GLYPH<s45> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s45> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s45> GLYPH<s50>GLYPH<s48> GLYPH<s45> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s50>GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s54>GLYPH<s48> GLYPH<s45> GLYPH<s51>GLYPH<s48> GLYPH<s48> GLYPH<s51>GLYPH<s48> GLYPH<s54>GLYPH<s48> GLYPH<s57>GLYPH<s48> GLYPH<s86> GLYPH<s110> GLYPH<s45>GLYPH<s86> GLYPH<s112> GLYPH<s32>GLYPH<s40>GLYPH<s77>GLYPH<s101>GLYPH<s86>GLYPH<s41> GLYPH<s40>GLYPH<s78>GLYPH<s45>GLYPH<s90>GLYPH<s41>GLYPH<s47>GLYPH<s65> GLYPH<s32>GLYPH<s83> GLYPH<s76>GLYPH<s121> GLYPH<s52> GLYPH<s32>GLYPH<s83> GLYPH<s107> GLYPH<s77>GLYPH<s42> GLYPH<s32>GLYPH<s70> GLYPH<s105>GLYPH<s116>GLYPH<s45>GLYPH<s83> GLYPH<s76>GLYPH<s121> GLYPH<s52>GLYPH<s44>GLYPH<s32>GLYPH<s86> GLYPH<s115> GLYPH<s61>GLYPH<s49>GLYPH<s55>GLYPH<s46>GLYPH<s48> GLYPH<s32>GLYPH<s70> GLYPH<s105>GLYPH<s116>GLYPH<s45>GLYPH<s83> GLYPH<s107> GLYPH<s77>GLYPH<s42>GLYPH<s44>GLYPH<s32>GLYPH<s86> GLYPH<s115> GLYPH<s61>GLYPH<s50>GLYPH<s54>GLYPH<s46>GLYPH<s57> GLYPH<s40> GLYPH<s98>GLYPH<s41> GLYPH<s83>GLYPH<s107> GLYPH<s77>GLYPH<s42> GLYPH<s83>GLYPH<s76>GLYPH<s121> GLYPH<s52> GLYPH<s102> GLYPH<s111>GLYPH<s114>GLYPH<s32>GLYPH<s110>GLYPH<s117>GLYPH<s99> GLYPH<s108>GLYPH<s101>GLYPH<s97>GLYPH<s114>GLYPH<s32>GLYPH<s109>GLYPH<s97>GLYPH<s116>GLYPH<s116>GLYPH<s101>GLYPH<s114> GLYPH<s74> GLYPH<s32>GLYPH<s40>GLYPH<s77>GLYPH<s101>GLYPH<s86>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s86> GLYPH<s115> GLYPH<s121> GLYPH<s109> GLYPH<s32>GLYPH<s40>GLYPH<s77> GLYPH<s101> GLYPH<s86>GLYPH<s41> GLYPH<s40> GLYPH<s97>GLYPH<s41> FIG. 3: (Color online) (a) Symmetry potential V$_{sym}$ of nuclear matter with 78 Skyrme forces. (b) The difference between the potential depth of neutrons and of protons as a function of mass asymmetry. The circled curve and the triangled curve denote the results fitted to the calculated results with SLy4 (short red dashes) and SkM* force (small gray squares) for a large number of nuclei, respectively. A similar equation is previously proposed in [21] based on perturbation theory, Due to the uncertainty of choosing the interaction parameters, there exists a large un- certainty for the value of V$_{sym}$ in different models. In Fig.3(a), we show the calculated symmetry potential V$_{sym}$ of nuclear matter with 78 Skyrme forces. The V$_{sym}$ has a value of about 10 ∼ 50 MeV according to the calculations. Brueckner-Hartree-Fock calculations show that the value of V$_{sym}$ is about 25 MeV [22]. These calculations indicate that the value of V$_{sym}$ is comparable to that of the symmetry energy coefficient J which is about 30 MeV. For finite nucleus, the isospin-asymmetric part V$_{s}$ of the single particle potential should be slightly different from the value of V$_{sym}$ . With the density distributions of nuclei obtained in [8], we calculate the potential depth of protons and neutrons for a large number of nuclei. We find that the difference V$_{n}$ − V$_{p}$ increases linearly with the isospin asymmetry I (see Fig.3(b)). The average value for the isospin-asymmetric part V$_{s}$ can be obtained by linearly 10 J = 1 2 V$_{sym}$ ( k$_{F}$ ) + 1 6 k$_{F}$ [ ∂V$_{0}$ ( k$_{m}$ ) ∂k$_{m}$ ]$_{k}$$_{m}$$_{=}$$_{k}$$_{F}$ + 1 3 ( ℏ 2 2 M ) k 2 $_{F}$. (18)