17 Momentum and Density Dependence of the Nuclear Mean Field …
257
0
0. 2
0. 4
0. 6
0.8
1
0
0.1
SEI(Gaussian)
DBHF
[m
*
/m]
n
-[m
*
/m]
p
β
Fig. 17.10 n-p effective mass splitting in ANM at normal nuclear matter density as a function of
isospin asymmetry β for l
ex =
2
3 ex . The corresponding DBHF results with Bonn B potential [39]
is also shown
the density dependence of NSE, E s (ρ). In panel (a) of Fig. 17.11, this is shown
for the variation of E
s (ρ 0 ) with in the range 17–24 MeV for the standard value of
E s (ρ 0 ) = 30 MeV. We want to determine the optimal value of E
s (ρ 0 ) and to this end
we consider the neutron star (NS) scenario. The core of the neutron star is mostly
composed of neutrons (n), proton (p), electron (e), and muons (μ) in beta-stable
charge neutral condition. The beta-stability condition is expressed as
μ n − μ p = μ e = μ μ ,
(17.67)
and the charge neutrality as
Y p = Y e + Y μ ,
(17.68)
where μ i , i = n, p, e, μ are the respective chemical potentials and Y i =
ρ i
ρ
with i =
n, p, e, μ are the corresponding particle fractions, ρ being the total density of the
neutron star matter (NSM). By solving the (17.67) and (17.68) simultaneously for
a given EOS of ANM, the equilibrium proton fraction Y p for the NSM at a given
density ρ can be obtained. The equilibrium Y p as a function of density ρ are shown
in panel (b) of Fig. 17.11 for the respective EOSs of ANM of panel (a). Once the
particle fractions are known as a function of ρ of NSM, then the total energy density
of the NSM can be written as the sum of the nucleonic and the leptonic parts,
H
N SM
= H N (ρ, Y p ) + H e (ρ e , Y e ) + H μ (ρ, Y μ ).
(17.69)
The asymmetric contribution of the energy density is crucial in deciding the particle
fractions in NSM. So the asymmetric part of the nucleonic contribution in NSM,
H N (ρ, Y p ) is calculated by taking out the symmetric contribution H (ρ, Y p =
1
2
),
257
0
0. 2
0. 4
0. 6
0.8
1
0
0.1
SEI(Gaussian)
DBHF
[m
*
/m]
n
-[m
*
/m]
p
β
Fig. 17.10 n-p effective mass splitting in ANM at normal nuclear matter density as a function of
isospin asymmetry β for l
ex =
2
3 ex . The corresponding DBHF results with Bonn B potential [39]
is also shown
the density dependence of NSE, E s (ρ). In panel (a) of Fig. 17.11, this is shown
for the variation of E
s (ρ 0 ) with in the range 17–24 MeV for the standard value of
E s (ρ 0 ) = 30 MeV. We want to determine the optimal value of E
s (ρ 0 ) and to this end
we consider the neutron star (NS) scenario. The core of the neutron star is mostly
composed of neutrons (n), proton (p), electron (e), and muons (μ) in beta-stable
charge neutral condition. The beta-stability condition is expressed as
μ n − μ p = μ e = μ μ ,
(17.67)
and the charge neutrality as
Y p = Y e + Y μ ,
(17.68)
where μ i , i = n, p, e, μ are the respective chemical potentials and Y i =
ρ i
ρ
with i =
n, p, e, μ are the corresponding particle fractions, ρ being the total density of the
neutron star matter (NSM). By solving the (17.67) and (17.68) simultaneously for
a given EOS of ANM, the equilibrium proton fraction Y p for the NSM at a given
density ρ can be obtained. The equilibrium Y p as a function of density ρ are shown
in panel (b) of Fig. 17.11 for the respective EOSs of ANM of panel (a). Once the
particle fractions are known as a function of ρ of NSM, then the total energy density
of the NSM can be written as the sum of the nucleonic and the leptonic parts,
H
N SM
= H N (ρ, Y p ) + H e (ρ e , Y e ) + H μ (ρ, Y μ ).
(17.69)
The asymmetric contribution of the energy density is crucial in deciding the particle
fractions in NSM. So the asymmetric part of the nucleonic contribution in NSM,
H N (ρ, Y p ) is calculated by taking out the symmetric contribution H (ρ, Y p =
1
2
),