I$_{1}$ = 1 24(2 π ) 7 ∫ d $^{3}$p$_{1}$ E$_{1}$ d $^{3}$p$_{2}$ E$_{2}$ ( E$_{1}$ + E$_{2}$ ) F$_{1}$F$_{2}$ [ 3 m 2 $_{e}$( p$_{1}$ · p$_{2}$ ) + 2( p$_{1}$ · p$_{2}$ ) 2 + m 4 e ] . (21) Q [2] ν ¯ ν = G 2 $_{F}$( a 2 + b $^{2}$) [ a $^{2}$( g e $_{V}$) 2 + b $^{2}$( g e $_{A}$) 2 − 4 a $^{2}$b2 a 2 + b $_{2}$g e $_{V}$g e A ] I$_{2}$, (22) Q [3] ν ¯ ν = G 2 $_{F}$( a 2 + b $^{2}$) [ a $^{2}$( g e $_{V}$) 2 − b $^{2}$( g e $_{A}$) 2 ] m 2 $_{e}$I$_{3}$ , (23) I$_{2}$ = I$_{1}$ = 1 24(2 π ) 7 ∫ d $^{3}$p$_{1}$ E$_{1}$ d $^{3}$p$_{2}$ E$_{2}$ ( E$_{1}$ + E$_{2}$ ) F$_{1}$F$_{2}$ [ 3 m 2 $_{e}$( p$_{1}$ · p$_{2}$ ) + 2( p$_{1}$ · p$_{2}$ ) 2 + m 4 e ] , (24) I$_{3}$ = 1 (2 π ) 7 ∫ d $^{3}$p$_{1}$ 2 E$_{1}$ d $^{3}$p$_{2}$ 2 E$_{2}$ ( E$_{1}$ + E$_{2}$ ) F$_{1}$F$_{2}$ [ m 2 e + ( p$_{1}$ · p$_{2}$ ) ] . (25) G ± s = 1 α 3+2 s ∫ ∞ α x 2 s $_{+1}$√$_{x}$ 2 − α 2 1 + e x ± β dx, (26) G ± s = 1 m 3+2 s e ∫ ∞ m e /KT E 2 s +1 √ E 2 − m 2 e 1 + e ( E ± µ e ) $_{/KT}$dE, (27) ∫ ∞ m e /KT E n √ E 2 − m 2 e 1 + e ( E ± µ e ) $_{/KT}$dE = m n +2 e G ± n$_{−}$ 1 2 , (28) ∫ ∞ m e /KT E n +1 √ E 2 − m 2 e 1 + e ( E ± µ e ) $_{/KT}$dE = m n +3 e G ± n $_{2}$, (29) ∫ ∞ m e /KT E n +2 √ E 2 − m 2 e 1 + e ( E ± µ e ) $_{/KT}$dE = m n +4 e G ± n +1 2 . (30) 8 From (28), (29) and (30), Eqs. (24) and (25) are expressed as therefore With these definitions, Eq. (26) becomes where α = m e $_{KT}$, β = µ e KT and x = E $_{KT}$. The calculation of the emissivity can be more easily performed by expressing the latest integrals in terms of the Fermi integral, which is defined as [33] where In a similar way for the second and third term of Eq. (16), we obtain