Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

where∆V t = T oρ o[( ρρ o) ǫ[ ǫρIn uniform matter, one finds∑t] ]ρ t (η L˜ρ t +η U ρ˜t ′)+η L˜ρ t +η U ρ˜t ′ +η Lˆρ t +η Uˆρ t ′ , (3.15)∫ˆρ t (r 1 ) =∆E = T ( )o ρ ǫ[ ]η L (ρ 2 nρ o ρ +ρ2 p )+2η Uρ n ρ p ,o∆V t = T ( ) ǫ [ (o ρ ρ 2 )nǫ η +ρ2 p ρ n ρ pL +2η Uρ o ρ o ρ ρ∆p = T oρ o( ρρ o) ǫ(1+ǫ)( ) ǫd 3 ρ2r 2 f(r 12 /a) ρ t2 . (3.16)ρ o][η L (ρ 2 n +ρ2 p )+2η Uρ n ρ p .+2η L ρ t +2η u ρ t ′],(3.17)In terms of the proton fraction,∆E( [)= T o u 1+ǫ η L x 2 +(1−x)]+2η 2 U x(1−x) ,ρ o∆p = T o ρ o u 2+ǫ (η L[x 2 +(1−x) 2 ]+2η U x(1−x)For standard nuclear matter, we now obtain[ǫ o 3= −B = T oρ o 5 − α 2 + β′′2 + η ]2p o = 0 = ρ o T o[ 25 − α 2 + 5 6 β′′ + η 2 (1+ǫ) ]).(3.18)K o = T o[6−9α+20β ′′ + 9η 2 (1+ǫ)(2+ǫ) ][K o ′ = T o 4−9α+ 1003 β′′ + 9η ]2 (1+ǫ)2 (2+ǫ)[ 1S v = T o3 + α 2 − 5 9 β′′ − η 2 −α L + 5 ]3 β′′ L +η L ,[ 2S v ′ = T o9 + α 2 − 2527 β′′ −(1+ǫ) η 2 −α L + 25 ]9 β′′ L +(1+ǫ)η L(3.19)43