Lifetime measurements in the ground-state band in ${}^{104}\mathrm{Pd}$

Lifetimes and reduced transition probabilities were determined in the ground-state band in ${}^{104}\mathrm{Pd}$ up to the ${12}^{+}$ state employing the recoil distance Doppler-shift method. Excited states were populated via the fusion-evaporation reaction ${}^{96}\mathrm{Zr}({}^{12}\mathrm{C},4n){}^{104}\mathrm{Pd}$ at 55 MeV. The $B(E2;2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+})$ value deviates from previous evaluated values obtained by Coulomb excitation and electron scattering. The transition strengths for higher-lying states were obtained for the first time, closing a gap in the medium-mass Pd isotope chain. Large-scale shell-model calculations were performed employing the SR88MHJM Hamiltonian along the isotope chain ${}^{96-106}\mathrm{Pd}$ for even-even nuclei and for high-spin states up to ${26}^{+}$ in ${}^{104}\mathrm{Pd}$.

Figure 1

$\gamma$-ray energy spectrum for the detector ring at ${45}^{\circ }$ with respect to the beam axis summed for all plunger distances. Marked $\gamma$ rays are assigned to (red) positive- and (blue) negative-parity states in ${}^{104}\mathrm{Pd}$, respectively. The labels indicate the energies from decays at rest, Doppler-shifted $\gamma$ rays are partially visible. $\gamma$ rays from ${}^{102}\mathrm{Ru}$ and ${}^{105}\mathrm{Pd}$ are marked with filled squares and crosses, respectively.

Figure 2

Correction factors $c\left(\tau \right)$ are deduced by comparing 17 simulated lifetimes with resulting analysed lifetime values and are shown for the $4_1^{+}$ state in ${}^{104}\mathrm{Pd}$. An exponential function is fitted to the data points and is shown in red.

Figure 3

$\gamma$-ray spectra of the yrast band in ${}^{104}\mathrm{Pd}$ for the decays of the $2_1^{+}, 4_1^{+}, 8_1^{+}, {10}_1^{+}$, and ${12}_1^{+}$ states [(a)–(e)]. Spectra are produced by employing gates on the Doppler-shifted component of the direct feeding transitions of the yrast band. Spectra of $2_1^{+}, 4_1^{+}, 8_1^{+}$, and ${12}_1^{+}$ decays are shown for six different target-to-stopper distances at a forward angle of ${45}^{\circ }$. The spectra for the ${10}_1^{+}\to 8_1^{+}$ transition are shown for backward angles due to the closely contaminating ${14}_1^{+}\to {12}_1^{+}$ transition observed for forward angles. The transition is visible at higher energies in the spectra (d1)–(d4). The fits to the unshifted and Doppler-shifted components are indicated by dashed red lines. The lifetime analysis of the $4^{+}$ state requires additional information on intensities of direct feeding transition in gated spectra due to a doublet in the positive-parity ground-state band.

Figure 4

$\tau$ curves of the (a) $2_1^{+}$ (d) $4_1^{+}$ (g) $8_1^{+}$ (j) ${10}_1^{+}$, and (m) ${12}_1^{+}$ states in ${}^{104}\mathrm{Pd}$ are shown exemplary for one analysis gate combination. Lifetimes and $\gamma$-ray intensities are presented in dependence of the target-to-stopper distance. The black solid lines indicate the weighted mean value of the individual lifetimes; surrounding lines mark the statistical uncertainty. Furthermore, the unshifted [(b), (e), (h), (k), and (n)] and shifted [(c), (f), (i), (l), and (o)] intensities of the depopulating transitions are shown. The polynomial fit function to the given intensities is presented as a dashed red line. Note the logarithmic distance scale.

Figure 5

Experimental and calculated ratios of $4_1^{+}$ and $2_1^{+}$ (a) excitation energies and (b) $B(E2$) values.

Figure 6

Experimental excitation energies (black) for even-even palladium isotopes of the positive-parity ground-state band up to the ${10}^{+}$ state, starting from the $N=50$ shell closure up to the midshell $N=60$ nucleus ${}^{106}\mathrm{Pd}$, compared with the calculated values using the SR88MHJM interaction (red).

Figure 7

Experimental transition strengths (black) for even-even palladium isotopes ${}^{96-106}\mathrm{Pd}$, compared with the calculated values using the SR88MHJM interaction (red). Only lower limits are known for transition strengths of the $2_1^{+}$ state in the lightest calculated isotopes.

Figure 8

Experimental and calculated (a) transition energies and (b) transition strength values. Results of the SR88MHJM interaction are shown in red triangles. Results with reduced $\nu {\mathrm{h}}_{11/2}$ SPE (SR88${\mathrm{MHJM}}^{*}$) are shown in blue circles. See text for more details.