Ab initio Prediction of the 163Ho Electron Capture Spectrum

在这个工作组中，我们将从头计算~(163)Ho的量热电子俘获光谱。从粒子物理学的角度来看，电子与质子的弱相互作用导致了中子和电子中微子的产生，这在理论上是直截了当的。在中性原子中，当同样的相互作用发生时，更复杂的过程将伴随着电子被原子核捕获。原子中的电子不是独立的身份，由于强大的库仑力，一旦一个电子被俘获，所有电子都会发生反应。因此，HO的量热测量光谱不是由分别来自3S到6S和3P1/2到5P1/2壳层的俘获事件的7个洛伦兹形峰给出的，而是出现了几个额外的具有多重态结构的震荡和震脱结构。对全谱的理论描述需要了解描述Dy原子随时间演化的格林函数传播子，其电子多组态多体波函数对应于具有一个附加核心空穴的Ho的基态。时间演化涉及到荧光，俄歇衰变为束缚态和连续态。这些衰变产生了光谱的尾部，最终产生了受中微子质量影响最大的光谱终点。结合量子化学(组态相互作用)和固态物理(格林函数和重整化群)中使用的数值方法，我们的目标是获得能够以前所未有的精度预测核能级衰变的多重态控制的光谱的数值精度。为了实现这一点，我们将包括所有可能的局部多重态(摇摆和摇摆)以及激发的俄歇和荧光产额衰减。我们还将进一步考虑局域HO_4F态与宿主金属的电子连续体的相互作用。我们将开发必要的数值方法来处理基态和激发态的多体关联，并以亚电子伏特的精度进行处理。此外，我们还将提供计算的误差估计，表明物理现实与计算光谱之间的最大差异。这些计算将首先提供对电子俘获共振及其结构的详细了解。其次，这些计算将提供多重态激发对终点区的影响程度，由于俄歇电子在基质材料中的多次散射事件而在光谱中扩展精细结构，以及与163Ho 4f壳层和163Ho核的磁矩排列有关的衰变过程中的选择规则。最终目的是提供对准确确定中微子质量所需的163Ho电子俘获谱的详细了解。

Within this workgroup, we will ab initio predict the calorimetric electron capture spectra of 163Ho. From the particle physics point of view, the weak interaction of an electron with a proton leading to the creation of a neutron and an electron neutrino is theoretically straightforward. In a neutral atom, when this same interaction occurs, more complex processes will accompany the electron capture by the nucleus. Electrons in an atom are not independent identities and due to strong Coulomb forces, all electrons react once one electron is captured. The calorimetrically measured spectrum of Ho is thus not given by just 7 Lorentzian shaped peaks originating from capture events from the 3s to 6s and 3p1/2 to 5p1/2 shell respectively, but several additional shake-up and shake-off structures with an involved multiplet structure emerge. The theoretical description of the full spectrum requires one to have knowledge about the Green’s function propagators describing the time evolution of a Dy atom with the electron multi-configurational many body wave-function corresponding to the ground-state of Ho with one additional core hole. The time evolution involves fluorescence and Auger decays into bound and continuum states. These decays produce the tails of the spectrum and ultimately create the end-point of the spectrum that is influenced most by the mass of the neutrino.Using a combination of numerical methods as used in quantum chemistry (configuration interaction) and solid state physics (Green’s functions and renormalization group) we aim to achieve a numerical accuracy able to predict the mulitplet governed spectra of the core level decay with unprecedented precision. In order to achieve this we will include all possible local multiplets (shake-up and shake-down) as well as Auger and fluorescence yield decay of the excitations. We furthermore will consider the interaction of the local Ho 4f states with the electronic continuum of the host metal. We will develop the needed numerical methods to handle the many body correlations of both the ground-state as well as the excited states with sub-electron volt accuracy. We will furthermore provide an error estimate of the calculations indicating the maximal difference between the physical reality and calculated spectra.These calculations will firstly provide a detailed understanding of the electron capture resonances and their structure. Secondly, these calculations will provide information how much the end-point region is influenced by mulitplet excitations, extended fine-structure in the spectra due to multiple scattering events of Auger electrons in the host material and selection rules in the decay process related to the alignment of the magnetic moment of the 163Ho 4f shell and the 163Ho nucleus. The final aim is to provide a detailed understanding of the 163Ho electron capture spectrum needed for the accurate determination of the neutrino mass.