Many dynamical explanations for dark energy imply that the fine structure constant α, which determines the strength of electromagnetic interactions, could vary over cosmological time scales. There are intriguing hints, from absorption spectra of interstellar matter, that α may have been smaller in the distant past than it is today. As first pointed out by Shlyakhter (in the mid-1970s), Oklo data constrains shifts in neutron capture resonance energies over the time since the reactors were last active (about 1.8 billion years ago), and, hence, changes in interaction coupling strengths in the nuclear Hamiltonian like α. Following Shlyakhter’s lead, Damour and Dyson concluded (in a study conducted in the mid-1990s) that Oklo data on the absorption of neutrons by 149Sm limit the change in α to less than 0.1 parts per million (ppm) over the last 1.8 billion years. Model dependent considerations indicate that it is difficult to reconcile this upper bound with the behavior of α inferred from interstellar absorption spectra, but there is a tendency in the literature to ignore the Oklo-based limit because of the perception that the nuclear physics invoked in its derivation is fraught with substantial unquantifiable uncertainties. We have addressed these and other uncertainties using a more detailed model of the pertinent state in the compound nucleus 150Sm and an improved choice of nuclear parameters. Central to our calculations are the neutron, proton and charge densities near the surface of the excited 150Sm nucleus. In lieu of experimental data, we argue that the eigenstate thermalization hypothesis allows us to adapt the micro-canonical ensemble treatment of mononuclear configurations formed in heavy ion reactions to the determination of the surface properties of the 150Sm compound nucleus. Key inputs include a study of the energetics of surface diffuseness by Myers and Swiatecki and the leptodermous expansion of the level density parameter, as well as the representation of densities as deformed Fermi functions. In all, four models, tuned to reproduce nuclear data, are used to compute the sensitivity of the relevant 150Sm resonance energy to changes in α. We employ the mean of the four results and their standard deviation as our best estimate for the sensitivity and its uncertainty, respectively. Subject to a weak and testable restriction on the change in light quark masses over the last 1.8 billion years, we deduce that the change in α is less than 0.01 ppm (95% C.L.). This bound reinforces the idea that, of the many dark energy models which predict that fundamental constants do change, only those which suppress the variation of α in the presence of matter are phenomenologically acceptable.

1.
P. A. M.
Dirac
,
Nature
139
,
323
(
1937
).
2.
J.-P.
Uzan
,
Rev. Mod. Phys.
75
,
403
455
(
2003
).
3.
J. K.
Webb
,
V. V.
Flambaum
,
C. W.
Churchill
,
M. J.
Drinkwater
and
J. D.
Barrow
,
Phys. Rev. Lett.
82
,
884
887
(
1999
).
4.
J. K.
Webb
,
J. A.
King
,
M. T.
Murphy
,
V. V.
Flambaum
,
R. F.
Carswell
and
M. B.
Bainbridge
,
Phys. Rev. Lett.
107
,
191101
(
2011
).
5.
S.-E.
Bentridi
,
B.
Gall
,
F.
Gauthier-Lafaye
,
A.
Seghour
and
D.-E.
Medjadi
,
C. R. Geoscience
343
,
738
748
(
2011
).
6.
E. D.
Davis
,
C. R.
Gould
and
E. I.
Sharapov
,
Int. J. Mod. Phys. E
23
,
1430007
(
2014
).
7.
A. I.
Shlyakhter
,
Nature
264
,
340
(
1976
).
8.
T.
Damour
and
F. J.
Dyson
,
Nucl. Phys. B
480
,
37
54
(
1996
).
9.
E. D.
Davis
and
L.
Hamdan
,
Phys. Rev. C
92
,
014319
(
2015
).
10.
G.
Scamps
,
D.
Lacroix
,
G. G.
Adamian
and
N. V.
Antonenko
,
Phys. Rev. C
88
,
064327
(
2013
).
11.
Y. K.
Gambhir
,
J. P.
Maharana
,
G. A.
Lalazissis
,
C. R.
Panos
and
P.
Ring
,
Phys. Rev. C
62
,
054610
(
2000
).
12.
B. K.
Agrawal
,
T.
Sil
,
S. K.
Samaddar
and
J. N.
De
,
Phys. Rev. C
63
,
024002
(
2001
).
13.
T.
Sil
,
B. K.
Agrawal
,
J. N. De and S. K.
Samaddar
,
Phys. Rev. C
63
,
064302
(
2001
).
14.
J. L.
Egido
,
L. M.
Robledo
and
V.
Martin
,
Phys. Rev. Lett.
85
,
26
29
(
2000
).
15.
V.
Martin
,
J. L.
Egido
, and
L. M.
Robledo
,
Phys. Rev. C
68
,
034327
(
2003
).
16.
F.
Borgonovi
,
F. M.
Izrailev
,
L. F.
Santos
and
V. G.
Zelevinsky
,
Phys. Rep.
626
,
1
58
(
2016
).
17.
W. D.
Myers
and
W. J.
Swiatecki
,
Phys. Rev. C
60
,
054313
(
1999
).
18.
J.
Toke
and
W.
Swiatecki
,
Nucl. Phys. A
372
,
141
150
(
1981
).
19.
C. R.
Gould
,
E. I.
Sharapov
and
S. K.
Lamoreaux
,
Phys. Rev. C
74
,
024607
(
2006
).
20.
C.
van de Bruck
,
J.
Mifsud
and
N. J.
Nunes
,
J. Cosmol. Astropart. Phys.
2015
,
018
(
2015
).
21.
T.
Naito
,
R.
Akashi
and
H.
Liang
,
Phys. Rev. C
97
,
044319
(
2018
).
This content is only available via PDF.