What detectors will be used? If sodium iodide detectors are used, you
should not need *many* microcuries; rather, you should be able to pull this
off with a license-exempt 1-uCi source. If much-less sensitive GeLi
detectors are used you will need more time, or a hotter source. I will
assume NaI because GeLi detectors are very expensive, and you probably don't
have two of them unless you are already familiar with gamma-coincidence
experiments.
The LBL reference Brian Whatcott provided is reasonable, except as mentioned
above, I don't see the need for a source hotter than a license-exempt source
unless you want a reasonably large separation between the detectors so the
angular correlation will have better resolution. I didn't see any reference
to the dimensions of the physical layout in the LBL description.
Here are a few more points...
(1) I take exception to calling this gamma-gamma coincidence. The 511-keV
photons from B+ annihilation are not gamma rays. Gamma rays come from the
nucleus and these definitely are not coming from the nucleus. They are more
properly referred to as annihilation photons, and the the shorthand way to
designate them is
(lower-case-Greek-letter-gamma)(superscript-plus/minus-symbol).
(2) These annihilation photons are not strictly 180 degrees apart because
they must conserve the momentum of the beta-plus. However, since the
beta-plus trajectories will be random, equal numbers of coincident photons
will be detected at angles both before and after the movable detector passes
through 180-degrees. Thus, the width of the observed 180-degree correlation
is partly caused by the non-180-degree correlation (while another part is
caused by the angular resolution of the goniometer/detector system). This
means if you lengthen the arms of the goniometer to get better resolution,
this will only narrow the peak up to some point, at which point further
narrowing won't be possible.
(3) The experimental set described in the LBL lab appears to be a counting
experiment only. The energies of the photons are not recorded. There
likely will be as many Compton-scattered photons detected (less than
511-kev) as 511-keV events. These Compton-scattered photos are fairly
isotropic, but "simultaneous" within the time resolution of the coincidence
experiment. This means they are true coincidences (not chance), but they do
not show show any angular correlation. Another source of true coincidences
that are not angularly-correlated at nearly 180 degrees are those between a
511-keV photon and a 1274-keV gamma.
These true (but not angularly-correlated) coincident photons might be the
background mentioned in the LBL lab under "analysis #3," but the wording of
"analysis #3" does not make any sense to me.
It is not clear in the LBL lab if the single-channel analyzers (SCA) are
making use of both upper and low-level discriminators (ULD and LLD) or just
LLD, or none. There is no mention of adjusting them "tightly" to single-out
the 511-keV photons. By "none" I mean that only the LLD is set, and it is
set just above noise events. This would mean the Compton events and
1274-keV events are not eliminated from the count. By properly setting the
ULD and LLD on a good SCA, one can indeed count primarily the 511-keV
photons. (There will still be Compton events from the 1274-keV gamma
falling in the 511-keV window. Perhaps this is what "analysis #3" is
talking about.)
(4) In a more sophisticated experiment, the spectrums from both detectors
would be recorded along with coincidence information. During analysis we
choose a peak in "spectrum one" then we have the computer show all the
events in "spectrum-two" that were in coincidence with the chosen events in
"spectrum one." If we choose the 511-keV peak in "spectrum one" then we
will see that both the 511-keV and the 1274-keV photons in "spectrum two"
often occur in coincidence. If we choose the 1274-keV peak in "spectrum one
then "spectrum-two's" 511-keV photon will often be in coincidence, but not
the 1274-keV photon. That's because two 1274-keV events could not have come
from the same beta-plus decay, and therefore are not coincident except for
chance coincidence.
Finding out which photons are coincident is a powerful tool for helping
elucidate decay schemes. If angular-correlation data are also obtained, the
technique is even more powerful.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu