On the shape consistency in the deformed shell-model approach

We show that the shape inconsistency (β^V_λ ? β^ρ_λ) between the average potential and the corresponding nucleonic density is generally small (～? 5%) for λ = 2, 3, 4 in both Nilsson and Woods-Saxon models. The properties of (β^V_λ ? β^?_λ) are analysed in detail and understood in terms of the extended Thomas-Fermi model. Approximate formulas β^ρ_λ = β^ρ_λ(β^V) are given and the microscopic reasons for the shape inconsistency discussed.