Positronium Lyman-α blueshift in ellipsoidal quantum dots

The confined states of a positronium (Ps) in an ellipsoidal quantum dot (QD) are theoretically investigated within the framework of the perturbation theory in two quantum confinement regimes: strong and weak. The expressions for the wave functions and energies of the Ps and independently quantized electron-positron pair are obtained in the weak and strong quantum confinement regimes, correspondingly. It is proved that in the first order of the perturbation theory the energy correction is non-zero and its dependence on ellipticity parameter β is linear. The Ps formation and binding energy dependences on the QD geometric parameters are discussed. Ps Lyman-α blueshift is revealed as a result of the ellipsoidal shape of the QD.