A microscopic description of nuclear fission for r-process nucleosynthesis

尽管核裂变的基本机制早在80多年前就已经由N.玻尔用量子隧穿理论解释过了。对所有相关的裂变机制——自发的、诱导的、β -延迟的、光裂变——提供精确的微观描述仍然是不可能的。核裂变的微观描述不仅意味着计算寿命，而且还意味着计算出出射碎片中电荷和质量的统计分布以及它们之间共享的系统总能量。这些信息对于理解我们宇宙中观测到的重元素丰度的模式至关重要，特别是在一些天体物理场景中。基于快中子捕获（r过程）形成比铁-56重的元素的标准模型大量涉及裂变的概念，因为它代表了机制的终点。根据裂变寿命和中子通量的长度，裂变可以产生新的种子，这些种子可以用于新的r过程事件，从而改变元素的相对丰度。此外，裂变本身也是中子和伽马射线的来源。这些额外的中子可以在外部中子通量停止后继续进行r过程。这种机制被称为裂变再循环，它涉及到中子非常丰富的原子核，无法通过实验测量得到。为了提供裂变的微观描述，核能密度泛函计算（NEDF）被用来计算势能面。考虑到这些能量面非常复杂的结构，人们需要执行数千次NEDF计算来探索整个能源景观。因此，NEDF裂变计算不是很常见，它们仅限于少数具体情况。高斯过程仿真（GPE）是一种机器学习的回归方法，可以用来减少这些大量计算的计算负担。GPE方法基于非常简单的数学假设：多维空间中给定的能量面可以用全局趋势项（多项式）和其上的一些高斯波动来建模。该项目旨在降低计算裂变势能面的计算成本，使用GPE，并使用其他数值工具来提高NEDF计算的效率。

Although the basic mechanism of nuclear fission has been already explained more than 80 years ago by N. Bohr in terms of quantum tunnelling. It is still not possible to provide a microscopic description of all relevant available fission mechanisms - spontaneous, induced, beta-delayed, photo-fission - to a high level of accuracy.A microscopic description of nuclear fission does not only imply calculating life-times, but also the statistical distribution of charge and mass in the outgoing fragments as well the total energy of the system shared among them. This information is essential, especially in several astrophysical scenarios, for understanding the patterns observed in abundances of heavy elements in our Universe.The standard model based on rapid-neutron capture (r-process) to form elements heavier than Iron-56 heavily involves the concept of fission, since it represents the end-point of the mechanism. According to the fission lifetime and the length of neutron flux, fission can produce new seeds that can be used for new r-process events, thus changing the relative abundances of elements. Moreover fission is itself a source of neutron and gamma rays. Such extra neutrons can keep going the r-process even after the external neutron flux has stopped. This mechanism is called fission recycling and it involves very neutron rich nuclei that are not accessible via experimental measurements.To provide a microscopic description of fission, nuclear energy density functional calculations (NEDF) are used to calculate potential energy surfaces. Given the very complicated structure of these energy surfaces, one needs to perform thousands of NEDF calculations to explore the entire energy landscape. Consequently NEDF fission calculations are not very common and they are restricted to a few specific cases.Gaussian Process Emulation (GPE), a regression method from machine learning, can be used to reduce the computational burden of these massive calculations. GPE methods are based on very simple mathematical assumptions: a given energy surface in a multidimensional space can be modelled by a global trend term (a polynomial) and some Gaussian fluctuations on top of it.This project seeks to reduce the computational cost of calculating potential energy surfaces for fission, using GPE, and using other numerical tools to improve the efficiency of the NEDF calculations.