Abstract—

An increase in the amplitude of the wave function of a massive nonrelativistic particle incident on a one-dimensional crystal is studied. Similarly to the case of light propagation in a one-dimensional periodic medium, a perturbation theory is constructed for small deviations in the energy of the incident particle from the boundary of the band gap. Formulas are derived for the wave function of the particle in the crystal and the reflection and transmission coefficients. The general features and differences between the initial equations, the obtained characteristics for the massive particle and the properties of the light field are analyzed in detail. It is found that the main properties of the wave function have the same features as the properties of the light field. Numerical estimates are given for the increase in the amplitude of the wave function of the particle inside the one-dimensional periodic medium with a period that is equal to the lattice constant of palladium. It is shown that, as the energy of the incident particle decreases, the amplitude of the wave function increases significantly, which correlates with the experimentally observed increase in the yield of D–D reactions for low-energy particles compared with the values obtained by extrapolating data from the high-energy region.

中文翻译：

---

关于大质量非相对论粒子入射到晶体上的波函数幅度的强烈增加（一维近似）

摘要——

研究了入射在一维晶体上的大质量非相对论粒子的波函数振幅的增加。类似于光在一维周期性介质中传播的情况，微扰理论是针对入射粒子的能量与带隙边界的微小偏差而构建的。推导出晶体中粒子的波函数以及反射和透射系数的公式。详细分析了初始方程的一般特征和差异、获得的大质量粒子特征和光场性质。发现波函数的主要性质与光场的性质具有相同的特征。给出了周期等于钯的晶格常数的一维周期性介质内粒子的波函数幅度增加的数值估计。结果表明，随着入射粒子的能量降低，波函数的幅度显着增加，这与实验观察到的低能粒子的 D-D 反应产率与通过外推获得的值相比增加相关来自高能区的数据。