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Next: Notes: Up: b) Collective model: Previous: 3.2.0.2 Coulomb deformation:

Nuclear deformation:

If U(R) is the potential shape to be deformed, the deformed nuclear potential can be constructed as

\begin{displaymath}
\mathbf{V}(\xi,\mathbf{R})=U(R-\delta(\hat{R}')),\end{displaymath} (28)

where $\hat{R}'$ are the angular coordinates $(\theta,\varphi)$ referred to the intrinsic reference frame. The function $\delta$ is normally expanded in multipoles:
\begin{displaymath}
\delta(\hat{R}')=\sum_{\lambda}\delta_{\lambda}Y_{\lambda0}(\hat{R}')\end{displaymath} (29)

As in the case of cluster form factors, it is convenient to expand the coupling potential V in spherical harmonics, giving rise to the radial multipoles $V_{N}^{\lambda}(R)$, whose reduced matrix elements are given by

\begin{displaymath}
\langle I'\vert\vert V_{N}^{\lambda}(R)\vert\vert I\rangle=-...
...lta_{\lambda}\vert\vert I\rangle}{\sqrt{4\pi}}\frac{dU(R)}{dR},\end{displaymath} (30)

with the same shape for all nuclear multipoles $\lambda>0$.

The values of $\langle I'\vert\vert\delta_{\lambda}\vert\vert I\rangle$ are model dependent:

Figure 2: Energy levels for the 19F considered in the CC calculation.
\includegraphics[%%
width=0.60\textwidth]{cc/cluster/cc.eps}


next up previous
Next: Notes: Up: b) Collective model: Previous: 3.2.0.2 Coulomb deformation:
Antonio Moro 2004-10-27