<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mi>Zr</mml:mi><mml:mprescripts /><mml:none /><mml:mn>92</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> cluster structure in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Mo</mml:mi><mml:mprescripts /><mml:none /><mml:mn>96</mml:mn></mml:mmultiscripts></mml:math>

In the evaluation of half-life neutrinoless double-$\ensuremath{\beta}$ decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) a doubly closed-subshell nucleus $^{96}\mathrm{Zr}$, structure $^{96}\mathrm{Mo}$ is essentially important. The $\ensuremath{\alpha}$-clustering aspects are investigated for first time. By studying nuclear rainbows in $\ensuremath{\alpha}$ scattering from $^{92}\mathrm{Zr}$ at high energies and characteristic excitation functions extreme backward angle low-energy region, interaction potential between particle determined well double folding model. validity model was reinforced by neighboring nuclei $^{90}\mathrm{Zr}, ^{91}\mathrm{Zr}$, $^{94}\mathrm{Zr}$. double-folding-model calculations reproduced all observed angular distributions over wide range incident functions. using obtained $\ensuremath{\alpha}+^{92}\mathrm{Zr}$ cluster spirit unified description structure. existence second-higher nodal band states with structure, which two more nodes excited relative motion compared ground band, demonstrated. calculation reproduces ground-band agreement experiment. experimental $B(E2)$ value transition also well. effect clustering on $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ $^{96}\mathrm{Zr}$ discussed.