We apply the calculable R-matrix method to determine the cross sections of the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$^{12,13}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>12</mn> <mo>,</mo> <mn>13</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>C(<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$p,\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>,</mo> <mi>γ</mi> </mrow> </math></EquationSource> </InlineEquation>)<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$^{13,14}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>13</mn> <mo>,</mo> <mn>14</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>N reactions using both local Woods-Saxon (WS) and nonlocal Perey-Buck (PB) potentials. Benchmark calculations are first performed for the <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$^{12}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>12</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>C(<InlineEquation ID="IEq11"> <EquationSource Format="TEX">$p,\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>,</mo> <mi>γ</mi> </mrow> </math></EquationSource> </InlineEquation>)<InlineEquation ID="IEq12"> <EquationSource Format="TEX">$^{13}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>13</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>N reaction, and the results show good agreement with the standard codes FRESCO and RADCAP, as well as with recent calculations in other works. Furthermore, the method is applied to investigate the <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$^{13}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>13</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>C(<InlineEquation ID="IEq14"> <EquationSource Format="TEX">$p,\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>,</mo> <mi>γ</mi> </mrow> </math></EquationSource> </InlineEquation>)<InlineEquation ID="IEq15"> <EquationSource Format="TEX">$^{14}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>14</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>N reaction. Analysis of the astrophysical S-factors for both reactions indicates no significant difference between the local and nonlocal potential calculations, with discrepancies limited to approximately 7%–8%. The successful application of the calculable R-matrix method to these <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$(p,\gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> processes provides a framework for future studies involving nonlocal potentials derived from microscopic models.

Application of the Calculable R-matrix to Study the $^{12,13}$C(p,$\gamma $)$^{13,14}$N Reaction

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发表日期：

2026年3月17日

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Nguyen Hoang Phuc,
Nguyen Tri Toan Phuc,
Do Cong Cuong

摘要

We apply the calculable R-matrix method to determine the cross sections of the $^{12,13}$ $^{12, 13}$ C( $p,\gamma $ $p, γ$ ) $^{13,14}$ $^{13, 14}$ N reactions using both local Woods-Saxon (WS) and nonlocal Perey-Buck (PB) potentials. Benchmark calculations are first performed for the $^{12}$ $^{12}$ C( $p,\gamma $ $p, γ$ ) $^{13}$ $^{13}$ N reaction, and the results show good agreement with the standard codes FRESCO and RADCAP, as well as with recent calculations in other works. Furthermore, the method is applied to investigate the $^{13}$ $^{13}$ C( $p,\gamma $ $p, γ$ ) $^{14}$ $^{14}$ N reaction. Analysis of the astrophysical S-factors for both reactions indicates no significant difference between the local and nonlocal potential calculations, with discrepancies limited to approximately 7%–8%. The successful application of the calculable R-matrix method to these $(p,\gamma )$ $(p, γ)$ processes provides a framework for future studies involving nonlocal potentials derived from microscopic models.

Application of the Calculable R-matrix to Study the \(^{12,13}\)C(p,\(\gamma \))\(^{13,14}\)N Reaction

摘要