Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Test of the theoretical hyperfine structure of the molecular hydrogen
  ion at the 1-ppm level   We revisit the $m \alpha^6 (m/M)$ order corrections to the hyperfine
splitting in the H$_2^+$ ion, and find a hitherto unrecognized second-order
relativistic contribution associated with the vibrational motion of the nuclei.
Inclusion of this correction term produces theoretical predictions which are in
excellent agreement with experimental data [K. B. Jefferts, Phys.\ Rev.\ Lett.\
\textbf{23}, 1476 (1969)], thereby concluding a nearly fifty years long
theoretical quest to explain the experimental results within their 1-ppm error.
The agreement between theory and experiment corroborates the proton structural
properties as derived from the hyperfine structure of atomic hydrogen. Our work
furthermore indicates that for future improvements, a full three-body
evaluation of the $m \alpha^6 (m/M)$ correction term will be mandatory.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex