Applications and the improvements of the N-K function for the analyses and observations of the high-energy cosmic neutrino and primary electrons

为了精确观测宇宙线电子谱，我们采用解析的方法计算了在贝加尔湖和冰立方计划中由水或冰中产生的μ子或电子簇射产生的Cherenkov光子的横向分布，并在CERN的200 GeV加速器电子束上验证了我们的能量测量误差在10%以内。电子的光谱形状的变化进行评估，在通过大气层的气球从暗物质起源的额外的可能的光谱。我们还估计了气球上方大气中产生的背景电子的精确数量。

We make analytic approaches to evaluate the lateral distributions of the Cherenkov Photons by muons or electron showers produced in the water or ice to observe the high-energy neutrino in the Baikal and IceCube Projects.For the precise observation of the cosmic-ray electron spectrum with our emulsion chambers, we confirm that the error of our energy determination is within 10% with the accelerator electron beam of 200GeV at CERN. The change of the spectral shape of electrons is evaluated during passing through the atmosphere over the balloons for an additional possible spectrum from the dark matter origin. We also estimate the precise amounts of background electrons produced in the atmosphere over the balloons.