252
T. R. Routray et al.
0
500
1000
E kinetic (MeV)
-80
-60
-40
-20
0
20
u(k,ρ
0
)(MeV)
SEI(Yukawa)
SEI (Gaussian)
MDYI
Fig. 17.5 Real part of optical potential u(k, ρ 0 ) as a function of kinetic energy of the nucleons for
both Yukawa and Gaussian form of SEI. The results of MDYI interaction [7] along with the data
extracted from the optical model analysis of scattering study [35] (filled circle) are also shown for
comparison
This is shown as a function of k in the Fig. 17.5 up to kinetic energy 1 GeV of the
nucleon for both the forms of SEI. The results of the MDYI interaction [7] along
with the results extracted from the optical model analysis of scattering data [35]
are also shown in the figure. It can be seen that the prediction of k-dependence of
u(k, ρ 0 ) for Yukawa form agrees to the MDYI results and optical model data quite
well over the whole range of energy. However, in case of the Gaussian form of SEI,
it approaches a lower asymptotic value much faster and does not produce well data
at energy E ≥ 400 MeV.
The complete behavior of the single particle potential in SNM u(k, ρ) (both ρ
and k-dependence) can be studied only after fixing all the six parameters, out of
which we have ascertained upto now only two namely, α and ex . The parameters
b can be calculated from (17.39) after fixing γ . Out of the rest three parameters
0 , , γ , and γ , the two parameters 0 and γ are determined from the saturation
properties,
de(ρ)
dρ
| ρ=ρ 0 = 0 and e(ρ 0 ), and γ has been kept as a free parameter. The
admissible values of γ are the ones for which the pressure-density curve (P ∼ ρ)
passes through the regions shown in the Fig. 17.6 those represent the results extracted
from the analysis of HI-collisions data [36] and sub-threshold k
+ production data
[37].
In both the cases of Yukawa and Gaussian forms of SEI, the values of γ can be
taken upto γ = 1. The value of γ in the exponent of the density dependent term of
the SEI determines the nuclear matter incompressibility K (ρ), defined as
K (ρ) = 9ρ
d = k f , ρ)
dρ
= 9ρ
2 d
2 e(ρ)
dρ 2 + 18ρ
de(ρ)
dρ
.
(17.62)
At saturation density ρ = ρ 0 , the K (ρ 0 ) = 9ρ
2 d
2 e(ρ)
dρ 2 | ρ=ρ 0 and the values of K (ρ 0 )
for γ =
1
3
,
1
2
,
2
3
, and 1 are 219.93, 237.47, 253.64, and 282.24 MeV for Yukawa and
T. R. Routray et al.
0
500
1000
E kinetic (MeV)
-80
-60
-40
-20
0
20
u(k,ρ
0
)(MeV)
SEI(Yukawa)
SEI (Gaussian)
MDYI
Fig. 17.5 Real part of optical potential u(k, ρ 0 ) as a function of kinetic energy of the nucleons for
both Yukawa and Gaussian form of SEI. The results of MDYI interaction [7] along with the data
extracted from the optical model analysis of scattering study [35] (filled circle) are also shown for
comparison
This is shown as a function of k in the Fig. 17.5 up to kinetic energy 1 GeV of the
nucleon for both the forms of SEI. The results of the MDYI interaction [7] along
with the results extracted from the optical model analysis of scattering data [35]
are also shown in the figure. It can be seen that the prediction of k-dependence of
u(k, ρ 0 ) for Yukawa form agrees to the MDYI results and optical model data quite
well over the whole range of energy. However, in case of the Gaussian form of SEI,
it approaches a lower asymptotic value much faster and does not produce well data
at energy E ≥ 400 MeV.
The complete behavior of the single particle potential in SNM u(k, ρ) (both ρ
and k-dependence) can be studied only after fixing all the six parameters, out of
which we have ascertained upto now only two namely, α and ex . The parameters
b can be calculated from (17.39) after fixing γ . Out of the rest three parameters
0 , , γ , and γ , the two parameters 0 and γ are determined from the saturation
properties,
de(ρ)
dρ
| ρ=ρ 0 = 0 and e(ρ 0 ), and γ has been kept as a free parameter. The
admissible values of γ are the ones for which the pressure-density curve (P ∼ ρ)
passes through the regions shown in the Fig. 17.6 those represent the results extracted
from the analysis of HI-collisions data [36] and sub-threshold k
+ production data
[37].
In both the cases of Yukawa and Gaussian forms of SEI, the values of γ can be
taken upto γ = 1. The value of γ in the exponent of the density dependent term of
the SEI determines the nuclear matter incompressibility K (ρ), defined as
K (ρ) = 9ρ
d = k f , ρ)
dρ
= 9ρ
2 d
2 e(ρ)
dρ 2 + 18ρ
de(ρ)
dρ
.
(17.62)
At saturation density ρ = ρ 0 , the K (ρ 0 ) = 9ρ
2 d
2 e(ρ)
dρ 2 | ρ=ρ 0 and the values of K (ρ 0 )
for γ =
1
3
,
1
2
,
2
3
, and 1 are 219.93, 237.47, 253.64, and 282.24 MeV for Yukawa and