17 Momentum and Density Dependence of the Nuclear Mean Field …
245
particle at saturation and mc
2 is the nucleonic mass. γ is the parameter in the exponent
of the density dependent term of the interaction in (17.38). The interaction proposed
in (17.38), hereafter shall be referred to as simple effective interaction (SEI), contains
altogether 11-number of parameters, namely, α, b, γ, t 0 , x 0 , t 3 , x 3 , W, B, H and M.
17.3 Energy Density and Single Particle Potentials in ANM
and SNM Using SEI
The energy density in ANM at T = 0 given in (17.14) together with (17.15) for the
SEI takes the form,
H (ρ n , ρ p ) =
3
2
10m
(k
2
n ρ n + k
2
p ρ p ) +
l
0
2ρ 0
(ρ
2
n + ρ
2
p )
+
ul
0
ρ 0
ρ n ρ p +
l
γ
2ρ
γ +1
0
(ρ
2
n + ρ
2
p ) +
ul
γ
ρ
γ +1
0
ρ n ρ p
ρ(
→
R)
1 + bρ(
→
R)
γ
+
l
ex
2ρ 0
(ρ
2
n J (k n ) + ρ
2
p J (k p )) +
ul
ex
ρ 0
ρ n ρ p J (k n , k p ),
(17.40)
where
J (k n( p) ) =
9 j
2
1 (k n( p) r )
(k n( p) r ) 2 f (r )d
3 r
f (r )d 3 r
,
(17.41)
and
J (k n , k p ) =
3 j 1 (k n r )
k n r
3 j 1 (k p r )
k p r
f (r )d
3 r
f (r )d 3 r
,
(17.42)
f (r ) being the form factor of the finite range interaction and the superscript indices
“l” and “ul” prescribe the contributions coming from the interactions between likepair and unlike-pair of nucleons. The energy density in (17.40) now contains 09parameters, namely, α, b, γ, ,
l
0 , ,
ul
0 , ,
l
γ , ,
ul
γ , ,
l
ex , and
ul
ex . The new parameters are
connected to the interaction parameters through the relations given as follows: