content_image/369168.jpg content_image/369174.jpg
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A similar equation is previously proposed in [21] based on perturbation theory, 

<img src='content_image/369174.jpg'>

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 

