Vibrational-$\gamma$ bands in even ${}^{104-118}\mathrm{Pd}$ isotopes

The structure of the vibrational-$\gamma$ bands in even ${}^{104-118}\mathrm{Pd}$ isotopes has been investigated in the framework of the IBA-2 model. A detailed comparison of experimental and predicted values of the available spectroscopic data has been performed. The role played by states of mixed symmetry character in the proton and neutron degrees of freedom in reproducing the properties of the vibrational-$\gamma$ bands has been highlighted.

Figure 1

The experimental excitation energies of the even-spin [panel (a)] and odd-spin [panel (b)] members of the vibrational-$\gamma$ band in ${}^{112}\mathrm{Pd}$ are compared to those calculated with the parameters of Table 1 [column (l)] and keeping the values of the Majorana parameters at 1 MeV [column (h)].

Figure 2

Comparison of the experimental (left side) decay of the odd-spin band in ${}^{114}\mathrm{Pd}$ with the IBA-2 model predictions (right side). The calculated $B\left(E2\right)$ values, reported on each transition, are given in ${10}^{-3}{e}^2{\mathrm{b}}^2$ units. Vertical dashed lines indicate transitions of negligible intensity.

Figure 3

Comparison of experimental and calculated decay pattern of the vibrational-$\gamma$ bands in ${}^{104}\mathrm{Pd}$ [panel (a)] and ${}^{106}\mathrm{Pd}$ [panel (b)]. New experimental levels are represented by thick lines; new data on the branching ratios are given in bold face. In the upper panel a dashed line represents the experimental 2678 keV, positive parity state, to which it has been assigned spin $J=6$ in Ref. [25] but $J=4$ in Ref. [26] (see text for details).

Figure 4

As Fig. 3, for ${}^{108}\mathrm{Pd}$ and ${}^{110}\mathrm{Pd}$. In ${}^{110}\mathrm{Pd}$ the experimental $5^{+}$ state, whose existence is doubtful (see text), is represented by a dashed line.

Figure 5

As Fig. 3, for ${}^{112}\mathrm{Pd}$ and ${}^{114}\mathrm{Pd}$. The relative intensities reported without errors in ${}^{112}\mathrm{Pd}$ and the excitation energies of the ${12}^{+}$ and ${15}^{+}$ states in ${}^{114}\mathrm{Pd}$ are taken from Ref. [8].

Figure 6

As Fig. 3, for ${}^{116}\mathrm{Pd}$ and ${}^{118}\mathrm{Pd}$. The experimental relative intensities of the $4_2^{+}\to 3_1^{+}$ and $5_1^{+}\to 4_2^{+}$ transitions in ${}^{116}\mathrm{Pd}$ are taken from Ref. [8].

Figure 7

Comparison of experimental (open symbols) and calculated (closed symbols) excitation energies of the even-spin yrare states (circles) and odd-spin yrast states (squares) of the vibrational-$\gamma$ bands in even ${}^{104-118}\mathrm{Pd}$ isotopes. The lines connecting the levels are drawn to guide the eye.

Figure 8

Excitation energies of FS and MS states in the $U_{\pi \nu }$(5) limit, for the particular case $N_{\pi }$ = 2 and $N_{\nu }$ = 6. States are separated in six groups, according to the different dependence of their excitation energies on the Majorana parameters (see, e.g., Ref. [51]). The $d$-boson number is reported in square brackets on the left of each $n_d$ multiplet.

Figure 9

$F$-spin and $n_d$ components (amplitude square) of even- and odd-spin states of the vibrational-$\gamma$ bands in ${}^{104-110}\mathrm{Pd}$ isotopes.

Figure 10

$F$-spin and $n_d$ components (amplitude square) of even- and odd-spin states of the vibrational-$\gamma$ bands in ${}^{112-118}\mathrm{Pd}$ isotopes.