correction part [18] to adjust the division between the two parts for giving better results in the calculation of fission barrier. It is necessary to investigate the influence of this parameter on the nuclear masses. We find that the rms deviation for the 2149 nuclear masses can be somewhat reduced with the introduced factor c$_{1}$ compared with the case setting c$_{1}$ = 1. To obtain the shell correction Δ E , we execute a computer code WSBETA [19] to calculate the single particle levels of an axially deformed Woods-Saxon potential and then perform the Strutinsky procedure. The single-particle Hamiltonian in the code WSBETA is written as with the spin-orbit potential where λ denotes the strength of the spin-orbit potential. In this work, we set λ = λ$_{0}$ ( 1 + N$_{i}$ A ) with N$_{i}$ = Z for protons and N$_{i}$ = N for neutrons. Here, the isospin-dependent spin-orbit interaction strength is obtained based on the Skyrme energy-density functional in which the spin-orbit potential is usually expressed as with the nucleon density ρ = ρ$_{p}$ + ρ$_{n}$ and the spin-orbit strength W$_{0}$ . M in Eq.(10) is the free nucleonic mass, ⃗ σ and ⃗ p are the Pauli spin matrix and the nucleon momentum, respectively [19]. The central potential V is described by an axially deformed Woods-Saxon form Where, the depth V$_{q}$ of the central potential ( q = p for protons and q = n for neutrons) is written as with the plus sign for neutrons and the minus sign for protons. V$_{s}$ is the isospin-asymmetric part of the potential depth. We assume V$_{s}$ = a$_{sym}$ in this work (detailed study of the relation between V$_{s}$ and a$_{sym}$ is given in the following part of this section). R defines the distance from the origin of the coordinate system to the point on the nuclear surface 8 R ( θ ) = c$_{0}$R [1 + β$_{2}$Y$_{20}$ ( θ ) + β$_{4}$Y$_{40}$ ( θ ) + ... ] , (13) V$_{q}$ = V$_{0}$ ± V$_{s}$I (12) V ( ⃗ r ) = V$_{q}$ 1 + exp( r −R ( θ ) a ) . (11) V s.o. q = 1 2 W$_{0}$ ∇ ( ρ + ρ$_{q}$ ) · ( ⃗ σ × ⃗ p ) ≈ 1 2 W$_{0}$ ( 1 + N$_{i}$ A ) ∇ ρ · ( ⃗ σ × ⃗ p ) , (10) V$_{s}$$_{.}$$_{o}$$_{.}$ = − λ ( ℏ 2 Mc ) 2 ∇ V · ( ⃗ σ × ⃗ p ) , (9) H = T + V + V$_{s}$$_{.}$$_{o}$$_{.}$, (8)