Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.     

V20+离子1s23d-1s2nf的跃迁能和振子强度

用全实加关联方法计算了类锂V20 离子1s23d-1s2nf的跃迁能和偶极振子强度.依据量子亏损理论,确定了1s2nf系列的量子数亏损,用这些作为能量的缓变函数的量子亏损,实现对该Rydberg系列任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与量子亏损理论相结合,得到在电离域附近束缚态间的偶极跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将V20 离子的这一重要光谱特性的理论预言外推到整个能域.     

高离化原子的解析波函数与能量积分的计算

最近十年来,高离化原子的研究有了很大的发展,类似于重离子核物理的发展速度,形成了重离子原子物理学.高离化原子物理与三种器件的建立有密切关系:1.带电粒子加速器;2.等离子体机器;3.高能激光器。因此,研究高离化原子具有很重要的实际意义。对高离化原子进行理论分析与参数的计算时,需要有适当的原子波函数。我们现在只限于研究含有1s、2s、2p电子的高离化原子。根据过去的经验,其波函数可以用简单的解析式来表示:     

Ionization energies and term energies of the ground states ls22s of lithium-like systems

We extend the Hamiltonian method of the full-core plus correlation （FCPC） by minimizing the expectation value to calculate the non-relativistic energies and the wave functions of ls22s states for the lithium-like systems from Z = 41 to 50. The mass-polarization and the relativistic corrections including the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic （QED） is also explored by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1 s22s are derived and compared with other theoretical calculation results. It is shown that the FCPC methods are also effective for theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.     

完全图全符号控制数的较小上界和下确界

设图G=G(V,E),令函数f∶V∪E→{-1,1},f的权w(f)=∑x∈V∪Ef[x],对V∪E中任一元素,定义f[x]=∑y∈NT[x]f(y),这里NT[x]表示V∪E中x及其关联边、邻点的集合.图G的全符号控制函数为f∶V∪E→{-1,1},满足对所有的x∈V∪E有f[x]1,图G的全符号控制数γT(G)就是图G上全符号控制数的最小权,称其f为图G的γT-函数.本文得到了完全图全符号控制数的一个较小上界和下确界.     

一类3-正则图的邻强边染色

对简单图G(V,E),f是从V(G)∪E(G)到{1,2,…,k}的映射,k是自然数,若f满足(1)uv,uw∈E(G),u≠w,f(uv)≠f(uw);(2)uv∈E(G),C(u)≠C(v).则称f是G的一个邻强边染色,最小的k称为邻强边色数,其中C(u)={f(uv)|uv∈E(G)}.给出了一类3-正则重圈图的邻强边色数.     

Cr~(21+)离子1s~23d-1s~2nf的跃迁能和偶极振子强度(英文)

用全实加关联方法计算了类锂Cr21+离子1s23d-1s2nf(4≤n≤9)的跃迁能和1s2nf(n≤9)态的精细结构.在类氢近似下估算了对能量的高阶相对论修正.依据量子亏损理论,确定了Rydberg系列1s2nf的量子数亏损.据此可以实现对任意高激发态(n≥10)的能量的可靠预言.计算了Cr21+离子1s23d-1s2nf(4≤n≤9)跃迁的振子强度.与量子亏损理论相结合,得到该离子从1s23d态到电离阈附近高激发束缚态间的偶极跃迁振子强度以及到相应连续态跃迁的振子强度密度,从而将Cr21+离子的这一重     

K_(1,3,p)和K_(1,4,p)的点可区别的IE-全染色及一般全染色

利用色集事先分配法,构造染色法,反证法探讨了完全三部图K_(1,3,p)和K_(1,4,p)的点可区别IE-全染色和点可区别一般全染色问题,确定了K_(1,3,p)和K_(1,4,p)的点可区别IE-全色数和点可区别一般全色数。