4He系统的广义约化R矩阵理论分析

doi:10.19596/j.cnki.1001-246x.8539

摘要/Abstract

摘要：

以广义约化R矩阵理论为基础, 运用RAC程序(R-matrix analysis code)综合分析有关⁴He系统的所有核反应的实验数据, 给出从0~30 MeV范围内一套完整的评价值, 各反应数据内部自恰。其中积分截面的拟合包括³He(n, total)、³He(n, n)³He、³He(n, d)D、³He(n, p)T、D(d, n)³He、D(d, p)T和T(p, n)³He, 同时给出相应的误差矩阵; 天体物理学S因子的拟合包括D(d, n)³He和D(d, p)T; 微分截面的拟合包括³He(n, n)³He、³He(n, p)T、D(d, d)D、D(d, n)³He和D(d, p)T。所有的拟合结果与实验数据和主流评价数据符合良好。在低能部分, 提高了D(d, n)³He反应和D(d, p)T反应各自积分截面的精确度。在高能部分, 将⁴He系统的评价数据进行了扩展。

关键词: R矩阵理论, 核反应截面, 核数据评价, ⁴He系统, D(d, n)³He反应

Abstract:

Based on a generalized reduced R-matrix theory, we analyze comprehensively all experimental data of nuclear reactions of ⁴He system with RAC (an R-matrix analysis code). A complete set of evaluations from 0 MeV or thresholds to 30 MeV is given. The data for each reaction is internally self-consistent. The fitting integral cross sections include those of ³He(n, total), ³He(n, n)³He, ³He(n, d)D, ³He(n, p)T, D(d, n)³He, D(d, p)T, and T(p, n)³He, with corresponding error matrix. The fitting astrophysical S-factors include those of D(d, n)³He and D(d, p)T. The fitting differential cross sections include those of ³He(n, n)³He, ³He(n, p)T, D(d, d)D, D(d, n)³He, and D(d, p)T. All fitting results are in good agreement with experimental data and mainstream evaluations. In the low-energy part, accuracy of integral cross-sections of D(d, n)³He and D(d, p)T are improved, respectively. In the high-energy part, the evaluation data of ⁴He system are extended.

Key words: R-matrix theory, nuclear reaction cross section, nuclear data evaluation, ⁴He system, D(d, n)³He reaction

周历波, 叶涛, 王佳, 孙伟力. ⁴He系统的广义约化R矩阵理论分析[J]. 计算物理, 2022, 39(6): 631-640.

Libo ZHOU, Tao YE, Jia WANG, Weili SUN. A Theoretical Analysis of Generalized Reduced R-Matrix of ⁴He System[J]. Chinese Journal of Computational Physics, 2022, 39(6): 631-640.

图/表 15

表1 反应道的道半径和阈值

Table 1 Radius and threshold of reaction channels

Reaction channel	Radius a_c/fm	Threshold/MeV
³He + n	3.530 0	0
D + d	5.956 3	-3.268 9
T + p	5.485 9	0.763 8
D + np	6.825 0	-5.493 4
P + 2np	6.825 0	-7.717 9

表2 实验数据的使用和光滑处理的相对误差

Table 2 The usage of experimental data and relative error of smoothing

Reaction	Cross section type	Incident energy region/MeV	Number of data points	Relative error of LOWESS results/%
³He(n, tot)	Total	1×10^-11 to 40	1639	1.9
³He(n, n)³He	Integral	1×10^-11 to 30	147	1.9
³He(n, p)³He	Integral	1×10^-10 to 30	237	4.5
³He(n, d)³He	Integral	4.36 to 30	58	9
D(d, p)T	Integral	0.014 5 to 38.5	78	1.2
D(d, n)³He	Integral	0.006 8 to 38.5	169	1.6
³He(n, np)D	Integral	7.9 to 23.7	5
³He(n, 2np)P	Integral	14 to 30	8
T(p, n)³He	Integral	0.35 to 14.44	397	4
D(d, d)D	Differential	0.96 to 13.45	1 038
D(d, n)³He	Differential	0.019 94 to 18	437
D(d, p)T	Differential	0.019 94 to 13.2	967
³He(n, d)D	Differential	14.4	12
³He(n, n)³He	Differential	1 to 30	396
³He(n, p)T	Differential	0.01 to 14.44	294
T(p, p)T	Differential	0.35 to 16.34	478
Total		1×10^-11 to 40	6 360

图1 D(d, n)3He积分截面

Fig.1 Integral cross sections of D(d, n)3He

图2 D(d, p)T积分截面

Fig.2 Integral cross sections of D(d, p)T

图3 3He(n, d)D积分截面

Fig.3 Integral cross sections of 3He(n, d)D

图4 3He(n, p)T积分截面

Fig.4 Integral cross sections of 3He(n, p)T

图5 中子全截面3He(n, tot)

Fig.5 Neutron total cross sections of 3He(n, tot)

图6 中子弹散3He(n, n)3He的积分截面

Fig.6 Elastic scattering cross sections of 3He(n, n)3He

图7 T(p, n)3He积分截面

Fig.7 Integral cross sections of T(p, n)3He

图8 RAC计算值的标准误差

Fig.8 Standard errors of RAC results

图9 D(d, n)3He反应S因子

Fig.9 S-factors of D(d, n)3He reaction

图10 D(d, p)T反应S因子

Fig.10 S-factors of D(d, p)T reaction

图11 3He(n, n)3He弹性散射微分截面(部分)，入射能分别为(a) =6 MeV；(b) =14.4 MeV；(c)16 MeV；(d)27 MeV

Fig.11 Differential cross sections of 3He(n, n)3He (partial) at incident energies (a)6 MeV; (b)14.4 MeV; (c)16 MeV; (d)27 MeV

图12 D(d, d)D弹性散射微分截面(部分)，入射能分别为(a)0.96 MeV；(b)2.51 MeV；(c)10.5 MeV；(d)13.2 MeV

Fig.12 Differential cross sections of D(d, d)D (partial) at incident energies (a)0.96 MeV; (b)2.51 MeV; (c)10.5 MeV; (d)13.2 MeV

图13 D(d, n)反应与D(d, p)反应截面比值

Fig.13 Cross section ratios of D(d, n) and D(d, p) reaction

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⁴He系统的广义约化R矩阵理论分析

A Theoretical Analysis of Generalized Reduced R-Matrix of ⁴He System

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