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A. Quddus and S. K. Patra
[12]. It is important to characterize the symmetry energy experimentally to interpret
neutron-rich nuclei and neutron star matter. However, limitation is that symmetry
energy is not directly measurable and thus extracted from the observables related to
it. In [11, 13], it has been shown theoretically that the symmetry energy of nuclei
can be used to indicate/determine magic nuclei.
The neutron pressure is an essential quantity in determining the equation of state
(EoS) of nuclear matter [11, 13–15]. For finite nuclei, the neutron pressure depends
on the interaction strength of nucleons and their distributions, while the symmetry
energy curvature is important for the scattering phenomenon. The symmetry energy,
neutron pressure, and symmetry energy curvature are collectively referred as effective
surface properties [11, 13]. The physical importance of the surface properties and
their sensitivity to density dependence have motivated us to pursue their systematic
study for the isotopic series of O, Ca, Ni, and Zr. There are various ways of calculating
the symmetry energy and the related quantities. Recently, the symmetry energy of
finite nuclei has been studied by using various formulae of the liquid drop model
[16–18], the random phase approximation based on the Hartree–Fock (HF) approach
[19], the energy density functional of Skyrme force [20–22], the relativistic nucleonnucleon interaction [23, 24], and the effective relativistic Lagrangian with densitydependent meson-nucleon vertex function [25]. In this work, we have calculated
the effective surface properties of the nuclei within the coherent density fluctuation
model (CDFM). The reason for choosing the CDFM approach is that it has the
following advantages over other methods. It takes care of (i) the fluctuation arises in
the nuclear density distribution via weight function | f (x)|
2 , and (ii) the momentum
distributions through the mixed density matrix (i.e., the Wigner distribution function)
[11, 13, 26]. In other words, the CDFM approach is adopted to comprise the variation
arise from the momentum and density distributions at the surface of finite nuclei. The
input to CDFM approach is density of a nucleus which has been calculated within the
relativistic mean field (RMF) approach with IOPB-I [27] and NL3 [28] parameter
sets.
The paper is organized as follows: in Sect. 18.2.1, we outline the relativistic
mean field model, which has been used to calculate the densities of the nuclei.
Section 18.2.1.1 contains the general idea of calculating symmetry energy and relevant quantities and how they are calculated within CDFM. The calculated results are
discussed in Sect. 18.3. Finally, the work is summarized in Sect. 18.4.
18.2 Formalism
The densities of the considered isotopes, as mentioned, are calculated within the
RMF formalism. These calculated densities are further used in the coherent density
fluctuation model to obtain the effective surface properties of finite nuclei from the
corresponding quantities of infinite nuclear matter. The formalism adopted here to
find the effective surface properties is briefed below.
A. Quddus and S. K. Patra
[12]. It is important to characterize the symmetry energy experimentally to interpret
neutron-rich nuclei and neutron star matter. However, limitation is that symmetry
energy is not directly measurable and thus extracted from the observables related to
it. In [11, 13], it has been shown theoretically that the symmetry energy of nuclei
can be used to indicate/determine magic nuclei.
The neutron pressure is an essential quantity in determining the equation of state
(EoS) of nuclear matter [11, 13–15]. For finite nuclei, the neutron pressure depends
on the interaction strength of nucleons and their distributions, while the symmetry
energy curvature is important for the scattering phenomenon. The symmetry energy,
neutron pressure, and symmetry energy curvature are collectively referred as effective
surface properties [11, 13]. The physical importance of the surface properties and
their sensitivity to density dependence have motivated us to pursue their systematic
study for the isotopic series of O, Ca, Ni, and Zr. There are various ways of calculating
the symmetry energy and the related quantities. Recently, the symmetry energy of
finite nuclei has been studied by using various formulae of the liquid drop model
[16–18], the random phase approximation based on the Hartree–Fock (HF) approach
[19], the energy density functional of Skyrme force [20–22], the relativistic nucleonnucleon interaction [23, 24], and the effective relativistic Lagrangian with densitydependent meson-nucleon vertex function [25]. In this work, we have calculated
the effective surface properties of the nuclei within the coherent density fluctuation
model (CDFM). The reason for choosing the CDFM approach is that it has the
following advantages over other methods. It takes care of (i) the fluctuation arises in
the nuclear density distribution via weight function | f (x)|
2 , and (ii) the momentum
distributions through the mixed density matrix (i.e., the Wigner distribution function)
[11, 13, 26]. In other words, the CDFM approach is adopted to comprise the variation
arise from the momentum and density distributions at the surface of finite nuclei. The
input to CDFM approach is density of a nucleus which has been calculated within the
relativistic mean field (RMF) approach with IOPB-I [27] and NL3 [28] parameter
sets.
The paper is organized as follows: in Sect. 18.2.1, we outline the relativistic
mean field model, which has been used to calculate the densities of the nuclei.
Section 18.2.1.1 contains the general idea of calculating symmetry energy and relevant quantities and how they are calculated within CDFM. The calculated results are
discussed in Sect. 18.3. Finally, the work is summarized in Sect. 18.4.
18.2 Formalism
The densities of the considered isotopes, as mentioned, are calculated within the
RMF formalism. These calculated densities are further used in the coherent density
fluctuation model to obtain the effective surface properties of finite nuclei from the
corresponding quantities of infinite nuclear matter. The formalism adopted here to
find the effective surface properties is briefed below.