In a recent article, we noticed that the electron density in condensed matter exhibits large spikes close to the atomic nuclei. We showed that the peak magnitude of these spikes in the electron densities, 3–4 orders larger than the average electron plasma density in the Sun’s core, have no effect on the neutrino emission and absorption probabilities or on the neutrinoless double beta decay probability. However, it was not clear if the effect of these spikes is equivalent to that of an average constant electron density in matter. We investigated these effects by a direct integration of the coupled Dirac equations describing the propagation of flavor neutrinos into, through, and out of the matter. We proposed a new iteration-based algorithm for computing the neutrino survival/appearance probability in matter, which we found to be at least 20 times faster than some direct integration algorithms under the same accuracy. With this method, we found little evidence that these spikes affect the standard oscillations probabilities. In addition, we show that the new algorithm can explain the equivalence of using average electron densities instead of the spiked electron densities. The new algorithm is further extended to the case of light sterile neutrinos.

中文翻译：

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中微子振荡物质效应的原子尺度电子密度分布和快速高效迭代算法的影响

在最近的一篇文章中，我们注意到，凝聚态物质中的电子密度在靠近原子核的位置出现大的尖峰。我们发现，这些电子密度峰值的峰值比太阳核心的平均电子等离子体密度大3-4个数量级，对中微子的发射和吸收概率或无中微子双β衰变概率没有影响。但是，尚不清楚这些尖峰的影响是否等于物质中平均恒定电子密度的影响。我们通过直接耦合Dirac方程的积分研究了这些影响，这些Dirac方程描述了风味中微子进入，穿过和流出物质的传播。我们提出了一种新的基于迭代的算法来计算物质中微子的存活/出现概率，在相同的精度下，我们发现它比某些直接积分算法至少快20倍。使用这种方法，我们发现很少有证据表明这些尖峰会影响标准振荡概率。此外，我们证明了新算法可以解释使用平均电子密度而不是尖峰电子密度的等效性。新算法进一步扩展到轻度无菌中微子的情况。