Abstract
A method is proposed for constructing fully antisymmetric $A$-body hyperspherical harmonics with well-defined orthogonal symmetry. These hyperspherical harmonics are obtained by diagonalizing the matrix of the second Casimir operator for the orthogonal group, calculated in the hyperspherical basis constructed with the help of the Slater determinants of the oscillator translation-invariant shell model. The introduction of orthogonal symmetry has computational benefits and also provides a physical insight into collective modes of motion of atomic nuclei. Numerical applications have been performed for $^{3\char21{}5,7}\mathrm{H}$ and $^{4\char21{}10}\mathrm{He}$.
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