Non-relativistic rates for the decay of 2s hydrogen atoms to the ground state by single-photon and two-photon emission in the presence of a homogeneous magnetic field of arbitrary strength (0<or=B<or=4.7*10 6 T) are calculated by variational procedures. Over the whole range of B, two-photon emission is the dominant process. As the magnetic field grows, the two-photon decay rate increases. It is found that the Markov approximation can be applied to the two-photon decay for magnetic fields of strength B>or=4.7*10 3 T.
Non-relativistic rates for the decay of 2s hydrogen atoms to the ground state by single-photon and two-photon emission in the presence of a homogeneous magnetic field of arbitrary strength (0<or=B<or=4.710 6 T) are calculated by variational procedures. Over the whole range of B, two-photon emission is the dominant process. As the magnetic field grows, the two-photon decay rate increases. It is found that the Markov approximation can be applied to the two-photon decay for magnetic fields of strength B>or=4.710 3 T.
Two-photon transitions for hydrogen and hydrogenlike ions in arbitrary magnetic fields are investigated using currently available nonrelativistic energy levels and one-photon dipole transition probabilities. For hydrogen, the 2s-1s two-photon spontaneous-decay rate is shown to increase rapidly with the strength of the applied field from its field-free value of 8.2284 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ to a maximum of 1.537\ifmmode\times\else\texttimes\fi{}108 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}106 T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}108 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}108 T. The transition rate is shown to scale as Z4 for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300Z2 T. The spectral distribution of the photons for the 2s-1s transition in a large field reveals interesting features including resonances due to migration of the 2p0 and 2${\mathit{p}}_{\mathrm{\ensuremath{-}}1}$ energy levels between the 1s and 2s levels and the appearance of minima resulting from destructive interference between the intermediate-state dipole terms. In the field-free case, these spectral features are only present for high-lying-state transitions, i.e., 3s-1s, 4s-1s, etc.
A simple and accurate variational method is formulated and applied to the ground and excited states of the hydrogen atom as well as the hydrogen molecule ion in a homogeneous magnetic field of arbitrary strength. For the ground state, the electronic wave function o is assumed to be a function of a single, appropriately chosen variable R which contains a variational parameter. The functional form of o, and the corresponding energy, are determined by solving a Schr6dinger- like equation, in which the variational parameter appears explicitly in the kinetic and potential energy terms. The variational parameter is optimized by minimizing the lowest eigenvalue of the equation. Excited states may also be obtained by a slight modification of the method, and explicit calculations are carried out for the m1 = - 1 first excited state of hydrogen and the ( )-state of H2 +. Numerical comparisons are made with some recent papers in the literature. Subject headings: atomic processes - magnetic fields - molecular processes - quantum mechanics
The two-photon decay mode of hydrogenic atoms from an arbitrary state (n1, l1, m1) to an arbitrary state (n2, l2, m2) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the 2s metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.
The hyperfine levels for the ground state of hydrogen are normally connected by magnetic dipole transitions. However, for astrophysical applications, it may be that two-photon electric dipole processes are also important over cosmological distances. This thesis sets up a general mathematical formalism for the calculation of two-photon processes within the hyperfine structure of an atom with spin 1/2, and applies it to the ground state of hydrogen. Rates are calculated for both spontaneous emission and absorption of radiation. Due to an extraordinary degree of cancellation in the matrix elements, the rates turn out to be too small to have a significant impact on astrophysical processes involving the absorption and emission of radiation. The results are nevertheless important in reducing the uncertainty due to possible contributions from these processes. Other two-photon processes involving Raman scattering are also considered and the relevant cross sections calculated. The calculations of the decay rate, absorption coefficient and Raman scattering cross section are extended to heavier hydrogenic ions as a function of the nuclear charge Z, using an approximate interpolation formula for the hyperfine splitting in the ground state. Results are presented for the hydrogenlike ions from He+ to Pb81+. Modifications for the case of isotopes with a nuclear spin greater than 1/2 are briefly considered
A sensitive test for any mixing of the 2S21 and 2P21 state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S 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 2S 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 2S 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.
A sensitive test for any mixing of the 2S21 and 2P21 state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S 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 2S 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 2S 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.