### Abstract

We study the theoretical foundations for the pressure shifts in high-precision 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 quasi-degenerate 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 quasi-degenerate 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 atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.

Original language | English |
---|---|

Article number | 075005 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 52 |

Issue number | 7 |

DOIs | |

Publication status | Published - Mar 19 2019 |

### Fingerprint

### Keywords

- collisional broadening
- collisional shift
- impact approximation
- Monte-Carlo approach
- van der Waals interaction

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics

### Cite this

*Journal of Physics B: Atomic, Molecular and Optical Physics*,

*52*(7), [075005]. https://doi.org/10.1088/1361-6455/ab08cc-1

**Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom-atom and atom-molecule interactions.** / Jentschura, U.; Adhikari, C. M.; Dawes, R.; Matveev, A.; Kolachevsky, N.

Research output: Contribution to journal › Article

*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 52, no. 7, 075005. https://doi.org/10.1088/1361-6455/ab08cc-1

}

TY - JOUR

T1 - Pressure shifts in high-precision hydrogen spectroscopy. I. Long-range atom-atom and atom-molecule interactions

AU - Jentschura, U.

AU - Adhikari, C. M.

AU - Dawes, R.

AU - Matveev, A.

AU - Kolachevsky, N.

PY - 2019/3/19

Y1 - 2019/3/19

N2 - We study the theoretical foundations for the pressure shifts in high-precision 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 quasi-degenerate 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 quasi-degenerate 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 atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.

AB - We study the theoretical foundations for the pressure shifts in high-precision 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 quasi-degenerate 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 quasi-degenerate 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 atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.

KW - collisional broadening

KW - collisional shift

KW - impact approximation

KW - Monte-Carlo approach

KW - van der Waals interaction

UR - http://www.scopus.com/inward/record.url?scp=85065177253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065177253&partnerID=8YFLogxK

U2 - 10.1088/1361-6455/ab08cc-1

DO - 10.1088/1361-6455/ab08cc-1

M3 - Article

AN - SCOPUS:85065177253

VL - 52

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 7

M1 - 075005

ER -