用可靠的外推方案改进预测并更好地理解因式分解
Improving Predictions with Reliable Extrapolation Schemes and Better Understanding of Factorization
摘要：
我们研究了低能核物理计算中两种不同的不确定性来源，并提出了解决这些不确定性的方法。谐振子基展开在从头计算原子核结构中有着广泛的应用。有限的计算资源通常要求在观测量完全收敛之前截断基，这就需要可靠的外推方案。我们表明，有限振子基础有效地施加了硬壁边界条件。我们准确地确定了作为振子空间参数的函数的硬壁的位置，推导出的能量和其他可观的外推公式，并讨论了这种方法的扩展到更高的角动量。核子敲除反应已被广泛用于研究和理解核性质。这样的分析隐含地假设探测器的效应可以与靶核的物理特性分开。这种原子核结构和反应组分之间的因式分解依赖于重整化标度和方案，并且还没有得到很好的理解。但它对于解释实验和提取与过程无关的核特性可能至关重要。利用相似性重整化群（SRG）变换，系统地研究了最简单的氘核电衰变敲除过程的因子分解的尺度依赖性。我们发现，规模依赖的程度强烈依赖于运动学，但在一个系统的方式。基于检查相关的重叠矩阵元素，我们能够定性地解释，甚至预测的性质尺度依赖的基础上考虑的运动学。
英文摘要：
We investigate two distinct sources of uncertainty in low-energy nuclear physics calculations and develop ways to account for them. Harmonic oscillator basis expansions are widely used in ab-initio nuclear structure calculations. Finite computational resources usually require that the basis be truncated before observables are fully converged, necessitating reliable extrapolation schemes. We show that a finite oscillator basis effectively imposes a hard-wall boundary condition. We accurately determine the position of the hard-wall as a function of oscillator space parameters, derive extrapolation formulas for the energy and other observables, and discuss the extension of this approach to higher angular momentum. Nucleon knockout reactions have been widely used to study and understand nuclear properties. Such an analysis implicitly assumes that the effects of the probe can be separated from the physics of the target nucleus. This factorization between nuclear structure and reaction components depends on the renormalization scale and scheme, and has not been well understood. But it is potentially critical for interpreting experiments and for extracting process-independent nuclear properties. We use similarity renormalization group (SRG) transformations to systematically study the scale dependence of factorization for the simplest knockout process of deuteron electrodisintegration. We find that the extent of scale dependence depends strongly on kinematics, but in a systematic way. Based on examination of the relevant overlap matrix elements, we are able to qualitatively explain and even predict the nature of scale dependence based on the kinematics under consideration.
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