Observation of the interference between the atmospheric and solar oscillation waves with the correct magnitude would provide another manifestation of the three-generation structure of leptons. As a prerequisite for such analyses we develop a method for decomposing the oscillation S matrix into the atmospheric and solar amplitudes. Though the similar method was recently proposed successfully in vacuum, once an extension into the matter environment is attempted, it poses highly nontrivial problems. Even for an infinitesimal matter potential, inherent mixture of the atmospheric and solar oscillation waves occurs, rendering a simple extension of the vacuum definition untenable. We utilize general kinematic structure as well as analyses of the five perturbative frameworks, in which the nature of matter-dressed atmospheric and solar oscillations are known, to understand the origin of the trouble, how to deal with the difficulty, and to grasp the principle of decomposition. Then, we derive the amplitude decomposition formulas in these frameworks, and discuss properties of the decomposed probabilities. We mostly discuss the \(\nu _{\mu } \rightarrow \nu _{e}\) channel, but a comparison with the \(\nu _{\mu } \rightarrow \nu _{\tau }\) channel reveals an interesting difference.

观测到具有正确幅度的大气和太阳振荡波之间的干扰将提供轻子三代结构的另一种表现形式。作为进行此类分析的前提，我们开发了一种分解振荡S的方法矩阵转换成大气和太阳振幅。尽管最近在真空中成功地提出了类似的方法，但是一旦尝试将其扩展到物质环境中，就会带来非常重要的问题。即使对于无限大的物质电势，也会发生大气和太阳振荡波的固有混合，这使得真空清晰度的简单扩展变得站不住脚。我们利用一般的运动学结构以及对五个扰动框架的分析来了解问题的根源，如何处理困难并掌握其原理，在五个扰动框架中，已知有受物质影响的大气和太阳振荡的性质。分解。然后，我们在这些框架中推导了振幅分解公式，并讨论了分解概率的性质。我们主要讨论\（\ nu _ {\ mu} \ rightarrow \ nu _ {e} \）通道，但是与\（\ nu _ {\ mu} \ rightarrow \ nu _ {\ tau} \）通道的比较显示了一个有趣的现象区别。