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arXiv 0904.1709nucl-th
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壳模型中无中子双β衰变算符的修正

Corrections to the Neutrinoless Double-Beta-Decay Operator in the Shell Model

Jonathan Engel, Gaute Hagen

备注：
7 pages, 6 figures
发表信息：
Phys.Rev.C79:064317,2009
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摘要：

我们利用图解微扰理论构造了一个有效的壳模型算符，用于~（82）Se的无中微子双β衰变.我们的出发点与最近用壳模型计算双β衰变时所用的生成哈密顿量的波恩-C核子-核子相互作用相同。在首先总结高能梯形图，占短程相关，然后添加图的G矩阵的低阶占较长的范围内的相关性，我们折叠的两体矩阵元素的有效运营商与过渡密度从最近的壳模型计算，以获得总的核矩阵元素，管理衰变。虽然高能梯形图在很短的距离上抑制了这种矩阵元，但在一到两个费米之间的距离上却增强了这种矩阵元，因此它们的整体影响很小。由于长程物理的修正是很大的，但相互抵消，使完全校正的矩阵元素是可比的裸运营商产生的。大的和物理上不同的低阶项之间的这种消除表明了可靠的非微扰计算的重要性。

英文摘要：

We use diagrammatic perturbation theory to construct an effective shell-model operator for the neutrinoless double-beta decay of 82Se. The starting point is the same Bonn-C nucleon-nucleon interaction that is used to generate the Hamiltonian for recent shell-model calculations of double-beta decay. After first summing high-energy ladder diagrams that account for short-range correlations and then adding diagrams of low order in the G matrix to account for longer-range correlations, we fold the two-body matrix elements of the resulting effective operator with transition densities from the recent shell-model calculation to obtain the overall nuclear matrix element that governs the decay. Although the high-energy ladder diagrams suppress this matrix element at very short distances as expected, they enhance it at distances between one and two fermis, so that their overall effect is small. The corrections due to longer-range physics are large, but cancel one another so that the fully corrected matrix element is comparable to that produced by the bare operator. This cancellation between large and physically distinct low-order terms indicates the importance of a reliable nonperturbative calculation.

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