Neutrino emission by the pair, plasma, and photo processes in the Weinberg-Salam model Page: 11 of 47
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warnings contained in that work. In the interval 1010 < T < 1011, we find that the error
in the fitting formula increases to about 40% at T = 101K (figure 6).
Dicus (1973) provided approximate multiplicative factors by which to multiply the
BPS fitting formulae to convert to the Weinberg-Salam theory of the weak interaction. We
choose from Dicus the following multiplicative factors to construct the fits we present below:
the plasma neutrino emissivity is multiplied by a factor of C2 + 2(Cv - 1)2 = 0.925, the
pair neutrino emissivity is multiplied by the same factor, and the photo neutrino emissivity
is multiplied by a factor of (Cy+2(C -1)2+5C+10(CA -1)2)/6 = 0.7791. We checked
these coefficients by comparing Dicus' predictions with the results we actually obtain by
numerical integration. Figure 7 shows the quantity AQ/Q, where AQ = (Q - Qappro),
vs. p/p, for three values of temperature: T = 10"K, T = 10'K, and T = 1010K.
As can be seen in the figure, the fits are reasonably good except at high density, where
the plasma neutrino rate is falling sharply. Table 1 presents the numerical values of the
coefficients which we use. The maximum error which we find in the temperature range
108 2K < T < 1010 K is about 20%. The error at 108-1K has a maximum of -60%.
In the interval 1010K < T < 101K, we modified the coefficients in the BPS fitting
formula by hand to construct a fitting formula which more nearly fits our results in this
region. The coefficients we use are also given in Table 1. Figure 8 compares this fitting
formula with our numerical results for T = 10108K and T = 10"K. The most difficult
regions to fit are those where the pair and plasma neutrino emissivities begin to drop
rapidly.
IV. CONCLUSION
In this paper, we have presented the results of our numerical calculations of the photo,
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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/m1/11/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.