Unified model of nuclear mass and level density formulas

Nuclear ground and excited state properties are described by using parameter systematics on mass and level density formulas. The formulas are based on an analytical expression of the single-particle state density by introducing the shell-pairing correlation in a new way. Main features are the shell, pairing, and deformation effects on the droplet model near the ground state, which are washed out at higher excitation energies. The main aim of the paper is to provide in the analytical framework the improved energy dependent shell, pairing, and deformation corrections generalized to the collective enhancement factors, which offer a systematic prescription over a great number of nuclear reactions. The new formulas are shown to be in close agreement with not only the empirical nuclear mass data but also the measured slow neutron resonance spacings and experimental systematics observed in the excitation energy dependent properties.

Figure 1

(Color online) Plots of pairing correlations vs thermodynamic temperature for three different models of FG, BCS and SPC, as a sample of even-even nuclei. Values of parameter, ${\Delta }_o=11/A^{1/2},a_0=0.137A,A\hspace{1em}=\hspace{1em}$mass number, $t_c=2{\Delta }_0/3.50$, the critical temperature of phase transition in BCS model.

Figure 2

(Color online) Plots of thermodynamic properties vs temperature for three different models of FG, BCS, and SPC, as a sample of paired even-even nuclei. (See also Fig. 1.)

Figure 3

(Color online) Microscopic corrections to FRDM based on Ref. 10 mass data. Values of corrections are derived by using the shellgroup wise average (SGWA) method, assuming the complete independence in interactions between proton and neutron shells on those corrections.

Figure 4

(Color online) Polynomial expressions of correction energies, shell (—– proton, —– neutron), pairing (× proton, + neutron), and deformation (□ proton, ▵ neutron) of new mass formula. Symbols (• even-proton, ◯ even-neutron) are the SGWA values of microscopic correction energies for FRDM model.

Figure 5

(Color online) Values of ground state deformation parameter ($\delta )$, which are calculated by using Eq. (21).

Figure 6

(Color online) Excitation energy dependence of the microscopic corrections. [Eqs. (23)].

Figure 7

(Color online) Plots of the moments of inertia and enhancement factors vs the excitation energy for ${}^{238}\mathrm{U}$ nucleus, [Eqs. (25)]. $\Im {}_{\perp }$ is the perpendicular moment of inertia, $\Im {}_3$ the parallel moment of inertia, $\Im {}_R$ the rigid-body moment of inertia.

Figure 8

(Color online) Systematics of level density parameter $\alpha$, based on Ref. 14 resonance spacings data and on three different level density models, FG, KRK, and SPC.

Figure 9

(Color online) Plots of LD vs the excitation energy of the medium and heavy nuclei. Smooth curves are polynomial fittings to those values of three different models, using the LD parameter systematics in Table . D${}_{\mathrm{obs}}$ corresponds to the average s-wave neutron resonance width and ${\rho }_{\mathrm{obs}}$ is a fixed point for all polynomial fitting curves.

Figure 10

(Color online) Plots of LD vs the excitation energy of closed-shell nuclei. See caption of Fig. 9.

Figure 11

(Color online) Plots of LD vs the excitation energy of deformed nuclei. See the caption of Fig. 9.