Calculation of the Bohr deformation parameters

In version (v1.75r), the Bohr deformation parameters $\alpha_{\lambda\mu}$ [5] are calculated using the first-order approximation. The code uses the simplest linearized expression (cf. Eq. (1.35) of Ref. [5]) relating deformation parameters to multipole moments of a sharp-edge uniformly charged shape, i.e.,

$$\alpha_{\lambda\mu} = \frac{4\pi\sqrt{1+\delta_{\mu0}}}{3NR_0^\lambda} \langle r^\lambda Y_{\lambda\mu}\rangle.$$ (1)

For $\mu$$\neq$0 the deformation parameters contain the standard factor of $\sqrt{2}$. This reflects the fact that for the assumed $\hat{S}_y$ simplex symmetry (see Sec. 3.1 of I), the values of multipole moments for $\mu$<0 are up to a phase equal to those for $\mu$>0. Neutron, proton, or mass deformation parameters are calculated from the corresponding neutron, proton, or mass multipole moments $\langle r^\lambda Y_{\lambda\mu}\rangle$, and by setting N in Eq. (3) equal to the number of neutrons, protons, or nucleons. The equivalent radii R₀ are respectively calculated from the neutron, proton, or mass rms radii as $\sqrt{5/3}\langle{r^2}\rangle^{1/2}$. One should note that for large deformations the neglected higher-order terms (see Eq. (1.35) of Ref. [5]) will in general be non-negligible. Therefore, the printed values of the Bohr deformation parameters should be used only as (often very) rough estimates.