Soviet Astronomy

Two-Photon Transitions between Hyperfine-Structure Levels of the 1S State of the Hydrogen Atom

V.P. Demidov

Published May 1, 1962• 0 citations

Abstract

The probabilities of two-photon transitions between hyperfine-structure levels of the ground state of the hydrogen atom in the presence and absence of an external field are computed. These are found to be extremely small; therefore two-photon processes cannot have any influence on radio-astronomical measurements on a wave length of 2l cm. (auth)

Related papers

Probabilities of single-photon 2s–1s transition in hydrogen and antihydrogen atoms in an external electric field

D. A. Solov’ev, V. Sharipov, L. N. Labzovskiǐ +1 more

The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in an external electric field are calculated. These quantities are different for H and $$ \bar H $$ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.

Optics and SpectroscopyApr 1, 20085 citations

Two Photon Processes within the Hyperfine Structure of Hydrogen

Spencer Dylan Percy

Jan 1, 20180 citations

Influence of an external electric field on the probabilities of two-photon transitions between 2s, 2p and 1s levels for hydrogen and antihydrogen atoms

Dmitry A. Solovyev, Leonti N Labzowsky, V. Sharipov

The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and $$ \bar H $$ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.

Optics and SpectroscopyJul 1, 20091 citation

Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and antihydrogen atoms and hydrogen-like ions

Dmitry A. Solovyev, V Sharipov, Leonti N Labzowsky +1 more

arXiv:0904.1503Journal of Physics B Atomic Molecular and Optical PhysicsMar 19, 201018 citations

Two-photon transitions to excited states in atomic hydrogen

A. Quattropani, F. Bassani, Sandra Carillo

Resonant two-photon transition rates from the ground state of atomic hydrogen to ns excited states have been computed as a function of photon frequencies in the length and velocity gauges in order to test the accuracy of the calculation and to discuss the rate of convergence over the intermediate states. The dramatic structure of the transition rates produced by intermediate-state resonances is exhibited. A two-photon transparency is found in correspondence to each resonance.

Physical Review AJun 1, 198262 citations

Magnetic-field-enhanced spontaneous two-photon emission of hydrogenic atoms

P. C. Stancil, G. E. Copeland

Physical Review AJul 1, 19938 citations

Soviet Astronomy

Two-Photon Transitions between Hyperfine-Structure Levels of the 1S State of the Hydrogen Atom

V.P. Demidov

Published May 1, 1962• 0 citations

OpenAlex

Abstract

Related papers

Probabilities of single-photon 2s–1s transition in hydrogen and antihydrogen atoms in an external electric field

D. A. Solov’ev, V. Sharipov, L. N. Labzovskiǐ +1 more

The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( $\bar H$ ) atoms in an external electric field are calculated. These quantities are different for H and $\bar H$ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in an external electric field are calculated. These quantities are different for H and $$ \bar H $$ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.

Optics and SpectroscopyApr 1, 20085 citations

Two Photon Processes within the Hyperfine Structure of Hydrogen

Spencer Dylan Percy

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 Pb $^{81+}$ . Modifications for the case of isotopes with a nuclear spin greater than $1/2$ are briefly consideredThe 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 Pb$^{81+}$. Modifications for the case of isotopes with a nuclear spin greater than $1/2$ are briefly considered

Jan 1, 20180 citations

Influence of an external electric field on the probabilities of two-photon transitions between 2s, 2p and 1s levels for hydrogen and antihydrogen atoms

Dmitry A. Solovyev, Leonti N Labzowsky, V. Sharipov

The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( $\bar H$ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and $\bar H$ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and $$ \bar H $$ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.

Optics and SpectroscopyJul 1, 20091 citation

Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and antihydrogen atoms and hydrogen-like ions

Dmitry A. Solovyev, V Sharipov, Leonti N Labzowsky +1 more

One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is also evaluated and possible applications of the results are discussed.One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is also evaluated and possible applications of the results are discussed.

arXiv:0904.1503Journal of Physics B Atomic Molecular and Optical PhysicsMar 19, 201018 citations

Two-photon transitions to excited states in atomic hydrogen

A. Quattropani, F. Bassani, Sandra Carillo

Physical Review AJun 1, 198262 citations

Magnetic-field-enhanced spontaneous two-photon emission of hydrogenic atoms

P. C. Stancil, G. E. Copeland

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{} ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{} ${10}^{6}$ T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{} ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{} ${10}^{8}$ T. The transition rate is shown to scale as ${\mathit{Z}}^{4}$ for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300 ${\mathit{Z}}^{2}$ 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 2 ${\mathit{p}}_{0}$ 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.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{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}${10}^{6}$ T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}${10}^{8}$ T. The transition rate is shown to scale as ${\mathit{Z}}^{4}$ for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300${\mathit{Z}}^{2}$ 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 2${\mathit{p}}_{0}$ 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.

Physical Review AJul 1, 19938 citations

The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen (

\bar H

) atoms in an external electric field are calculated. These quantities are different for H and

\bar H

due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.

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 Pb

^{81+}

. Modifications for the case of isotopes with a nuclear spin greater than

1/2

are briefly considered

The probabilities of two-photon decay for hydrogen (H) and antihydrogen (

\bar H

) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and

\bar H

atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.

{10}^{8}

${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 1.41\ifmmode\times\else\texttimes\fi{}

{10}^{6}

T, approaching that of the 2p-1s one-photon rate, and to drop slightly to 1.055\ifmmode\times\else\texttimes\fi{}

{10}^{8}

${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 4.7\ifmmode\times\else\texttimes\fi{}

{10}^{8}

T. The transition rate is shown to scale as

{\mathit{Z}}^{4}

for hydrogenic ions with nuclear charge Z in fields \ensuremath{\ge}3300

{\mathit{Z}}^{2}

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 2

{\mathit{p}}_{0}

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.