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Journal of Physics B Atomic and Molecular Physics

The two-photon emission from the triplet metastable state of He I

Oleg Bely

Published Jul 1, 1968• 13 citations
Publisher

Abstract

The theoretical expression for the probability of two-photon decay of helium in the 2 3 S 1 metastable level is derived. It is found that this expression is quite different from the corresponding expression for the 2 1 S 0 -> 1 1 S 0 transition. It is shown that the transition probability computed by Mathis in 1957 is overestimated by a very large amount and that A (2 3 S 1 -> 1 S 0 ) less, similar 10 -10 s -1 .

DOI
10.1088/0022-3700/1/4/323

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•Jan 1, 2023•2 citations
The theoretical expression for the probability of two-photon decay of helium in the 2 3 S 1 metastable level is derived. It is found that this expression is quite different from the corresponding expression for the 2 1 S 0 -> 1 1 S 0 transition. It is shown that the transition probability computed by Mathis in 1957 is overestimated by a very large amount and that A (2 3 S 1 -> 1 S 0 ) less, similar 10 -10 s -1 .
The two-photon decay mode of hydrogenic atoms from an arbitrary state (n1{n}_{1}n1​, l1{l}_{1}l1​, m1{m}_{1}m1​) to an arbitrary state (n2{n}_{2}n2​, l2{l}_{2}l2​, m2{m}_{2}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 2s2s2s 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.
It has been found by Breit and Teller that double photon emission is the principal cause of decay of interstellar hydrogen atoms from their metastable 2s2s2s state and the mean life corresponding to this decay was bracketed by them between upper and lower limits. In the present note an account is given of a more accurate evaluation of the transition probability ${A}_{\ensuremath{\tau}}=(8.226\ifmmode\pm\else\textpm\fi{}0.001){Z}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, where ZZZ is the atomic number. Relativistic effects on the atomic wave functions have been neglected in the calculations which are therefore accurate only for small ZZZ.
There have been relatively few investigations of multiphoton ionization from metastable helium. Of particular interest has been the work of Haberland et al. 1987 and Haberland and Oschwald 1988. In both the 1987 and 1988 papers they have described the two photon ionization of metastable helium. In each of these studies they have reported the occurrence of unexplained structure along the wings of their resonance profiles. Upon the performance of similar measurements by this study, the unexplained structure is not seen and the agreement of the experiment's measurements with the theoretical shape of the resonance curves has been good. To experimentally verify these resonance effects, we have used a tunable dye laser in conjunction with a time of flight mass spectrometer to create and detect ions from metastable helium by two-photon absorption. The use of a metastable state instead of the ground state is advantageous because of its proximity to the ionization continuum and its extended lifetime. Using a metastable state as a starting point for multiphoton absorption requires fewer photons to reach the ionization threshold. The extended lifetime of the state also makes it easy to access experimentally. For helium the singlet metastable state 2$\sp1$S lies at 20.61 eV above the ground level with a natural lifetime of close to a millisecond. Two photons of 501.7 nm and 504.35 nm are required for the ionization processes in resonance with the 3$\sp1$P and the 3$\sp1$D states. This thesis is the accounting of the experimental process involved in the measurement of the dipole and quadrupole resonances of two photon ionization from singlet metastable helium. The study includes the description of the laser, electron gun assembly for metastable helium creation, and the time of flight mass spectrometer. A discussion of the theory of multiphoton processes is included along with the discussion of the data, its reduction and analysis, and a comparison with theoretical prediction. This study has not only involved the acquisition of definitive atomic spectra data sets, but has also established a facility for resonant ionization spectroscopy at The American University.