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Renormalisation of Hydrogen Partition Function and Saha Ionisation Equation

  • George Savvidy
  • Pengming Zhang
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Abstract

An important physical quantity that is part of the Saha ionisation equation is the partition function of the neutral hydrogen atoms. An immense uncertainty is caused by the divergency of the neutral atom partition function arising due to the fast growing degeneracy factor of its excited n-state. We suggested a regularisation and renormalisation procedure for the partition function of the neutral hydrogen atoms. The renormalised partition function is well defined and allows to calculate the population of the energy levels and the ionisation state of the hydrogen plasma as a function of its temperature and pressure. In the low-temperature limit the behaviour of these functions smoothly transforms to the Saha equation, which is used in the description of the low-temperature plasma. At higher temperatures the renormalised ionisation equation describes the deviation from the Saha equation. The application of the renormalised ionisation equation to the solar core and atmosphere is considered.

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Cite

BibTeXRIS
BibTeX
@misc{savvidy2026renormalisation,
  title = {{Renormalisation of Hydrogen Partition Function and Saha Ionisation Equation}},
  author = {George Savvidy and Pengming Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03671},
  eprint = {2611.03671},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03671},
}
RIS
TY  - UNPB
TI  - Renormalisation of Hydrogen Partition Function and Saha Ionisation Equation
AU  - George Savvidy
AU  - Pengming Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.03671
UR  - https://arxiv.org/abs/2611.03671
AB  - An important physical quantity that is part of the Saha ionisation equation is the partition function of the neutral hydrogen atoms. An immense uncertainty is caused by the divergency of the neutral atom partition function arising due to the fast growing degeneracy factor of its excited n-state. We suggested a regularisation and renormalisation procedure for the partition function of the neutral hydrogen atoms. The renormalised partition function is well defined and allows to calculate the population of the energy levels and the ionisation state of the hydrogen plasma as a function of its temperature and pressure. In the low-temperature limit the behaviour of these functions smoothly transforms to the Saha equation, which is used in the description of the low-temperature plasma. At higher temperatures the renormalised ionisation equation describes the deviation from the Saha equation. The application of the renormalised ionisation equation to the solar core and atmosphere is considered.
ER  -