Quantum Mechanics of One- and Two-Electron Atoms

Bethe, Hans A.; Salpeter, E. E.

doi:10.1007/978-3-662-12869-5

Cited by 4,199 publications

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“…In the case of H, the transition moments ⟨n ′ ′ m ′ μ α n m⟩ in Eq. (4) can be determined analytically as products of a radial and an angular integral [1,2]. In nonhydrogenic atoms, the radial part is determined numerically, e.g., using the Numerov integration method described in Ref.…”

Section: A Spontaneous Emissionmentioning

confidence: 99%

“…For low-Rydberg states, the scaling with n of τ n m is primarily determined by the n −3 2 dependence of the amplitude of Rydberg-electron wave function in the immediate vicinity of the ion core. Because the transition frequency ω GS,n m approaches a constant at high-n values, the lifetimes of low-states scale as [1,2] τ n m ∝ n 3 ,…”

Section: A Spontaneous Emissionmentioning

confidence: 99%

“…In the case of n = 30, m = 0 Stark states, the hard-sphere radius r hs is about 10 µm and Γ coll is 2.7 ⋅ 10 −5 cm −1 , which is of the same order of magnitude as ∆E (2) ij,Stark in the relevant range of electric-field strengths. In general, however, interacting atoms separated by a distance r experience slightly different electric-field strengths because of the inhomogeneity of the trapping field so that there is a first-order contribution ∆E (1) ij,Stark (F ) = 1.5 ∂F ∂r a 0 enr (24) to the energy change. Taking into account the typical field gradient (∂F ∂r) of 1.2 ⋅ 10 6 V/m 2 in the trap, one obtains ∆E (1) ij,Stark (F ) (hc) = 2.3 ⋅ 10 −4 cm −1 at a distance of 10 µm corresponding to the hard-sphere radius of an n = 30 Stark state, which is much larger than the estimated collisional broadening and effectively breaks the resonance condition and reduces the values of the hard-sphere radii.…”

Section: A Collision-induced Transitions Between Near-degenerate Levmentioning

confidence: 99%

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Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Seiler¹,

Agner²,

Pillet³

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

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Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number n in the range between 25 and 35, have been deflected by 90 ○ , decelerated and loaded into off-axis electric traps at initial densities of ≈ 10 6 atoms/cm −3 and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 K and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as n −4 and corresponding closely to the natural lifetimes of the initially prepared Rydberg-Stark states. The decay rate was found to continually decrease over time and to reach an almost n-independent rate of more than (1 ms) −1 after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. The calculations revealed that the atoms that remain in the trap for the longest times have larger absolute values of the magnetic quantum number m than the optically prepared RydbergStark states, and this observation led to the conclusion that a much more efficient mechanism than a purely radiative one must exist to induce transitions to Rydberg-Stark states of higher m values. While searching for such a mechanism, we discovered that resonant dipole-dipole collisions between Rydberg atoms in the trap represent an extremely efficient way of inducing transitions to states of higher m values. The efficiency of the mechanism is a consequence of the almost perfectly linear nature of the Stark effect at the moderate field strengths used to trap the atoms, which permits cascades of transitions between entire networks of near-degenerate Rydberg-atom-pair states. To include such cascades of resonant dipole-dipole transitions in the numerical simulations, we have generalized the two-state Förster-type collision model used to describe resonant collisions in ultracold Rydberg gases to a multi-state situation. It is only when considering the combined effects of collisional and radiative pr...

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Section: A Spontaneous Emissionmentioning

confidence: 99%

Section: A Spontaneous Emissionmentioning

confidence: 99%

Section: A Collision-induced Transitions Between Near-degenerate Levmentioning

confidence: 99%

See 1 more Smart Citation

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Seiler¹,

Agner²,

Pillet³

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

“…However, it turns out that in the Coulomb gauge (and also in the Landau gauge to that order) the twophoton contribution cancels the quadratic terms arising from the one-photon exchange diagram and one then is left with the Breit hamiltonian [2,19]. This explains why the Breit equation in its linearized approximation provides a correct result to order α 4 .…”

Section: C;mentioning

confidence: 99%

“…We begin with the Constraint Theory wave equations describing a system of two spin-1/2 particles composed of a fermion of mass m 1 and an antifermion of mass m 2 , in mutual interaction [7] : where α 1 (α 2 ) refers to the spinor index of particle 1 (2). γ 1 is the Dirac matrix γ acting in the subspace of the spinor of particle 1 (index α 1 ); it acts on Ψ from the left.…”

Section: The Covariant Breit Equationmentioning

confidence: 99%