content_image/331263.jpg content_image/331273.jpg content_image/331272.jpg content_image/331271.jpg content_image/331270.jpg content_image/331269.jpg
elements of ˆ V$_{int}$ between states (6) have the following form 

where the reduced matrix elements of the boson operators can be calculated using the boson fractional parentage coefficients 

<img src='content_image/331263.jpg'>

<img src='content_image/331273.jpg'>

## B. Two-level solution 

Our numerical calculations have shown that with a good accuracy the ground-state band and the first excited negative parity band can be presented with a good accuracy as a superposition of two basis states of the form (6). For the ground state band the two level approximation yields the wave function of the form ( I can have only even values) 

<img src='content_image/331272.jpg'>

where 

and for the energy we obtain 

In the last expressions Δ = 3 ℏ 2 µR 2 − ℏ ω . For the first excited negative parity bands we have 

<img src='content_image/331271.jpg'>

<img src='content_image/331270.jpg'>

<img src='content_image/331269.jpg'>

