Rashba coupling in three-electron-quantum dot under cylindrical symmetry: An exact solution

► We theoretically investigate a three-electron-quantum dot in the presence of Rashba spin-orbit interaction by an exact analytical methodology. ► By using the Jacobi transformations as well as the hyperspherical coordinates we calculate the wavefunction and the energy spectra. ► Our obtained energy relation reveals that the Rashba interaction appears solely in the center of mass section.