Zakopane 2026 Conference on Nuclear Physics

The dynamics of the nuclear many-body system emerge from an intricate interplay between single-particle motion of individual nucleons and their correlated, collective behavior. The interplay between the two regimes is especially pronounced in the vicinity of semi-magic nuclei, where the onset of collective behavior occurs. An experimental signal for nuclear collectivity in semi-magic even-even nuclei is a strong electric quadrupole ($E$2) transitions between their low-lying states. The same principle holds true in the neighboring odd-even nuclei even though the $E$2 strength is fragmented over many states. Therefore, one effective approach to identify the onset of collectivity is by studying the odd-even neighbors of semi-magic even-even nuclei. The particle-core coupling model is a good framework for studying this concept [1-5]. This was empirically demonstrated in the studies on $^{113,115}$In (a proton hole in Z=50) where their total electric quadrupole strengths are consistent with those of their $^{114,116}$Sn cores [6,7].
However, recent results on $^{129}$Sb have shown significant enhancement of the quadrupole excitation strength compared to its even-even core neighbour $^{128}$Sn, indicating onset of collectivity [8]. The analogous case of $^{129}$Sb in the vicinity of the double-magic nucleus $^{208}$Pb is $^{205}$Bi. Therefore, we have investigated how the sum rule plays out in $^{205}$Bi. In our study we have determined the lifetimes of four excited states of $^{205}$Bi by means of the Recoil Distance Doppler Shift method. The excited states of the nucleus were populated using an 1$p$-transfer reaction. The lifetimes of the $11/2_1^-$, $7/2_1^-$, $5/2_1^-$, $7/2_2^-$ states were determined to be $\leq$ 9.5 ps, 5.6(11) ps, 10(5) ps, and 4.3(5) ps, respectively. The quadrupole strengths of these states were compared in the framework of the particle-core coupling model with the $0_1^+ \to 2_1^+$ transition strength of $^{204}$Pb indicating low quadrupole collectivity in the structure of these states. On the other hand, the shell model calculations failed to reproduce both the ordering of the states and the newly measured transition strengths between them. More surprisingly the same shell model calculations accurately reproduce the excitation energies and level ordering of the low-lying states in $^{207}$Bi. To address the question whether the shell model can consistently describe both the energies and the transition strengths of the low-lying states of $^{207}$Bi, we measured their lifetimes. The results from this experiment compared with the shell-model calculations will be presented and discussed as well.

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