I looked at those papers yesterday and while I don't feel I studied them enough
to offer a firm and authoritative opinion, I do have some concerns:
-It appears that the source is also rotating. The rotation speeds are quite high,
and it only takes a fraction of a mm/sec to shift the Mossbauer peak significantly.
(see figure 2a in second cited paper) I wonder if the deviations from k=0.5 is
an experimental artifact due to small effective velocity of the source?
-If I was setting up this experiment I would have the source stationary. To
eliminate this issue.
-It is pretty well accepted that there should be a shift due to the relativistic
Doppler shift due to the lateral speed of the rotating absorber. The
question is, is there another shift due to the radial acceleration? I might be
wrong, but I don't believe the "metric" used in the second paper makes
sense in this experiment, particularly the g_00 which would contribute
to a red or blue shift. I just don't think that is applicable here.
-If the source and absorber were both accelerating, or were in a
gravitational field, THEN a red/blue shift due to the acceleration would
be applicable, but in this rotating frame, not.
-The one effect of the radial acceleration I do wonder about has to do
with the extended duration of the Mossbauer interaction. The reason
the line width is so narrow is that the emission has a long decay time,
and as a result the recoil is taken up by many atoms in the lattice. If
during this time the absorber has an effective velocity wrt the source,
then there might be a shift in resonance. I'm skeptical of this mechanism
however because it would work both ways and broaden the resonance
rather than shift it. I'm also a bit skeptical that this mechanism would
apply at all.
My suspicion is that the measured deviation from k=0.5 is an experimental
artifact and not real.