晶格上任意多个耦合通道的散射相移和混合角
Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice
摘要：
我们提出了一个晶格方法确定散射相移和混合角的情况下，任意数量的耦合通道。以前的核晶格有效场论模拟仅限于两个自旋$1/2$粒子散射的两个分波的混合，这不足以分析核子-核或核-核散射过程。在所提出的方法中，相移和混合角提取的径向波函数通过投影到分波基的三维晶格哈密顿获得。我们使用一个球壁势作为边界条件，以及通道混合辅助势来构造满秩$S$矩阵。我们的方法可以适用于任何自旋的粒子，但我们在这里集中在两个自旋$1$玻色子散射涉及多达四个耦合通道。对于所考虑的测试势，在晶格上提取的相移和混合角与通过求解连续介质中的薛定谔方程计算的相移和混合角一致。
英文摘要：
We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to two partial waves for scattering of two spin-$1/2$ particles, which is insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering processes. In the proposed method, the phase shifts and mixing angles are extracted from the radial wave functions obtained by projecting the three-dimensional lattice Hamiltonian onto the partial wave basis. We use a spherical wall potential as a boundary condition along with a channel-mixing auxiliary potential to construct the full-rank $S$ matrix. Our method can be applied to particles with any spin, but we focus here on scattering of two spin-$1$ bosons involving up to four coupled channels. For a considered test potential, the phase shifts and mixing angles extracted on the lattice are shown to agree with the ones calculated by solving the Schrödinger equation in the continuum.
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