论文标题
部分可观测时空混沌系统的无模型预测
Higher-order isospin-symmetry breaking corrections to nuclear matrix elements of superallowed $0^+\to 0^+$ Fermi $β$ decay of $T=1$ nuclei
论文作者
论文摘要
我们研究了壳模式形式主义，包括包括isospin-Memortry-quretry-quctry-qurething校正（$δ_{c} $），以$ 0^+\ to 0^+$ fermi $β$衰减为$ t = 1 $ nuclei。基于少量的扰动扩展，例如质子和中子径向波之间的重叠积分与统一或与其isospin-Memmetry-MemmeTrysy值的过渡密度之间的重叠积分的偏差，我们得出$Δ_C$可以作为六个术语（包括两个领先的序列（LO）序列（nlo）序列（n-）序列（n上）（n上）（n上），nlo-efer-udec $Δ_c$ nlo上（n-）序列（n-术语和一个接下来的接头订单（nnnlo）术语。在一系列的Towner和Hardy以及最近对本作者的计算中，已经考虑了前两个术语，而其余四个术语通常被忽略。在$ P $，$ SD $和$ PF $ shells的下部进行了13个过渡的数值计算。我们的结果表明，所有高阶条款总和的大小为$ 10^{ - 3} $％。该数字远低于具有木材 - 撒克逊径向波函数的壳模型中量化的典型理论错误。
We study the shell-model formalism to include the isospin-symmetry-breaking correction ($δ_{C}$) to nuclear matrix element of superallowed $0^+\to 0^+$ Fermi $β$ decays of $T=1$ nuclei. Based on a perturbation expansion in a small quantity, such as the deviation of the overlap integral between proton and neutron radial wave functions from unity or of the transition density from its isospin-symmetry value, we derive that $δ_C$ can be obtained as a sum of six terms, including two leading order (LO) terms, two next-to-leading order (NLO) terms, one next-to-next-to-leading order (NNLO) term and one next-to-next-to-next-to-leading order (NNNLO) term. The first two terms have been considered in a series of shell-model calculations of Towner and Hardy as well as in the recent calculation of the present authors, while the remaining four terms are usually neglected. A numerical calculation has been carried out for 13 transitions in the $p$, $sd$ and the lower part of $pf$ shells. Our results indicate that the magnitude of the sum of all higher order terms is of the order of $10^{-3}$ %. This number is well below typical theoretical errors quantified within the shell model with Woods-Saxon radial wave functions.
