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arXiv 2104.04688nucl-th
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重核的收敛从头计算

Converged ab initio calculations of heavy nuclei

T. Miyagi, S. R. Stroberg, P. Navrátil, K. Hebeler, J. D. Holt

摘要:

提出了一种新的存储方案,用于原子核从头计算中广泛使用的正常有序两体近似中的三核子(3N)相互作用矩阵元。该方案将所需的存储器减少了大约两个数量级,这允许用$E_{\rm 3max}=28$的标准截断生成3N个相互作用矩阵元素,远远超过先前的18个限制。我们证明了这足以得到$^{132}$ Sn的基态能量收敛到几MeV之内的$E_{\rm 3max}$截断.此外,我们研究了渐近收敛行为,并进行外推到未截断的限制.最后,我们调查截断的影响时,不断发展的自由空间3N相互作用的相似性重整化群。我们发现,具有角动量的块$J_{\rm rel}>9/2$对基态能量的贡献主要由基底截断伪影所决定,这种伪影在大空间极限下消失,因此这些计算代价很高的分量可以忽略不计.对于在这项工作中使用的两套核相互作用,得到的结合能的$^{132}$锡同意与实验值的理论不确定性。这项工作使收敛从头计算的重核。

英文摘要:

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{\rm 3max}=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of $^{132}$Sn converged to within a few MeV with respect to the $E_{\rm 3max}$ truncation.In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{\rm rel}>9/2$ to the ground-state energy is dominated by a basis-truncation artifact which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of $^{132}$Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

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