Long-Range Interactions for Hydrogen: 6P–1S and 6P–2S Systems

Adhikari, Chandra Mani

doi:10.3390/atoms5040048

Cited by 9 publications

(16 citation statements)

References 29 publications

(106 reference statements)

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“…Just like in Ref. [19], we shall use the notation |n, ℓ, J, F, F z for the thusly obtained states, using the vector coupling coefficients, with principal quantum number n, orbital quantum number ℓ, total electron angular quantum number J, total angular quantum number F (electron+nucleus), and total magnetic projection quantum number F z . Up to the hyperfine-fine-structure mixing term, which is discussed in Eq.…”

Section: Explicit Construction Of the Statesmentioning

confidence: 99%

“…I of Ref. [19], we here recall how to construct the atomic states for the hyperfine-resolved 4P 1/2 -1S interaction. The relevant quantum numbers are…”

Section: Explicit Construction Of the Statesmentioning

confidence: 99%

“…In full analogy to the 1S-6P system analyzed in Ref. [19], we have ordered the basis vectors in ascending order of the quantum numbers, starting from the last member in the list. The Hamiltonian matrix evaluates to…”

Section: Manifoldmentioning

confidence: 99%

“…Phenomenologically, transitions to the 4P state have been much more relevant than, say, transitions to P states with n = 6 (see Ref. [19]), because of the much better accessible frequency range of the transition for lasers (see Refs. [13,20]).…”

Section: Introductionmentioning

confidence: 99%

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Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom–atom and atom–molecule interactions

Adhikari

Dawes

Matveev

et al. 2019

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

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We study the theoretical foundations for the pressure shifts in highprecision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P 1/2 and 4P 3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P -2S interaction, where the inclusion of quasidegenerate 4S-2P 1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasidegenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R 6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atommolecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.Pressure Shifts in High-Precision Hydrogen Spectroscopy: I. states, which are removed from each other only by the Lamb shift, fine-or hyperfine structure. Namely, the fine-structure and the hyperfine-structure splittings in the case of atom-atom interactions are very small compared to the energy differences between atomic and molecular quasi-degenerate levels, even if one consider possible excitations to ro-vibrational levels. For example, in the case of the 4P (H)-1S(H) interaction, the fine structure and the hyperfine structure splitting parameters are of the order of 2×10 −7 E h and 9 × 10 −9 E h , respectively, where E h = 27.211396 eV is the Hartree energy [21]. However, in the case of the 4P (H)-1S(H 2 ) interaction, the atom-molecules degenerate states' separation is in the order of 2 × 10 −2 E h and the ro-vibrational level splitting is at-most ∼ 5.5 × 10 −5 E h . The oscillator strengths, in either cases, are of the same order of magnitude. As the respective energy differences appear in the denominator of the propagator denominators within perturbation theory, which determine the C 6 coefficients, we can anticipate that the so-called van der Waals C 6 coefficients are enhanced for atom-atom as compared to atom-molecule collisions. This is explained in greater detail in Sec. 5.In order to understand the systems more deeply, we should consider the particular properties of the van der Waals Hamiltonian mediating the interaction. Let us refer to the atoms participating ...

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Section: Explicit Construction Of the Statesmentioning

confidence: 99%

“…I of Ref. [19], we here recall how to construct the atomic states for the hyperfine-resolved 4P 1/2 -1S interaction. The relevant quantum numbers are…”

Section: Explicit Construction Of the Statesmentioning

confidence: 99%

Section: Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom–atom and atom–molecule interactions

Adhikari

Dawes

Matveev

et al. 2019

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

Self Cite

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“…We shall notice that in our theoretical works (Refs. [14,18]), the energy shift for both the 1S and 2S collisions are averaged over all possible hyperfine states. The particular interest of the current work is concentrated on the 2S-4P and 2S-6P experiments at the Max Planck Institute at Garching, where atoms are prepared in the metastable 2S(F = 0) state [1].…”

Section: Cross Sectionsmentioning

confidence: 99%

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

Matveev

Kolachevsky

Adhikari

2019

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

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We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.

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Pressure shifts in high-precision hydrogen spectroscopy. I. long-range atom–atom and atom–molecule interactions

Adhikari¹,

Dawes²,

Matveev³

et al. 2019

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

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Long-Range Interactions for Hydrogen: 6P–1S and 6P–2S Systems

Cited by 9 publications

References 29 publications

Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom–atom and atom–molecule interactions

Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom–atom and atom–molecule interactions

Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

Pressure shifts in high-precision hydrogen spectroscopy. I. long-range atom–atom and atom–molecule interactions

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