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The well-aligned ZnO nanorod arrays were fabricated through a simple chemical process under low temperature. The nanorod arrays were characterized by XRD, SEM, TEM, HRTEM and SAED, and their optical performances were investigated with Raman and PL spectroscopy. The results show that the as-prepared ZnO nanorod arrays are dense, the individual ZnO nanorod is hexagonal shape and grows along c-axis perpendicular to the substrate surface with good single crystal in nature. The Raman property of nanorod arrays displays change with the altering the preparation conditions. Moreover, the PL performances of ZnO nanorod arrays exhibit tunable character with adjusting the synthesis conditions.

It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally −90 • in charmonium decays. ψ ′ decaying into pseudoscalar pair provides a possibility to test this conjecture. However, the experimentally observed cross section for such a process is depicted by the two-fold integral which takes into account the initial state radiative (ISR) correction and energy spread effect. Using the generalized linear regression approach, a complex energy-dependent factor is approximated by a linear function of energy. Taking advantage of this simplification, the integration of ISR correction can be performed and an analytical expression with accuracy at the level of 1% is obtained. Then, the original two-fold integral is simplified into a one-fold integral, which reduces the total computing time by two orders of magnitude. Such a simplified expression for the observed cross section usually plays an indispensable role in the optimization of scan data taking, the determination of systematic uncertainty, and the analysis of data correlation.