18 Effective Surface Properties of Light and Medium Mass Exotic-Nuclei
269
with
∞
0 dx| f (x)|
2
= 1. For a detailed analytical derivation, one can follow
[36, 37]. The CDFM allows us to make a transition from the properties of nuclear
matter to those of finite nuclei. The symmetry energy S, neutron pressure P, and
symmetry energy curvature K for a finite nucleus are defined below, within the
CDFM, by weighting the corresponding quantities for infinite nuclear matter [26,
36–38],
S =
∞
0
dx| f (x)|
2 S
N M
0 (ρ(x)),
(18.23)
P =
∞
0
dx| f (x)|
2 P
N M
0
(ρ(x)),
(18.24)
K =
∞
0
dx| f (x)|
2
K
N M
0
(ρ(x)).
(18.25)
Here, the quantities on the left-hand-side of (18.23)–(18.25) are the surface weighted
average of the corresponding nuclear matter quantities with local density approximation, which have been determined within the method of Brueckner et al.
[33, 34].
18.3 Results and Discussions
18.3.1 Densities and Weight Functions for the Nuclei
The total density and the weight function for the
40,52 Ca isotopes as representative
cases corresponding to the NL3, and IOPB-I parameter sets are shown in Fig. 18.1.
The black color with circles represents the curve for NL3 set while the red one with
squares is the curve for the IOPB-I set. This representation is same throughout the
work. It can be noticed from the figure that the density corresponding to IOPB-I
set is larger as compared to that of NL3. These calculated densities of the isotopes
are further used in (18.22) to obtain the weight functions for the corresponding
nucleus. From the right panel of the figure, it can be noticed that the behavior of
the density profile (left panel) is reflected in weight function curve. The lower value
of the central density yields the lesser height of the weight function for an isotope
of the particular nucleus. The NL3 parameter set predicts larger value of the weight
function for all the nuclei as compared to the IOPB-I set. The weight function is used
to make a transition from infinite nuclear matter to finite nuclei. That is, properties of
infinite nuclear matter are folded with the weight function to find the corresponding
properties for finite nuclei. The reason to call the symmetry energy, neutron pressure,
and symmetry energy curvature as an effective surface properties is well illustrated
in [36].
269
with
∞
0 dx| f (x)|
2
= 1. For a detailed analytical derivation, one can follow
[36, 37]. The CDFM allows us to make a transition from the properties of nuclear
matter to those of finite nuclei. The symmetry energy S, neutron pressure P, and
symmetry energy curvature K for a finite nucleus are defined below, within the
CDFM, by weighting the corresponding quantities for infinite nuclear matter [26,
36–38],
S =
∞
0
dx| f (x)|
2 S
N M
0 (ρ(x)),
(18.23)
P =
∞
0
dx| f (x)|
2 P
N M
0
(ρ(x)),
(18.24)
K =
∞
0
dx| f (x)|
2
K
N M
0
(ρ(x)).
(18.25)
Here, the quantities on the left-hand-side of (18.23)–(18.25) are the surface weighted
average of the corresponding nuclear matter quantities with local density approximation, which have been determined within the method of Brueckner et al.
[33, 34].
18.3 Results and Discussions
18.3.1 Densities and Weight Functions for the Nuclei
The total density and the weight function for the
40,52 Ca isotopes as representative
cases corresponding to the NL3, and IOPB-I parameter sets are shown in Fig. 18.1.
The black color with circles represents the curve for NL3 set while the red one with
squares is the curve for the IOPB-I set. This representation is same throughout the
work. It can be noticed from the figure that the density corresponding to IOPB-I
set is larger as compared to that of NL3. These calculated densities of the isotopes
are further used in (18.22) to obtain the weight functions for the corresponding
nucleus. From the right panel of the figure, it can be noticed that the behavior of
the density profile (left panel) is reflected in weight function curve. The lower value
of the central density yields the lesser height of the weight function for an isotope
of the particular nucleus. The NL3 parameter set predicts larger value of the weight
function for all the nuclei as compared to the IOPB-I set. The weight function is used
to make a transition from infinite nuclear matter to finite nuclei. That is, properties of
infinite nuclear matter are folded with the weight function to find the corresponding
properties for finite nuclei. The reason to call the symmetry energy, neutron pressure,
and symmetry energy curvature as an effective surface properties is well illustrated
in [36].