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arXiv 2406.01896nucl-th
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在协变密度泛函理论中迈向精确的核质量表

Towards accurate nuclear mass tables in covariant density functional theory

A. Taninah, B. Osei, A. V. Afanasjev, U. Perera, S. Teeti

AI总结:

本研究在协变密度泛函理论框架内分析了ABOA优化方法,全局研究了基组截断对结合能的数值误差影响,并提出新程序以更好地控制这些误差。

摘要:

本研究重点详细分析了基于锚点的优化方法(ABOA),将其与其他全局拟合协议进行了比较,并对结合能计算中基组截断效应进行了全局分析。结果表明,ABOA提供的解接近于其他方法所得的解,但仅需其计算时间的一小部分。在ABOA的几次初始迭代后应用较软的校正函数,可稳定并加速其收敛。首次在协变密度泛函理论(CDFT)框架内,针对对应于无限基组的渐近值,全局研究了与玻色子和费米子基组截断相关的结合能计算数值误差。这些误差通常随着核的质量和形变的增加而增大。为了将几乎所有质子数$Z<120$的原子核在玻色子部分的误差降至10 keV以下,应将玻色子基组截断在$N_B=28$,而非目前使用的$N_B=20$。相比之下,在CDFT中通过截断费米子基组来降低结合能误差在数值上的计算成本显著更高。本文首次表明,结合能作为由$N_F$给出的费米子基组大小的函数,其收敛的模式和速度取决于协变能量密度泛函的类型。使用介子-核子耦合常数或点耦合的显式密度依赖性,会大幅降低结合能作为$N_F$函数的收敛速度。本文提出了一种寻找结合能渐近值的新程序:它允许更好地控制数值误差。

英文摘要:

The current investigation focuses on detailed analysis of the anchor based optimization approach (ABOA), its comparison with alternative global fitting protocols and on the global analysis of the truncation of basis effects in the calculation of binding energies. It is shown that ABOA provides a solution which is close to that obtained in alternative approaches but at small portion of their computational time. The application of softer correction function after few initial iterations of ABOA stabilizes and speeds up its convergence. For the first time, the numerical errors in the calculation of binding energies related to the truncation of bosonic and fermionic bases have been globally investigated with respect of asymptotic values corresponding to the infinite basis in the framework of covariant density functional theory (CDFT). These errors typically grow up with the increase of the mass and deformation of the nuclei. To reduce such errors in bosonic sector below 10 keV for almost all nuclei with proton number $Z<120$ one should truncate the bosonic basis at $N_B=28$ instead of presently used $N_B=20$. The reduction of the errors in binding energies due to the truncation of the fermionic basis in CDFT is significantly more numerically costly. For the first time it is shown that the pattern and the speed of the convergence of binding energies as a function of the size of fermionic basis given by $N_F$ depend on the type of covariant energy density functional. The use of explicit density dependence of the meson-nucleon coupling constants or point couplings slows down substantially the speed of convergence of binding energies as a function of $N_F$. A new procedure for finding the asymptotic values of binding energies is suggested in the present paper: it allows better control of numerical errors.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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