Effects of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:mi>γ</mml:mi></mml:mrow></mml:math>coupling in transitional nuclei and the validity of the approximate separation of variables

Exact numerical diagonalization is carried out for the Bohr Hamiltonian with a \ensuremath{\beta}-soft, axially stabilized potential. Wave function and observable properties are found to be dominated by strong $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ coupling effects. The validity of the approximate separation of variables introduced with the $X(5)$ model, extensively applied in recent analyses of axially stabilized transitional nuclei, is examined, and the reasons for its breakdown are analyzed.

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