TY - JOUR
T1 - The Coulomb Attraction in Hydrogen May Not Be of Long Range
AU - Cheng-Gang Gu
JO - Journal of Atomic and Molecular Sciences
VL - 4
SP - 325
EP - 336
PY - 2010
DA - 2010/01
SN - 1
DO - http://doi.org/10.4208/jams.020210.050710a
UR - https://global-sci.org/intro/article_detail/jams/8094.html
KW - hydrogen atom, hyperfine structure sectra, Lamb shift, Lande $g$ factor, Coulomb force, gravitation, dark energy.
AB - <p style="text-align: justify;">A quantum stationary wave has been examined in an exchange field, which induces 
the force of the form $F(r)=f_{2}(1/r^{2}-f_{1}/r)$. For the Coulomb attraction 
in hydrogen atom, the inexplicable discrepancy (0.0023 MHz) between the theoretical 
and experimental frequencies for its $^{1}S_{1/2}$ has been verified. It is found 
that the tiny $f_{1}$ is $7.45\times10^{-12}a_{1}$$^{-1}$($a_{1}$ is the 1st 
Bohr radius). Meanwhile, when such an $f_{1}$ is considered in the $n=2$ Lamb 
shift, it causes -0.034 MHz difference, which is in good agreement with the 
deviation of -0.039 MHz between the experimental and one of the theoretical 
predictions. Similar of searchings are made for the Lande $g$ factor for the 
$H_{\beta}$ spectrum. This $f_{1}$ contributes a ratio $\Delta g/g=5.58\times10^{-11}$ 
and makes both the experiment and theory well agreed within the experimental 
relative uncertainty $\pm4\times10^{-12}$. In other words, these phenomena can 
be treated as the reliable physical evidences for the existence of the same 
repulsion. More importantly, they consistently and strongly imply that the maximum 
radius for the Coulomb attraction in hydrogen atom can not exceed 7.11$m$ 
(if extrapolated). In addition, this analysis prompts us similar cases probably 
occur in the gravitation because it is also an exchange field, and the repulsion 
at remote distance may be one kind of dark energy that may have been ignored.</p>