一般单体算子的平移不变矩阵元
Translationally invariant matrix elements of general one-body operators
摘要：
对标准模型的精确测试和对标准模型之外的物理学的研究通常需要输入原子核结构。在能够提供精确的核波函数的核从头算技术的发展方面已经有了巨大的进展。为了计算观测量，需要计算复杂算子的矩阵元素。通常，这些矩阵元素将包含来自质心（COM）运动的虚假贡献。当寻求精确结果时，这可能是有问题的。在这里，我们推导出一个变换依赖于谐振子波函数的属性，允许一个精确的COM运动污染适用于任何一个身体运营商取决于核子坐标和动量。如果核本征函数分解为本征分量和COM分量的乘积，则得到的多核子矩阵元是几何不变的，例如，在无核壳模型方法中。该变换最近已在计算~6He β衰变的原子核结构反冲修正中得到应用。
英文摘要：
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing accurate nuclear wave functions. For the calculation of observables, matrix elements of complicated operators need to be evaluated. Typically, these matrix elements would contain spurious contributions from the center-of-mass (COM) motion. This could be problematic when precision results are sought. Here, we derive a transformation relying on properties of harmonic oscillator wave functions that allows an exact removal of the COM motion contamination applicable to any one-body operator depending on nucleon coordinates and momenta. Resulting many-nucleon matrix elements are translationally invariant provided that the nuclear eigenfunctions factorize as products of the intrinsic and COM components as is the case, e.g., in the no-core shell model approach. An application of the transformation has been recently demonstrated in calculations of the nuclear structure recoil corrections for the beta-decay of 6He.
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