Experimental study of the lifetime and phase transition in neutron-rich ${}^{98,100,102}\mathrm{Zr}$

Rapid shape changes are observed for neutron-rich nuclei with A around 100. In particular, a sudden onset of ground-state deformation is observed in the Zr and Sr isotopic chains at N = 60: Low-lying states in $N\le 58$ nuclei are nearly spherical, while those with $N\ge 60$ have a rotational character. Nuclear lifetimes as short as a few picoseconds can be measured using fast-timing techniques with ${\mathrm{LaBr}}_3$(Ce) scintillators, yielding a key ingredient in the systematic study of the shape evolution in this region. We used neutron-induced fission of ${}^{241}\mathrm{Pu}$ and ${}^{235}\mathrm{U}$ to study lifetimes of excited states in fission fragments in the $A\sim 100$ region with the EXILL-FATIMA array located at the PF1B cold neutron beam line at the Institut Laue-Langevin. In particular, we applied the generalized centroid difference method to deduce lifetimes of low-lying states for the nuclei ${}^{98}\mathrm{Zr}$ (N = 58), ${}^{100}\mathrm{Zr}$, and ${}^{102}\mathrm{Zr}$ ($N\ge 60$). The results are discussed in the context of the presumed phase transition in the Zr chain by comparing the experimental transition strengths with the theoretical calculations using the interacting boson model and the Monte Carlo shell model.

Figure 1

Evolution of the $2_1^{+}$ excitation energy as a function of neutron number in the A $\sim 100$ region. The transition energies are taken from National Nuclear Data Center [7] and the recent results for ${}^{98,100}\mathrm{Kr}$ are adopted from Ref. [6].

Figure 2

PRD curve obtained using a ${}^{152}\mathrm{Eu}$ source.

Figure 3

The double-gated spectrum of ${}^{138}\mathrm{Xe}$ which is a complementary partner of ${}^{100}\mathrm{Zr}$ and ${}^{102}\mathrm{Zr}$. Prominent peaks in the spectrum (shown in different colors) correspond to transitions in ${}^{100}\mathrm{Zr}$, ${}^{102}\mathrm{Zr}$, and ${}^{138}\mathrm{Xe}$.

Figure 4

Lifetime determination using the slope method for the $2_1^{+}$ state of ${}^{100}\mathrm{Zr}$. (a) Displays the delayed (red) and the antidelayed [green (light gray)] time distributions of the state of interest from ${}^{235}\mathrm{U}$ fission, and (b) from ${}^{241}\mathrm{Pu}$ fission.

Figure 5

Lifetime analysis for the $2_1^{+}$ state in ${}^{100}\mathrm{Zr}$. (a) and b) The double-gated Ge (shown in black) and ${\mathrm{LaBr}}_3$ [green (gray)] spectra. (c) and d) The Compton background correction procedure (see text for details).

Figure 6

Lifetime determination for the $2_1^{+}$ state of ${}^{102}\mathrm{Zr}$ using the ${}^{241}\mathrm{Pu}$ target data. The independent antidelayed time spectrum resulting from the FEP events is inverted and aligned before being summed to the delayed time distribution. The slope was determined by fitting the data in the range from 25.5 to 35 ns.

Figure 7

Lifetime analysis for the $4_1^{+}$ state in ${}^{102}\mathrm{Zr}$. (a) and (b) Double-gated Ge (shown in black) and ${\mathrm{LaBr}}_3$ [green (light gray)] spectra. (c) and (d) The Compton background correction procedure (see text for details).

Figure 8

Two independent time distributions (delayed and antidelayed) for the $4_1^{+}$ state of ${}^{102}\mathrm{Zr}$.

Figure 9

Known B(E2 $\downarrow$; $2_1^{+}\to 0_1^{+}$), B(E2 $\downarrow$; $4_1^{+}\to 2_1^{+}$), and B(E2 $\downarrow$; $6_1^{+}\to 4_1^{+}$) values [a), (b), and (c), respectively] in ${}^{98,100,102,104,106}\mathrm{Zr}$, compared with the IBM-1 [42] and MCSM [24] calculations. The B(E2)$\downarrow$ values obtained in the present study (see Table 1) are plotted in red and the literature values [2, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44] in green (light gray). All values are expressed in $e^2{b}^2$.