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Physical Review A

Measurement of the polarizability of calcium

Thomas M. Miller, Benjamin B. Bederson

Published Oct 1, 1976• 59 citations
Publisher

Abstract

The static electric dipole polarizability of the $4{s}^{2}(^{1}S_{0})$ ground state of the calcium atom has been measured using an electric deflection technique. The result is normalized to the polarizability of lithium by comparing deflections of calcium and lithium beams passing through an inhomogeneous electrostatic field. We find (25 \ifmmode\pm\else\textpm\fi{} 2.5) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$ for the polarizability of calcium.

DOI
10.1103/physreva.14.1572

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The static electric dipole polarizability of the 4s2(1S0)4{s}^{2}(^{1}S_{0})4s2(1S0​) ground state of the calcium atom has been measured using an electric deflection technique. The result is normalized to the polarizability of lithium by comparing deflections of calcium and lithium beams passing through an inhomogeneous electrostatic field. We find (25 \ifmmode\pm\else\textpm\fi{} 2.5) \ifmmode\times\else\texttimes\fi{} 10\ensuremath−24{10}^{\ensuremath{-}24}10\ensuremath−24 cm3{\mathrm{cm}}^{3}cm3 for the polarizability of calcium.
The static electric dipole polarizabilities of barium and strontium atoms have been measured using an electric deflection technique. The results are normalized to the polarizability of lithium by comparing deflections of the alkaline-earth beams to deflections of a lithium beam passing through an inhomogeneous electrostatic field. The measured polarizabilities are (39.7 \ifmmode\pm\else\textpm\fi{} 3.2) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3 for barium and (27.6 \ifmmode\pm\else\textpm\fi{} 2.2) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3 for strontium.
The static dipole polarizability of helium atoms in the metastable 23S12^{3}S_{1}23S1​ and 21S02^{1}S_{0}21S0​ states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\ensuremath{\alpha}(2^{3}S_{1})=(44.6\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3 and $\ensuremath{\alpha}(2^{1}S_{0})=(108\ifmmode\pm\else\textpm\fi{}13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3, agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.
We have measured the static electric dipole polarizability of ground state 49115In5s25p(2P12)_{ 49}^{115}\mathrm{In}5{s}^{2}5p(^{2}P_{\frac{1}{2}})49115​In5s25p(2P21​​) with a small (\ensuremath{\sim}9%) admixture of metastable 5s25p(2P32)5{s}^{2}5p(^{2}P_{\frac{3}{2}})5s25p(2P23​​). Three different methods were used: (a) $E\ensuremath{-}H$ gradient balance, (b) comparison of deflection in an inhomogeneous electric field with an alkalimetal-atom "standard," and (c) a deflection analysis using a computer program with no adjustable parameters except the polarizability itself. All methods agree to within 11%. Our weighted final result is (10.18\ifmmode\pm\else\textpm\fi{}1.20)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3. This is in very close agreement to a recent computation by Liberman and Zangwill, using fully relativistic wave functions and including electron correlation.
The electric dipole polarizability of the alkali-metal atoms Na, K, Rb, and Cs are determined by measuring the deflection of a velocity-selected beam by an inhomogeneous electric field. It is shown experimentally that scattering of slower beam atoms by background gas in the apparatus is an important systematic error in measurements of this kind if a beam-velocity selector is not used, and that this scattering is responsible for the discrepancies between different, earlier beam-deflection measurements of polarizability. The polarizability values obtained in this work are $\ensuremath{\alpha}(\mathrm{Na})=24.4\ifmmode\pm\else\textpm\fi{}1.7$ A˚3{\mathrm{\AA{}}}^{3}A˚3, $\ensuremath{\alpha}(\mathrm{K})=45.2\ifmmode\pm\else\textpm\fi{}3.2$ A˚3{\mathrm{\AA{}}}^{3}A˚3, $\ensuremath{\alpha}(\mathrm{Rb})=48.7\ifmmode\pm\else\textpm\fi{}3.4$ A˚3{\mathrm{\AA{}}}^{3}A˚3, and $\ensuremath{\alpha}(\mathrm{Cs})=63.3\ifmmode\pm\else\textpm\fi{}4.6$ A˚3{\mathrm{\AA{}}}^{3}A˚3.
We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium $\ensuremath{\alpha}=(24.33\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}$ with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for our largest field, is measured with a ${10}^{\ensuremath{-}3}$ accuracy.
We measured the ground-state static electric-dipole polarizabilities of Cs, Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam interferometer. Our measurements provide benchmark tests for atomic structure calculations and thus test the underlying theory used to interpret atomic parity-nonconservation experiments. We measured ${\ensuremath{\alpha}}_{\mathrm{Cs}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}59.39(9)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3},{\ensuremath{\alpha}}_{\mathrm{Rb}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}47.39(8)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$, and ${\ensuremath{\alpha}}_{\mathrm{K}}=4\ensuremath{\pi}{\ensuremath{\epsilon}}_{0}\ifmmode\times\else\texttimes\fi{}42.93(7)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3}$. In atomic units, these measurements are ${\ensuremath{\alpha}}_{\mathrm{Cs}}=401.2(7),{\ensuremath{\alpha}}_{\mathrm{Rb}}=320.1(6)$, and ${\ensuremath{\alpha}}_{\mathrm{K}}=290.0(5)$. We report ratios of polarizabilities ${\ensuremath{\alpha}}_{\mathrm{Cs}}/{\ensuremath{\alpha}}_{\mathrm{Rb}}=1.2532(10),{\ensuremath{\alpha}}_{\mathrm{Cs}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.3834(9)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.1040(9)$ with smaller fractional uncertainty because the systematic errors for individual measurements are largely correlated. Since Cs atom beams have short de Broglie wavelengths, we developed measurement methods that do not require resolved atom diffraction. Specifically, we used phase choppers to measure atomic beam velocity distributions, and we used electric field gradients to give the atom interference pattern a phase shift that depends on atomic polarizability.