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一、引言晶体中稀土离子的4f电子由于屏蔽作用受到晶场的作用较小,数量级一般为10~2 cm~(-1),小于自旋-轨道相互作用.这样使得它们主要保持了自由离子特征,同时也产生了反映晶场特征的斯塔克能级.稀土离子的自由状态通常按Racah群链分类,本征态表为|nl~NaSLJM〉,nl~N表示径向部分,S、L和J分别为自旋、轨道和总角动量量子数,M为J在z方向上的投影,α为其他量子数.然而,嵌入晶体的稀土离子,总角动量量子数J一般不再为好的量子数,体系的状态应由点群的不可约可表示来描述,Racah群链应扩展到点群,这时为使状态完全分类还要增补一段群链,O_3(?)G_a(?)G_Γ(?)G_γ,其中,O_3为三维旋转群,G_a、G_Γ和G_γ为三个不同的点群,a、Γ和γ分别为这些点群的不可约表示.这时体系本征态表为| nl~NaSLJaΓγ〉,它和自由离子本征态有如下关系,
I. INTRODUCTION The 4f electrons of the rare earth ions in the crystal are less affected by the crystal field due to the shielding effect, and the order of magnitude is generally 10 ~ 2 cm -1, which is smaller than the spin-orbit interaction, so that they mainly maintain the free ions Characteristics, but also produced a Stark level reflecting the crystalline field characteristics.The free state of rare earth ions are usually classified by Racah group chain, the eigenstates are | nl ~ NaSLJM>, nl ~ N represent the radial part, S, L and J are the spin, orbit, and total angular momentum quantum, respectively, M is the projection of J in the z direction, and a is the other quantum number. However, the rare earth ions embedded in the crystal, the total angular momentum quantum number J, is generally no longer A good quantum number, the state of the system should be described by the irreducible representation of the point group, Racah group chain should be extended to point group, in order to make the state completely classified but also to add a group of chain, O_3 (?) G_a (? ) G_Γ (?) G_γ, where O_3 is a three-dimensional rotation group, G_a, G_Γ and G_γ are three different point groups, a, Γ and γ are the irreducible representations of these point groups respectively. For | nl ~ NaSLJaΓγ>, it has the following relation with the free ion eigenstate,