Circular Scale of Time Applied in Classifying the Quantum-Mechanical Energy Terms Entering the Framework of the Schrodinger Perturbation Theory

The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.

Ionization energies and term energies of the ground states 1s^22s 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.

Characteristics and Causes of Changes of Pan Evaporation in China During 1957-2001

Evaporation is an important component of surface heat and water balance, and is affected directly by land use and climate change. This paper studies the changes of evaporation in China associated with the global climate change, and explores characteristics of the corresponding regional water cycle variations. The 20-cm-caliber pan evaporation measurements collected from 427 meteorological stations in China from 1957 to 2001 are analyzed to disclose the small-pan evaporation variation trend in China and the associated causes. The results show that although the annual average temperature over China exhibits an upward tendency of 0.2℃/10 yr for the past 45 years, the pan evaporation on the whole has decreased by -34.12 mm/10 yr. Nonetheless, a significant increase of pan evaporation is observed in a few areas such as the northern part of the Greater Hingan Mountains in Northeast China and the Beishan Mountains in Inner Mongolia. The largest decrease of pan evaporation lies in East China, northern parts of Northwest China, South China, and southern Tibet. An analysis of energy balance and aerodynamics using Penman＇s formula proves that the drop of pan evaporation in East China is mainly due to a significant decline of source energy for evaporation, while that in West China is mostly attributed to an aerodynamic reduction. The analysis on tendencies of various meteorological and other related factors shows that wind speed and sunshine hours are two most important factors causing the pan evaporation reduction in China.