简单的量子力学解释了GSI达姆施塔特振荡即使是未被检测到的中微子;动量守恒需要在初始和最终状态产生振荡的相同干扰
Simple quantum mechanics explains GSI Darmstadt oscillations Even with undetected neutrino; Momentum conservation requires Same interference producing oscillations in initial and final states
摘要：
研究放射性离子K俘获衰变振荡的GSI实验研究了中微子质量和混合，但没有检测到中微子。即使中微子没有被探测到，量子力学也会把初态和终态联系起来。基本的物理原理非常简单。在β衰变中发射的中微子是不同质量、不同动量、相同能量的状态的相干线性组合。由于产生中微子的弱相互作用保持了动量，跃迁前的初始态也必须包含具有相同动量差和明确定义的相对幅度和相位的状态的相干线性组合。一个具有确定动量差的单粒子态也有一个容易计算的能量差。在离子产生和衰变之间的时间间隔内，具有不同能量的两个状态的线性组合在时间上振荡。测量振荡周期可以得到两个中微子质量本征态的中微子质量平方之差。对于动量空间中的“双缝”或“哪条路径”实验，从没有自由参数的粗略近似中获得的值与KAMLAND实验中观察到的结果相差不到10%。仅观察离子消失而不检测中微子避免了由低中微子吸收截面引起的信号抑制
英文摘要：
GSI experiment studying oscillations in K-capture decay of radioactive ion investigates neutrino masses and mixing without detecting neutrino. Even when neutrino is not detected quantum mechanics relates initial and final states. The basic physics is very simple. Neutrinos emitted in beta decay are coherent linear combinations of states with different masses, different momenta and same energy. Since the weak interaction producing the neutrino conserves momentum, the initial state before the transition must also contain a coherent linear combination of states with the same momentum difference and a well defined relative magnitude and phase. A one-particle state with a definite momentum difference also has an easily calculated energy difference. In the time interval between creation of the ion and its decay a linear combination of two states with different energies oscillates in time. Measuring the oscillation period gives a value for the difference between squared neutrino masses of the two neutrino mass eigenstates. The value obtained from a crude approximation with no free parameters for this "two-slit" or "which path" experiment in momentum space differs by less than 10% from the result observed in the KAMLAND experiment. Observing only ion disappearance without detecting neutrino avoids signal suppression by low neutrino absorption cross section
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