperature in these plasmas ranges from 1-1000 K and the ion temperature is around 1 K. The density can approach 101110^{11}1011 cm−3^{-3}−3. Fundamental interest stems from the possibility of creating strongly-coupled plasmas, but recombination, collective modes, and thermalization in these systems have also been studied. Optical absorption images of a strontium plasma, using the Sr+^++ 2S1/2−>2P1/2{^2S_{1/2}} -> {^2P_{1/2}}2S1/2​−>2P1/2​ transition at 422 nm, depict the density profile of the plasma, and probe kinetics on a 50 ns time-scale. The Doppler-broadened ion absorption spectrum measures the ion velocity distribution, which gives an accurate measure of the ion dynamics in the first microsecond after photoionization.
Ultracold neutral plasmas are formed by photoionizing laser‐cooled atoms near the ionization threshold. Through the application of atomic physics techniques and diagnostics, these experiments stretch the boundaries of traditional neutral plasma physics. The electron temperature in these plasmas ranges from 1–1000 K and the ion temperature is around 1 K. The density can be as high as 1010 cm−3. Fundamental interest stems from the possibility of creating strongly‐coupled plasmas, but recombination, collective modes, and thermalization in these systems have also been studied. Optical absorption images of a strontium plasma, using the Sr+ 2S1/2 → 2P1/2 transition at 422 nm, depict the density profile of the plasma, and probe kinetics on a 50 ns time‐scale. The Doppler‐broadened ion absorption spectrum measures the ion velocity distribution, which gives an accurate measure of the ion dynamics in the first microsecond after photoionization.
We report a systematic experimental and numerical study of the expansion of ultracold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities, v0{v}_{0}v0​, of ultracold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature, Te,0=mionv02/kB{T}_{e,0}={m}_{\mathrm{ion}}{v}_{0}^{2}/{k}_{B}Te,0​=mion​v02​/kB​ (where mion{m}_{\mathrm{ion}}mion​ is the Rb+{\mathrm{Rb}}^{+}Rb+ ion mass), as a function of the original Rydberg atom density and binding energy, Eb,i{E}_{b,i}Eb,i​. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range ${10}^{7}--{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$, for states with principal quantum number n>40,Te,0n>40, {T}_{e,0}n>40,Te,0​ is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity kBTe,0{k}_{B}\phantom{\rule{0.16em}{0ex}}{T}_{e,0}kB​Te,0​ is strongly correlated with the fraction of atoms which ionize, and is in the range $0.6\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|\ensuremath{\lesssim}{k}_{B}{T}_{e,0}\ensuremath{\lesssim}2.5\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|$. On the other hand, plasmas from Rydberg samples with $n\ensuremath{\lesssim}40$ evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where Te,0{T}_{e,0}Te,0​ is determined by their Coulomb coupling parameter, ${\mathrm{\ensuremath{\Gamma}}}_{e}\ensuremath{\sim}0.01$.
Photoionizing laser-cooled atoms produces ultracold neutral plasmas with initial temperatures of 1–1000 K and densities as high as 10 10 cm −3 . Applied radio frequency fields can excite plasma oscillations that are used to monitor the expansion of the unconfined plasma. Significant three-body recombination of electrons and ions into Rydberg atoms takes place during the plasma expansion. Previous experiments have been done with xenon, but a new experiment is planned with laser-cooled strontium. The strontium ion has an optically allowed transition at a convenient blue wavelength. This will allow direct imaging of the plasma through fluorescence or absorption, and may enable laser cooling and trapping of the plasma.
When ultracold plasma is generated using the photoionization of laser-cooled atoms, some atoms reach only up to Rydberg states. These, in turn, interact with the free electrons of the plasma and get ionized further, thus enhancing the plasma. Theoretical models until date have used a semiclassical approach that does not explain all the properties of Rydberg ionization. We present an analytical solution for the Rydberg–electron ionization cross section using the Quantum-mechanical scattering process, which shows a good agreement with experimental data. In particular, the dependency of ionization on the Rydberg state is clearly shown in the form of relation with orbital size and the scattering length. This calculation is valid for all alkali atoms and, hence, is useful for estimating the electron density of ultracold plasma.