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Physical Review A

Measurement of the nonlinear Stark effect in the 2 P122 state of hydrogen

K J Kollath, Hans Kleinpoppen

Published Nov 1, 1974• 10 citations
Publisher

Abstract

Level crossings between the substates $2 ^{2}P_{\frac{3}{2}}$, ${m}_{j}=\ensuremath{-}\frac{3}{2}$ and $2 ^{2}P_{\frac{1}{2}}$, ${m}_{j}=\frac{1}{2}$ of atomic hydrogen have been observed for electric fields up to 250 kV/m. A nonlinear low-field Stark effect has been measured for the $2 ^{2}P_{\frac{1}{2}}$ state, in agreement with theoretical calculations which include Lamb shift and hyperfine structure.

DOI
10.1103/physreva.10.1519

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Level crossings between the substates 22P322 ^{2}P_{\frac{3}{2}}22P23​​, mj=\ensuremath−32{m}_{j}=\ensuremath{-}\frac{3}{2}mj​=\ensuremath−23​ and 22P122 ^{2}P_{\frac{1}{2}}22P21​​, mj=12{m}_{j}=\frac{1}{2}mj​=21​ of atomic hydrogen have been observed for electric fields up to 250 kV/m. A nonlinear low-field Stark effect has been measured for the 22P122 ^{2}P_{\frac{1}{2}}22P21​​ state, in agreement with theoretical calculations which include Lamb shift and hyperfine structure.
The nonlinear low-field Stark effect in the level n=2 of hydrogen has been investigated. \nThe experiment employed the level crossing technique, measuring the position of the crossings between the Zeeman states: \n2P3/2, mj=-3/2 and 2P1/2, mj=1/2; and \n2P3/2, mj=-3/2 and 2S1/2, mj=1/2; \nas the electric field was varied from 0 to 500 kV/m. \nA beam of atomic hydrogen, produced by thermal dissociation, was subjected to parallel electric and magnetic fields. Lymman –α (Lyα) resonance radiation was generated in an electrodeless microwave discharge lamp. The profile of the Lyα line emitted by the lamp has been investigated experimentally. \nThe level crossings were detected as changes of the Lyα resonance fluorescence intensity observed in a certain direction. The crossing positions were determined from the observed crossing signals of Lorentzian profile by a least squares computer programme. \nThe experimental results for the crossing positions as afuction of the electric field have been compared with theoretical calculations. The theoretical values were obtained by numerical diagonalization of the matrix of the eigenstates |2ℓjFmF> for perturbation by combined electric and magnetic fields. Radiative corrections were included. \nTheoretical values and experimental results agreo within the experimental uncertainties of 2%.
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We have observed the crossing of the atomic hydrogen levels ${\ensuremath{\beta}}_{B}(2{S}_{\frac{1}{2}}, {m}_{J}=\ensuremath{-}\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ and ${e}_{B}(2{P}_{\frac{1}{2}}, {m}_{J}=+\frac{1}{2}, {m}_{I}=\ensuremath{-}\frac{1}{2})$ near 605 G. A new atomic-beam method is used. H atoms are excited to the metastable 2S2S2S state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The 2S(mJ=+12)2S({m}_{J}=+\frac{1}{2})2S(mJ​=+21​) beam passes through a zero-field region where 13\frac{1}{3}31​ of it is converted to the single hyperfine level ${\ensuremath{\beta}}_{B}$. The ${\ensuremath{\beta}}_{B}$ atoms enter a uniform magnetic field parallel to the beam. With no externally applied electric field, 92% of them reach the detector. When we apply an electrostatic field of about 0.7 V/cm perpendicular to the beam, the ${\ensuremath{\beta}}_{B}$ atoms are strongly quenched near the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing point. Observed quenching agrees with the Bethe-Lamb theory of the 2S2S2S lifetime in external fields. We measure magnetic field by the nuclear magnetic resonance frequency of protons in water. Natural asymmetry and minor experimental corrections reduce the observed center of the ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ quenching resonance by 1 part in 104{10}^{4}104. The corrected ${\ensuremath{\beta}}_{B}\ensuremath{-}{e}_{B}$ crossing occurs at 2577.57\ifmmode\pm\else\textpm\fi{}0.25 kc/sec, proton nmr in water. From this, we calculate the Lamb shift S\mathcal{S}S in H, n=2n=2n=2. With a diamagnetic shielding correction, and the accurately known 2S2S2S hyperfine interval, we get $\mathcal{S}=1058.07\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. This disagrees with $\mathcal{S}=1057.77\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec from the Lamb experiments.
In the spectral range between 480 nm and 630 nm the Stark effect of the transitions n1Q-21S, n1Q-21P and n3Q-23P(n=3÷9, Q=S, P,...) was studied using electric field up to 1500 kV/cm. For such a high field the Stark splitting becomes greater than the simple structure of the atom. Hence, anticrossings of the Stark components of the same magnetic quantum number occur. The experimental results have been compared with the theoretically determined shifts. The results of caluclations show good agreement with observation not only for low field values, but also in high fields and in case of level anticrossings.
The method of level-crossing spectroscopy has been extended to a study of the Stark effect on the 3P3P3P term of lithium. Lithium atoms in a broad atomic beam are subjected to collinear electric and magnetic fields. The field values required to produce a level crossing or degeneracy are determined by observing the change in the angular distribution of the fluorescence resulting from the optical excitation of the 3P3P3P term. The magnetic field required to produce the crossing is found to shift to higher values as the electric field is applied. The shift increases as the square of the electric field and is given by $\ensuremath{\Delta}H=+0.056(11){E}^{2}$, where $\ensuremath{\Delta}H$ is in gauss and EEE is in kilovolts per centimeter. The coefficient is in good agreement with the value 0.048 obtained from second-order perturbation theory and the Bates and Damgaard approximation.
In the spectral range between 480 nm and 630 nm the Stark effect of the transitions n 1Q-2 1S, n 1Q-2 1P and n 3Q-2 3P (n=3÷10, Q=S, P,...) was studied using electric field up to 1500 kV/cm. For such a high field the Stark splitting becomes greater than the simple structure of the atom. Hence anticrossings of the Stark components of the same magnetic quantum number occur. The experimental results have been compared with the theoretically determined shifts. The results of calculations show good agreement with observation.