Nonadiabatic transitions in state-selection experiments on beams of metastable hydrogen atoms (
2S21) display oscillations in the population of the
F=1, $m=\ensuremath{-}1$ state R. D. Hight and R. T. Robiscoe, [Phys. Rev. A 17, 561 (1978)]. In this paper, theoretical calculations using exact and model solenoid fields averaged over a velocity distribution show that the population oscillations arise from the presence of at least two nonadiabatic regions in the solenoid. No oscillations occur theoretically if only a single nonadiabatic region exists, unless the unlikely assumption of a coherent hydrogen-atom beam is invoked.
Model calculations are presented for nonadiabatic passage of an oriented spin through a reversing solenoidal magnetic field; these are useful for comparison with experiments described elsewhere. The model corresponds closely to the well-known Landau-Zener-Stueckelberg model of a two-state curve crossing in molecular collision theory; various modifications appropriate to the Majorana problem are considered. The resulting transition amplitudes are discussed for the
F=1 hyperfine component of the
22S21 metastable state of atomic hydrogen as an example.
Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between
(2s,2p) and
(2p,2p) states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.
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(mJ=+21) beam passes through a zero-field region where
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
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
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 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.
The linear polarization of Lyman-\ensuremath{\alpha} radiation emitted when hydrogen atoms in the metastable 2
s1/2 state traverse an external electric field is studied as a function of the effective rise time of the field for field strengths extending from very small values up to 6 keV/cm. With decreasing rise time, the measured polarization exhibits a transition from adiabatic to sudden behavior. The transition region is centered at a rise time which is approximately equal to the characteristic time associated with the 2${\mathit{s}}_{1/2\mathrm{\ensuremath{-}}}
2{\mathit{p}}_{1/2}$ Lamb splitting in the unperturbed hydrogen system. The experimental data are well described by the results of a time-dependent theory.
The evolution of a (n=2) hydrogen atom passing through a linearly increasing or decreasing electric field is calculated in a three-state approximation. The observable fraction of 2p 1/2 , 2s 1/2 and 2p 3/2 quantum state in the resulting coherent mixture is calculated. The amplitude of the oscillations, which appear when the field parameters are varied, is shown to depend only on the rate of change of the field, as seen by the atom. Maps of oscillation amplitudes and average values are given for the metastable atom. Comparison is made with the sudden and adiabatic approximations.