Theoretical analysis of the reactions induced by interaction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts></mml:math> with <mml:ma

We determine cross sections and astrophysical <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>S</a:mi></a:math> factors of the reactions generated in collisions between <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>Li</b:mi><b:mprescripts/><b:none/><b:mn>6</b:mn></b:mmultiscripts></b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mmultiscripts><c:mi mathvariant="normal">H</c:mi><c:mprescripts/><c:none/><c:mn>3</c:mn></c:mmultiscripts></c:math> and between <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi>Li</e:mi><e:mprescripts/><e:none/><e:mn>6</e:mn></e:mmultiscripts></e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mmultiscripts><f:mi>He</f:mi><f:mprescripts/><f:none/><f:mn>3</f:mn></f:mmultiscripts></f:math>. A microscopic three-cluster model is employed to study the dynamics of reactions occurring in the mirror nuclei <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mmultiscripts><g:mi>Be</g:mi><g:mprescripts/><g:none/><g:mn>9</g:mn></g:mmultiscripts></g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mmultiscripts><h:mi mathvariant="normal">B</h:mi><h:mprescripts/><h:none/><h:mn>9</h:mn></h:mmultiscripts></h:math>. In a previous study [], this model was successfully applied to investigate the resonance structure of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mmultiscripts><j:mi>Be</j:mi><j:mprescripts/><j:none/><j:mn>9</j:mn></j:mmultiscripts></j:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mmultiscripts><k:mi mathvariant="normal">B</k:mi><k:mprescripts/><k:none/><k:mn>9</k:mn></k:mmultiscripts></k:math>, as well as reactions induced by the interaction of deuterons with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mmultiscripts><m:mi>Li</m:mi><m:mprescripts/><m:none/><m:mn>7</m:mn></m:mmultiscripts></m:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mmultiscripts><n:mi>Be</n:mi><n:mprescripts/><n:none/><n:mn>7</n:mn></n:mmultiscripts></n:math>. A fairly good agreement between theoretical results and available experimental data was achieved. To the best of our knowledge, appropriate experimental data for the astrophysical <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mi>S</o:mi></o:math> factors of the reactions generated by the interaction of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mmultiscripts><p:mi>Li</p:mi><p:mprescripts/><p:none/><p:mn>6</p:mn></p:mmultiscripts></p:math> with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mmultiscripts><q:mi mathvariant="normal">H</q:mi><q:mprescripts/><q:none/><q:mn>3</q:mn></q:mmultiscripts></q:math> and with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mmultiscripts><s:mi>He</s:mi><s:mprescripts/><s:none/><s:mn>3</s:mn></s:mmultiscripts></s:math> are currently unavailable. Thus, our results can serve as a guideline for future experimental efforts. Published by the American Physical Society 2024