各向异性激子的超球理论
Hyperspherical theory of anisotropic exciton
摘要：
基于Fock变换，提出了一种新的各向异性激子理论，在一个赤平投影的动量的单位四维（4D）球。超球函数被用作微扰理论的基础。数值计算得到了伸长激子和扁平激子的结合能、波函数和振子强度。结果表明，随着各向异性程度的增加，振子强度显着重新分配之间的光学活性和以前的非活性状态，使后者的光学活性。得到了考虑角动量守恒项的各向异性激子问题的近似解析解。该解给出了中等各向异性激子的结合能，具有很好的精度，并提供了一个有用的能级演化的定性描述。
英文摘要：
A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution.
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