superdeformation. Nevertheless, neither theoretical studies of the SD state nor the triaxiality of $^{40}$Ar have progressed. The purpose of this study is to investigate the structure of the SD band in $^{40}$Ar focusing on triaxiality. Competitions of deformations favored by protons and neutrons are also discussed. To obtain the wave functions in low-lying states, the parity and angular momentum pro- jection (AMP) and the generator coordinate method (GCM) with deformed-basis AMD wave functions were performed. A deformed-basis AMD wave function | Φ 〉 is a Slater determinant of triaxially deformed Gaussian wave packets, such that | Φ 〉 = ˆ A| ϕ 1 , ϕ 2 , · · · , ϕ$_{A}$ 〉 , (1) | ϕ$_{i}$ 〉 = | φ$_{i}$ 〉 ⊗ | χ$_{i}$ 〉 ⊗ | τ$_{i}$ 〉 , (2) 〈 r | φ$_{i}$ 〉 = ∏ σ = x,y,z ( 2 ν$_{σ}$ π ) 1 4 exp   − ν$_{σ}$ ( σ − Z$_{iσ}$ √ ν$_{σ}$ ) 2   , (3) where ˆ A is the antisymmetrization operator and | ϕ$_{i}$ 〉 are single-particle wave functions. The variables | φ$_{i}$ 〉 , | χ$_{i}$ 〉 , and | τ$_{i}$ 〉 are a spatial part, a spin part, and an isospin part, respectively, of every single-particle wave function | ϕ$_{i}$ 〉 . The values ν = ( ν$_{x}$, ν$_{y}$, ν$_{z}$ ) are real parameters that indicate the width of the Gaussian single-particle wave function, and Z$_{i}$ = ( Z$_{ix}$, Z$_{iy}$, Z$_{iz}$ ) are complex parameters that indicate centroids of the single-particle wave functions. The width parameters ν are common to all nucleons. The complex parameters χ ↑ i and χ ↓ i represent spin directions. Basis wave functions of the GCM were obtained by the energy variation with a constraint on the quadrupole deformation parameter β of a total system after the projection to positive parity states. Variation parameters were ν , Z$_{i}$ , and χ ↑ , ↓ i . The isospin part of each single-particle wave function was fixed as a proton or a neutron. The Gogny D1S force was used as an effective interaction. Details of the framework are provided in Refs. 21–23. Calculated values of energy, triaxiality γ , and harmonic oscillator (H.O.) quanta Δ N H . O . for protons and neutrons measured from the lowest allowed states are shown as functions of the quadrupole deformation parameter β in the upper, middle, and lower panels, respectively, of Fig. 1. As for the energy curves, energies of the positive parity states and J π = 0 + and 2 + states, which were projected from each basis wave function, are plotted. K -mixing was 3 | χ$_{i}$ 〉 = χ ↑ i | ↑〉 + χ ↓ i | ↓〉 , | τ$_{i}$ 〉 = | π 〉 or | ν 〉 , (4)