a$_{s}$ , a$_{c}$ , c$_{sym}$ , κ , a$_{pair}$ , g$_{1}$ , g$_{2}$ , c$_{1}$ , V$_{0}$ , r$_{0}$ , a , λ$_{0}$ for the nuclear mass. By varying these parameters and searching for the minimal deviation of the 2149 nuclear masses from the experimental data, we obtain a parameter set labeled as WS which is listed in Table 1. To find the minimal energy E ( A, Z, β ) with respect to a set of deformation parameters for a given nucleus, the downhill searching method is adopted. We re-execute the downhill algorithm for several times starting from different initial deformation parameters in order to find the lowest energy of a nucleus from some possible local minima on the energy surface E ( A, Z, β ). In the calculation of nuclear masses with the obtained binding energies, the electron binding energies are not included. In the parameter searching procedure, the downhill searching method and the simulated annealing algorithm [25] are incorporated. The former is used for the parameters of the microscopic part, while the latter is for the macroscopic part. TABLE II: rms σ deviations between data AME2003 [6] and predictions of several models (in MeV). The line σ ( M ) refers to all the 2149 measured masses, the line σ ( S$_{n}$ ) to the 1988 measured neutron separation energies S$_{n}$ . The calculated masses with FRDM are taken from [2]. The masses with HFB-14 and HFB-17 are taken from [3] and [4], respectively. FRDM HFB-14 HFB-17 WS σ ( M ) 0 . 656 0 . 729 0 . 581 0 . 516 σ ( S$_{n}$ ) 0 . 399 0 . 598 0 . 506 0 . 346 N$_{p}$ 31 24 24 15 In this section, we first show the calculated rms deviations of the nuclear masses and of the neutron separation energies. In addition, the change of magic number in light neutron- rich nuclei and the shape coexistence phenomena for some nuclei have been checked with the model. Then, the shell corrections of super-heavy nuclei and the location of the center area of the super-heavy island are investigated with the proposed mass formula. The corresponding rms deviations of nuclear masses for the 2149 measured nuclei with the parameter set WS is listed in Table 2. In addition, the results of FRDM and Hartree- Fock Bogoliubov (HFB-14 [3] and HFB-17 [4]) are also listed for comparison. N$_{p}$ denotes A. Test of the Model III. RESULTS AND DISCUSSION 12