Here is a short note on setting thresholds in the neutron bars. Similar
considerations will hold for the LADS bars, but the numbers need to be
adjusted for the thicknesses.
For the Ohio n-bars, they are 10 cm thick to neutrons and 22.5 cm thick
to cosmics. It has always been planned to use cosmics as a calibration
standard, including using a "cosmics" trigger between the top and
bottom bars. Note that this trigger still allows for cosmics to pass
through a much larger thickness than the 22.5 cm vertical dimension
as long as they are still in the plane of the n-wall. A cut on the
time difference between the n-bar ends in the top and bottom bars will
pick out (almost) vertical cosmics.
Assuming we pick out almost vertical cosmics, they lose 45 MeV in each
n-bar. So the question to ask is: what is the useful range of neutron
energy deposition in the n-bar?
Assuming that the most interesting region for BLAST to contribute to
a measurement of Gen is in the low Q^2 region, like 0.1 to 0.3 GeV^2,
we need to optimize for that region. Let's assume we want to go as low
as Q^2 = 0.05 GeV^2. Neglecting the Fermi momentum in the deuteron for
the moment, the corresponding neutron energy is 25 MeV. The corresponding
momentum is a hair less than 220 MeV/c. Taking into account the Fermi
momentum spreads that momentum by +/- 50 MeV/c. So we can have neutrons
with momentum as low as 170 MeV/c, corresponding to neutron kinetic
energies of 15 MeV. The energy loss in the n-bar comes from mainly
s-wave scattering off protons which produces a proton spectrum that is
theoretically uniform from 0 to 15 MeV. However, whereas the conversion
from energy deposition to light is essentially 100% efficient for
relativistic particles (electrons, cosmics), it is much less efficient
for lumbering behemoths such as slow protons. There exists an old rule
of thumb that gives the light yield in this energy range as 0.6*E - 1.3
meaning a 15 MeV proton produces light equivalent to a 7.7 MeV electron
energy loss. Given that the light spectrum from 15 MeV neutrons will be
a roughly uniform distribution, therefore, from 0 to 7.7 MeV electron
equivalent, if we want 6/7 of the theoretical efficiency offered by the
10 cm thickness of the n-bar, we need to set the threshold of the
discriminator to the equivalent of a 1.1 MeV electron energy loss, or
about 1/40 of the cosmic signal.
This is relaxed by about a factor of 2 if we only care about Q^2 of
0.1 or higher. However it is my suspicion that, at present, the thresholds
on the n-bar discriminators are MUCH higher than this and that this is
probably the explanation of Vitaliy's weak neutron yield in comparison
to Igor P.'s thesis from NIKHEF.
-- John R. Calarco Dept. of Physics Univ. of New Hampshire Durham, NH 03824 phone: (603)862-2088 FAX: (603)862-2998 email: calarco@unh.edu
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