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

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

Abstract

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

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.

Figures/Tables 15

References 26

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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

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

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

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

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

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