Bohr Hamiltonian with different mass coefficients for the ground- and γ bands from experimental data

Based on experimental data for axially symmetric well deformed nuclei it is shown that the “Grodzins product” of the energy of the $2_{\gamma }^{+}$ state with the $B(E2;2_{\gamma }^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+})$ for the transition from the $2_{\gamma }^{+}$ state to the ground state is a relatively smooth function of $Z$ and $A$. It is shown also that a ratio of the mass coefficients for the γ-motion and for the rotational ground band extracted from the experimental data take the values in the limits 3–5. The implied large difference between the two mass coefficients means that the mass tensor of the Bohr Hamiltonian cannot be reduced to a scalar as it usually assumed.

Figure 1

Evolution of the values $P_{\mathrm{g}.\mathrm{s}.}=E(2_1^{+})B(E2;0_1^{+}\to 2_1^{+})Z^{-2}{A}^{2/3}$ and $P_{\gamma }=E(2_{\gamma }^{+})B(E2;0_1^{+}\to 2_{\gamma }^{+})Z^{-2}{A}^{2/3}$ given in the units keV $e^2{b}^2$ over a range of isotopes. The average values $\langle P_g\rangle =2.790$ and $\langle P_{\gamma }\rangle =0.712$ over all considered isotopes are plotted as dotted lines. The experimental data are taken from [16].