It is known that the lines of exciton (X) and exciton trapped by an ionized donor $(D^{+},X$) are often very close which makes very difficult their experimental identification. In order to facilitate their distinction in spherical quantum dots, we investigate the effect of an applied magnetic field studying the binding energy of the complex $(D^{+},X$) as function of dot size and the ionized donor position. Our calculation is using a variational approach taking into account the interactions between all charge carriers. Our results show that the complex is more sensitive to the magnetic field than the exciton and that the energy of the exciton is not sufficiently affected when the ionized donor is placed at the edge of the quantum dot. Finally our results are in a fairly good agreement with experimental data and can predict the behaviour law of the diamagnetic effect relating to $(D^{+},X)$.

已知激子线（X）和被电离给体捕获的激子线 $（d^{+}，X$）通常非常接近，因此很难进行实验识别。为了促进它们在球形量子点中的区分，我们研究了研究复合物结合能的施加磁场的作用$（d^{+}，X$）作为点大小和电离供体位置的函数。我们的计算使用了一种变分方法，其中考虑了所有电荷载流子之间的相互作用。我们的结果表明，该复合物比激子对磁场更敏感，并且当将电离的施主置于量子点的边缘时，激子的能量没有受到足够的影响。最后，我们的结果与实验数据吻合得很好，并且可以预测与$（d^{+}，X）$。