Neutrino emission by the pair, plasma, and photo processes in the Weinberg-Salam model Page: 9 of 47
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Q/R, in units of keV. Notice that the pair neutrino process emits the most energetic
neutrinos and antineutrinos for all T. The average energy of pair neutrinos at T = 108K
is not shown since the pair emissivity is completely negligible compared to the photo and
pair emissivities there.
Note that the photo neutrino results do not extend beyond p> 1011 gm cm-3. This is
because the plasma frequency W becomes > 2mec2/h. At this point, numerical difficulties
prevent further calculation. However, by this time the plasma neutrino process is so
enormously dominant that we felt no need to continue calculations of the photo neutrino
emissivity and rate. BPS show that the photo neutrino emissivity at high density is ~ 10-6
of the plasma neutrino emissivity. The reaction plasmon -> e+ + e-+v + v can also occur
when the plasma frequency exceeds 2mec2/h.
The photoneutrino results shown in figures 2, 3, and 4 were done using 50000 random
points for the Monte Carlo integration. The formal errors are less than a percent for all
densities and temperatures where the photoneutrino emissivity dominates. The formal
error increased rapidly at high densities where the electron degeneracy becomes large. We
also performed Monte Carlo calculations using a finer grid in p - T space using only 5000
random points for each integration. The temperature range covered was from 108K <
T < 1011K in steps of A]log(T(K)) = 0.1 and the density range was 101 gm cm-3 < p <
101 gm cm-3 in steps of A log([p/pj}(gm cm-3)) = 0.125. The formal errors were only
a few percent for those densities and temperatures where the photoneutrino emissivity
dominates. The 5000 point results agree very well with the more accurate 50000 point
results for those temperatures and densities where they were both calculated. The 5000
point results were used to calibrate our fitting formulae, which we now present.
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Schinder, P. J.; Schramm, D. N.; Witta, P. J.; Margolis, S. H. & Tubbs, D. L. Neutrino emission by the pair, plasma, and photo processes in the Weinberg-Salam model, report, June 1, 1986; United States. (https://digital.library.unt.edu/ark:/67531/metadc1060022/m1/9/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.