$^{16}$O $^{24}$O $^{40}$Ca $^{48}$Ca $^{90}$Zr $^{132}$Sn $^{208}$Pb $^{270}$Hs $^{288}$114 $^{292}$114 $^{298}$114 $^{294}$116 WS − 0 . 7 − 4 . 6 2 . 0 − 1 . 2 − 1 . 3 − 9 . 8 − 11 . 0 − 6 . 4 − 5 . 3 − 6 . 1 − 6 . 1 − 6 . 2 FRDM 2 . 1 0 . 3 2 . 3 0 . 1 − 1 . 6 − 11 . 6 − 12 . 8 − 6 . 5 − 7 . 8 − 8 . 9 − 7 . 6 − 8 . 7 TABLE III: Shell corrections of some nuclei (in MeV). The data of FRDM are taken from the microscopic energies E$_{mic}$ of the table of Ref. [2]. In [29], the authors observed the shape coexistence phenomena for nuclei $^{82}$Sr and Kr iso- topes from the low and high spin states. The shape coexistence phenomena of these nuclei could be observed from the corresponding potential energy surface. In Fig.5, we show the calculated potential energy surface of $^{82}$Sr. The coexistence of oblate and prolate deformed configurations can be clearly observed. The similar coexistence phenomena for Kr isotopes can also be observed with our model. The precise calculation for the shell corrections of super-heavy nuclei is of great impor- tance for the synthesis of new super-heavy nuclei, especially for the prediction of the location of the super-heavy island. Furthermore, the fission barriers of super-heavy nuclei are roughly estimated by the values of the corresponding shell corrections [18, 30] since the macroscopic fission barriers disappear at super-heavy region in general. It is known that the fission bar- rier is a very sensitive parameter in the realistic calculations for the survival probabilities of the produced compound nuclei. It is therefore necessary to investigate the shell corrections of super-heavy nuclei. In Table 3, we list the calculated shell corrections Δ E of some nuclei. The corresponding microscopic energy obtained in the FRDM are also listed for comparison. For super-heavy nuclei such as nucleus $^{292}$114, the microscopic energies obtained with the FRDM are much lower (absolute value larger about 2 ∼ 3 MeV) than our calculated Δ E . Because these nuclei are (nearly) spherical in shape according to the calculations. It follows that the deviations of shell energies between the two models are about 2 ∼ 3 MeV for nuclei around $^{292}$114. Because the shell correction can not be measured directly, it is still difficult to quantitatively compare the reliability of model through the calculated shell corrections of nuclei. In addition, we study the central area of the super-heavy island based on the calculated shell energies. Fig.6 15 B. Shell Corrections of Super-heavy Nuclei