Mirror symmetry and cluster structures of resonant states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Be</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>9</mml:mn> </mml:mmultiscripts> </mml:math> and <mml

We apply the complex-scaling method (CSM) to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>α</a:mi> <a:mo>+</a:mo> <a:mi>α</a:mi> <a:mo>+</a:mo> <a:mi>N</a:mi> </a:mrow> </a:math> three-body model to study the nuclear structure of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Be</b:mi> <b:mprescripts/> <b:none/> <b:mn>9</b:mn> </b:mmultiscripts> </b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mmultiscripts> <c:mi mathvariant="normal">B</c:mi> <c:mprescripts/> <c:none/> <c:mn>9</c:mn> </c:mmultiscripts> </c:math> nuclei, focusing mainly on mirror symmetry in the resonant states. In our previous paper [], we reported the energy-level structure below about 15 MeV excitation energy in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Be</e:mi> <e:mprescripts/> <e:none/> <e:mn>9</e:mn> </e:mmultiscripts> </e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mmultiscripts> <f:mi mathvariant="normal">B</f:mi> <f:mprescripts/> <f:none/> <f:mn>9</f:mn> </f:mmultiscripts> </f:math> nuclei and discussed the significant effect of the Coulomb force. In this paper, we investigate the wave functions of these states, i.e., the matter- and charge-distribution radii, and the cluster-channel amplitudes. The results show a clear mirror-symmetry breaking between <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mmultiscripts> <h:mi>Be</h:mi> <h:mprescripts/> <h:none/> <h:mn>9</h:mn> </h:mmultiscripts> </h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mmultiscripts> <i:mi mathvariant="normal">B</i:mi> <i:mprescripts/> <i:none/> <i:mn>9</i:mn> </i:mmultiscripts> </i:math> nuclei, which is mainly due to the Coulomb interaction.