无中微子双贝塔衰变机制的理论研究及其核矩阵元的计算

Neutrinoless double beta decay is the key to the puzzle of neutrino, and also gives us implications on the possible new physics beyond Standard Model. The studies of these decays involves both the lepton number violation mechanisms in particle physics and the complicated nuclear structure problems. Our studies will focus on both sides, first a thorough understanding on the breaking of the lepton number symmetry with the constraints from current high energy experiments; secondly the realization of the mechanisms under the complicated nuclear environments, the corresponding lepton number violating nuclear process. The nuclear structure problem is a complicated many-body problem, we resort to the Nuclear Shell Model or QRPA approaches to solve this problem. We start by calculating the structure for the parent and daughter nuclei as well as intermediate states, and then with the transition operators we calculate the transition rates (nuclear matrix elements) for the decay, combined with the corresponding electrons' phase space factors, we could finally obtain the half-lives of the neutrinoless double beta decay for various double beta decay candidates. Our results are important for the future double beta decay experiments and is crucial for the determination of the neutrino absolute mass, it has the key importance to solve the neutrino mass problems.

无中微子双贝塔衰变的研究是解开中微子谜题的一把钥匙，同时也是研究超出标准模型的新物理的一个窗口。对这种衰变的研究不单单涉及到粒子物理里面轻子数破缺的机制，也涉及到复杂的核结构问题。我们的研究将着眼于这两方面，深入研究超出标准模型的轻子数破缺机制，通过现有的数据对这些机制作出限制；另一方面，研究这些机制在复杂核环境下的实现，即对应的核过程。核的结构是一个复杂的多体问题，我们主要求诸壳模型和QRPA方法来尝试求解这些复杂的结构。我们首先计算衰变母核，子核以及中间态的结构，进而通过对应的转变算符计算出最终的衰变核跃迁几率（即核矩阵元），与相应的电子相空间因子结合，最终得到各种双贝塔同位素的无中微子双贝塔衰变寿命。我们的计算结果对于无中微子双贝塔衰变实验有着重要意义，同时也是评估中微子绝对质量的必须条件，对于解开中微子质量之谜有着重要的作用。

无中微子双贝塔衰变是寻找超出标准模型的新物理的重要过程之一，在精确的核矩阵元的帮助下，它可以用来限制各类新物理模型。我们通过使用基于现实核力的准粒子无规相位近似方法来计算这些物理量。我们的结果得到合理的核矩阵元，同时其他的预言也能与实验相符合。在结合其他中微子实验如JUNO的基础上，我们能给出双贝塔衰变半衰期的预言，这些结果有助于双贝塔衰变相关实验的设计。