Jahn–Teller distortion of the Wigner molecule in a three-electron quantum dot and a magnetic field

We considered a two-dimensional three electron quantum dot in a magnetic field in the Wigner limit. Using an unitary coordinate transformation of the Hamiltonian into a sum of three quasi-particle Hamiltonians, and the Pauli principle for the resulting product of quasi-particle functions, we have shown that the three electrons in the ground state of the Wigner molecule form an equilateral triangle (as expected from naive reasoning) only, if the state is a quartet View the MathML source and the orbital angular momentum is a magic quantum number (ML=3m,m=integer). Otherwise the triangle is isosceles. For ML=3m+1 one of the sides is longer and for ML=3m-1 one of the sides is shorter than the other two.