<p>A machine learning approach based on Bayesian neural networks was developed to predict the complete fusion cross-sections of weakly bound nuclei. This method was trained and validated using 475 experimental data points from 39 reaction systems induced by <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{6,7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>6</mn> <mo>,</mo> <mn>7</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Li, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^9\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>9</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Be, and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{10}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>10</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>B. The constructed Bayesian neural network demonstrated a high degree of accuracy in evaluating complete fusion cross-sections. By comparing the predicted cross-sections with those obtained from a single-barrier penetration model, the suppression effect of <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{6,7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>6</mn> <mo>,</mo> <mn>7</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Li and <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^9\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>9</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Be with a stable nucleus was systematically analyzed. In the cases of <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>6</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Li and <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1779_Article_IEq13.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>7</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Li, less suppression was predicted for relatively light-mass targets than for heavy-mass targets, and a notably distinct dependence relationship was identified, suggesting that the predominant breakup mechanisms might change in different mass target regions. In addition, minimum suppression factors were predicted to occur near target nuclei with neutron-closed shell.</p>

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Predictions of complete fusion cross-sections of \(^{6,7}\)Li, \(^9\)Be, and \(^{10}\)B using a Bayesian neural network method

  • Kai-Xuan Cheng,
  • Rong-Xing He,
  • Chun-Yuan Qiao,
  • Chun-Wang Ma

摘要

A machine learning approach based on Bayesian neural networks was developed to predict the complete fusion cross-sections of weakly bound nuclei. This method was trained and validated using 475 experimental data points from 39 reaction systems induced by \(^{6,7}\) 6 , 7 Li, \(^9\) 9 Be, and \(^{10}\) 10 B. The constructed Bayesian neural network demonstrated a high degree of accuracy in evaluating complete fusion cross-sections. By comparing the predicted cross-sections with those obtained from a single-barrier penetration model, the suppression effect of \(^{6,7}\) 6 , 7 Li and \(^9\) 9 Be with a stable nucleus was systematically analyzed. In the cases of \(^{6}\) 6 Li and \(^{7}\) 7 Li, less suppression was predicted for relatively light-mass targets than for heavy-mass targets, and a notably distinct dependence relationship was identified, suggesting that the predominant breakup mechanisms might change in different mass target regions. In addition, minimum suppression factors were predicted to occur near target nuclei with neutron-closed shell.