(untitled) (Journal of Atomic and Molecular Sciences, 2014)
Influence of the magnetic field on the energy of the spin polarization state of a two-electron system in two-dimensional quantum dots (QDs) is studied by using the method of few-body physics. As example, a numerical calculation is performed for a GaAs semiconductor QD to show the variations of the ground-state energy E_0, the spin-singlet energy E_1(A) and spin-triplet energy E_1(S) of the first excited state and the energy difference (i.e. Δ E(A) and Δ E(S)) between the first excited and ground states with the effective radius R_0 of the QD and the magnetic field B. The results show that E_0 increases with increasing B, but decreases with increasing R_0; in the magnetic field, the spin-singlet energy E_1(A) of the first excited state splits into two levels as E_1+1(A) and E_1-1(A), the spin-triplet energy E_1(S) of the first excited state splits into two sets as E_1+1(S) and E_1-1(S), and each set consists of three "fine structures" which correspond to M_S=1,0,-1, respectively; each energy level (set, energy difference) decreases with increasing R_0, but there are great differences among the changes of them with B: E_1+1(A), E^M_S_1+1(S), Δ E_1+1(A), and Δ E^M_S_1+1(S) increase significantly with increasing B, but the variations of E_1-1(A), E^M_S_1-1(S), Δ E_1-1(A), and Δ E^M_S_1-1(S) with B are relatively slow; the splitting degree of each energy level (set, energy difference) is proportional to the first power of the magnetic field B.