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Physical Review

Observation of Level Crossing in H, n=2

R. T. Robiscoe

Published Apr 5, 1965• 66 citations
Publisher

Abstract

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 $2S$ state by electron bombardment. The $2S({m}_{J}=\ensuremath{-}\frac{1}{2})$ state is quenched in the bombardment region. The $2S({m}_{J}=+\frac{1}{2})$ beam passes through a zero-field region where $\frac{1}{3}$ 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 $2S$ 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 ${10}^{4}$. 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 $\mathcal{S}$ in H, $n=2$. With a diamagnetic shielding correction, and the accurately known $2S$ 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.

DOI
10.1103/physrev.138.a22

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The angular distribution of scattered Lyman-$\ensuremath{\alpha}$ photons from atomic hydrogen is calculated as a function of an applied magnetic field. The intensity of the scattered radiation is a function of the energy difference of the excited-2P2P2P levels and shows an extremum at the point where two levels cross. Neglecting hyperfine structure, there are two level crossings of interest: one at 3484 G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\frac{1}{2}}$), and the other 5223G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$), respectively. The coher$\stackrel{\mathrm{\ifmmode \breve{}\else \u{}\fi{}}}{\mathrm{e}}$nt and incoherent resonance scattering is determined near these crossing points by using a Hamiltonian that includes hyperfine structure and higher-order radiative effects. In the low-field region (3484 G), the hyperfine crossings that contribute to the coherent signal are at 3476.06 and 3491.93 G, respectively. The radiative width of the levels is considerably larger than the hyperfine splittings, and the total scattering intensity has a single peak at 3483.97 G. In the high-field region (5223 G), two hyperfine levels with ${m}_{F}=\ensuremath{-}1$ repel each other (anticross) with a minimum energy separation of 15.3 Mc/sec at 5200.1 G. Resonances occur at 5220.6 and 5223.9 G, and the maximum of the total signal is at 5222.6 G.
A sensitive test for any mixing of the 2S122{S}_{\frac{1}{2}}2S21​​ and 2P122{P}_{\frac{1}{2}}2P21​​ state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S2S2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S2S2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S2S2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S2S2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.
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A sensitive test for any mixing of the 2S122{S}_{\frac{1}{2}}2S21​​ and 2P122{P}_{\frac{1}{2}}2P21​​ state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S2S2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S2S2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S2S2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S2S2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.
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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