We’re coming up on the golden anniversary of some very important experiments that were milestones in confirming relativity and were enabled by a breakthrough in nuclear physics, the Mossbauer effect. Mossbauer’s discovery (published in 1958) of the Mossbauer effect (what were the odds of that happening?) was that nuclei in a lattice had essentially no recoil when emitting gammas, since effectively they shared the mass of the entire sample. Normally, the conservation of momentum from the recoil of a nucleus shifted the gamma’s energy out of resonance, meaning that the gamma would not be reabsorbed by an identical nucleus; even though the recoil from the emission of a 100 keV gamma would only cause a shift of a few thousandths of a eV in the gamma’s energy, this is significantly larger than the width of the transition. However, effectively increasing the mass of the emitter by even a small fraction of Avogadro’s number — which you can do with just a speck of material — all but eliminates that energy shift, and the ground-state nucleus will absorb the photons emitted by the excited state.
This incredible new tool set the stage for several experiments in General and Special Relativity. One is the famous Pound-Rebka experiment that took place at the Jefferson Lab tower at Harvard. The premise of the experiment was that a photon climbing or falling in a potential well would be red- or blueshifted, and this could be compensated for by moving the source; when the Doppler shift canceled the gravitational effect, the photons would be on resonance and be absorbed by the target, but at other speeds would not be absorbed. This would cause a variation in the number of photons striking a detector. The gravitational redshift is small, $latex gh/c^2 = 2.45 x10^-15 $ and the Doppler shift necessary to compensate is just $latex 7 x 10^-7 m/s$ . This sensitivity is doubled by reversing the experiment and looking for the blueshift of a falling photon. The source, Fe-57 (from a decay in Co-57) has a transition at 14.4 keV, and is narrow (about 10^-8 eV) owing to a ~100 ns lifetime.
The simplicity of the basic experiment masks some subtleties of device. The source and absorber needed to be specially prepared; the Co was diffused into a thin Fe sheet so that the source was in a very thin layer near the surface, and for the target a thin layer of Fe was electroplated onto a Be disc. These were vertically separated by 22.5 meters, and to reduce absorption by air, this space was taken by a mylar bag filled with Helium. The source was put on a transducer, i.e. a speaker cone, and oscillated at low frequency. To eliminate thermal effects, since the difference in thermal motion between the source and target materials could shift the nuclei out of resonance, they were stabilized to the same temperature.
The second order Doppler shift resulting from
lattice vibrations required that the temperature
difference between the source and absorber be
controlled or monitored. A difference of 1ºC
would produce a shift as large as that sought, so
the potential difference of a thermocouple with
one junction at the source and the other at the
main absorber was recorded. An identical system
was provided for the monitor channel.
The results agreed to about 10%, and a later experiment by Pound and Snider agreed to 1%
But it doesn’t end there. A lesser-know cousin to this experiment was carried out to observe the frequency shift in a rotating system. Once again using the Mossbauer spectroscopy of Fe-57, the source and target were mounted on the axle and rim of a cylinder, which was then rotated at some speed. In this case, one can look at the effect either by viewing this as a pseudo-gravitational potential or as a kinematic time dilation effect (both approaches, not surprisingly, yield the same answer), with the fractional frequency shift of $latex v^2/2c^2 $ . The cylinder was rotated at different speeds and the increase in the counting rate was observed, as the target moved out of resonance with the source due to the frequency shift of the target.
Gravitational Red-Shift in Nuclear Resonance
Phys. Rev. Lett. 3, 439 – 441 (1959)
R. V. Pound and G. A. Rebka, Jr.
Apparent Weight of Photons
Phys. Rev. Lett. 4, 337 – 341 (1960)
R. V. Pound and G. A. Rebka, Jr.
Measurement of the red shift in an accelerated system using the Mossbauer effect in Fe-57
Phys. Rev. Letters. 4, 165 (1960)
H. J. Hay, J. P. Schiffer, T. E. Cranshaw, and P. A. Egelstaff
Measurement of Relativistic Time Dilatation using the Mössbauer Effect
Nature 198, 1186 – 1187 (22 June 1963)
D. C. Champeney, G. R. Isaak and A. M. Khan