理论研究晶体场效应和电荷转移效应对Co2+的2p电子X射线L2,3吸收边光谱的影响

运用多重态计算方法研究了在正八面体对称性的晶体场中Co²⁺离子的2p电子X射线L_2,3吸收边光谱, 研究了Co²⁺离子和周围的配位离子之间的正八面体(O_h)晶体场效应和相应的电荷转移效应对于吸收光谱的影响. 系统讨论了在多重态计算中起作用的所有物理参数对CoO和CoCl₂的X射线吸收光谱特性的特定影响及其物理机制. 将计算得出的光谱数据和同样具有O_h对称性结构Co²⁺离子的CoO和CoCl₂实验光谱数据进行了对比, 在实验光谱数据中发现的特征被确定为来自不同自旋态, 并且光谱强度的变化与晶体场的强度相关, 揭示了其中包含的电荷转移效应. 本文为低对称性复杂系统的多重态计算提供了一个基础的参考标准, 可以适用于含有钴元素或其它过渡金属的复杂体系的X射线吸收光谱的理论计算.     

Ramanujan’s modular equations of degree 5

We provide alternative derivations of theta function identities associated with modular equations of degree 5. We then use the identities to derive the corresponding modular equations.     

Oscillation death in a coupled van der Pol–Mathieu system

We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.