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arXiv 2109.02205nucl-thnucl-ex
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在Gogny相互作用壳模型中分析的$β$衰变中张量力的作用

Tensor force role in $β$ decays analyzed within the Gogny-interaction shell model

B. Dai, B. S. Hu, Y. Z. Ma, J. G. Li, S. M. Wang, C. W. Johnson, F. R. Xu

摘要:

背景资料:著名的$^{14}$ C $β$衰变的半衰期非常长,有不同的机制:张量力,跨壳层混合和三体力,被提出来解释导致小过渡矩阵元的抵消。目的:我们重新审视并分析张量力对$^{14}$ C以及邻近同位素的$β$衰变的作用。方法:在Gogny相互作用中加入张量力,导出壳模型计算的有效哈密顿量。计算在$p$ - $sd$模型空间中进行,以研究跨壳层效应。此外,我们根据总轨道角动量$L$分解波函数,以分析张量力和跨壳层混合的影响。结果:张量力的引入显著改善了碳同位素$β$衰变性质的壳模型计算。特别是,$^{14}$ C的$β$衰变异常缓慢,可以用张量力的同位旋$T=0$部分来解释,它改变了$^{14}$ N的轨道角动量分量$L=0,1$,并导致伽莫夫-泰勒跃迁强度的显著抑制。同时,改进了对其它邻近$β$衰变的描述.结论:波函数分解成$L$分量说明张量力如何修改核子波函数,特别是抑制$β$ -衰变矩阵元素。壳层间混合对$β$ -衰减强度也有明显影响。包含张量力似乎并没有显着改变,但是,结合能的核内的现象相互作用。

英文摘要:

Background: The half-life of the famous $^{14}$C $β$ decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. Purpose: We revisit and analyze the role of the tensor force for the $β$ decay of $^{14}$C as well as of neighboring isotopes. Methods: We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a $p$-$sd$ model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum $L$ in order to analyze the effects of the tensor force and cross-shell mixing. Results: The inclusion of the tensor force significantly improves the shell-model calculations of the $β$-decay properties of carbon isotopes. In particular, the anomalously slow $β$ decay of $^{14}$C can be explained by the isospin $T=0$ part of the tensor force, which changes the components of $^{14}$N with the orbital angular momentum $L=0,1$, and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby $β$ decays are improved. Conclusions: Decomposition of wave function into $L$ components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of $β$-decay matrix elements. Cross-shell mixing also has a visible impact on the $β$-decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

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