AREG Benchmark (2025).
paperAuthors
Credibility Rating
Good quality. Reputable source with community review or editorial standards, but less rigorous than peer-reviewed venues.
Rating inherited from publication venue: arXiv
This physics paper on nuclear recoil and finite-size effects in hydrogenic systems is not directly relevant to AI safety; it addresses quantum electrodynamics calculations for atomic systems.
Paper Details
Metadata
Abstract
Formulas for the combined nuclear-recoil and finite-nuclear-size effects of order $(Z\,α)^5$ and $(Z\,α)^6$ are derived without any expansion in the nuclear charge radius $r_C$, making them applicable to both electronic and muonic atoms. The obtained results are particularly relevant for high-precision determinations of root-mean-square charge radii from muonic atom spectroscopy. We demonstrate that calculations of the atomic isotope shift based on the widely used Breit approximation give rise to an unphysical nuclear-size contribution that is linear in the nuclear charge radius $r_C$ at order $(Z\,α)^5$. This spurious term vanishes in a full QED treatment, leaving the correct contribution quadratic in $r_C$. For electronic atoms, this quadratic term is significantly smaller than the spurious linear contribution.
Summary
This paper derives precise formulas for combined nuclear-recoil and finite-nuclear-size effects in hydrogenic systems at orders (Zα)⁵ and (Zα)⁶ without expanding in nuclear charge radius, applicable to both electronic and muonic atoms. A key finding is that the widely-used Breit approximation produces an unphysical linear dependence on nuclear charge radius at order (Zα)⁵, which vanishes in full QED treatment, leaving only the correct quadratic contribution. These results are particularly important for high-precision determinations of nuclear charge radii from muonic atom spectroscopy and isotope shift measurements.
Cited by 1 page
| Page | Type | Quality |
|---|---|---|
| Large Language Models | Capability | 60.0 |
Cached Content Preview
[2502.09455] Recoil nuclear size corrections in hydrogenic systems
Recoil nuclear size corrections in hydrogenic systems
Krzysztof Pachucki
Faculty of Physics, University of Warsaw,
Pasteura 5, 02-093 Warsaw, Poland
Vojtěch Patkóš
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague
2, Czech Republic
Vladimir A. Yerokhin
Max–Planck–Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
Abstract
Formulas for the combined nuclear-recoil and finite-nuclear-size effects of order ( Z α ) 5 (Z\alpha)^{5} and ( Z α ) 6 (Z\alpha)^{6} are derived without any expansion in the nuclear charge radius r C r_{C} , making them applicable to both electronic and muonic atoms. The obtained results are particularly relevant for high-precision determinations of root-mean-square charge radii from muonic atom spectroscopy.
We demonstrate that calculations of the atomic isotope shift based on the widely used Breit approximation give rise to an unphysical nuclear-size contribution that is linear in the nuclear charge radius r C r_{C} at order ( Z α ) 5 (Z\alpha)^{5} . This spurious term vanishes in a full QED treatment, leaving the correct contribution quadratic in r C r_{C} . For electronic atoms, this quadratic term is significantly smaller than the spurious linear contribution.
I Introduction
The finite nuclear size modifies the Coulomb potential in the vicinity of the nucleus.
Although this effect occurs in the range of just a few femtometers — much smaller
than the typical localization region of the wave function ∼ 10 5 \sim 10^{5} fm’s —
the resulting shift of energy levels is significant.
For example, the 1 S 1S - 2 S 2S transition in hydrogen is affected by as much as 1 MHz, which should be
compared to
the experimental accuracy of 10 Hz [ 1 , 2 ]
and the theoretical uncertainty of 1 kHz [ 3 ] .
It is possible to determine the proton charge radius (and, simultaneously, the Rydberg constant)
from observed hydrogen transition energies. A comparison of the extracted radius with an
independent determination from the muonic hydrogen [ 4 ] resulted in a long-standing
discrepancy, known as the “proton radius puzzle”. This discrepancy has now been largely
resolved in favor of the muonic-hydrogen radius [ 3 ] .
For atoms with more than one electron, absolute charge radius determinations are not yet feasible, as theoretical precision has not reached the required level. However, it is possible to determine differences of nuclear charge radii between two isotopes of the same element.
Of particular interest is the comparison of the nuclear radius differences obtained from electronic and muonic atoms. This comparison is highly sensitive to nuclear polarizability effects and provides an opportunity to test fundamental interaction theories.
This field has been developing rapidly in recent years. For instance, the diffe
... (truncated, 86 KB total)965fd9843dbf74c4 | Stable ID: ZmJlOTAwMT