Lifetime measurements in ${}^{99}\mathrm{Nb}$ and ${}^{99}\mathrm{Zr}$: Investigation of shape coexistence

The $A\approx 100$ mass region is of special interest due to a rapid shape transition, observed by going from neutron number 58 to 60, especially pronounced in the Zr isotopes, where ${}^{98}\mathrm{Zr}$ is weakly and ${}^{100}\mathrm{Zr}$ is strongly deformed. To further examine this intricate phenomenon, in this work lifetimes of low-lying excited states in the nuclei ${}^{99}\mathrm{Zr}$ and ${}^{99}\mathrm{Nb}$ were determined using fast-timing techniques and an experimental setup consisting of four ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ detectors. Neutron rich $A=99$ fragments were produced in neutron induced fission and separated by the spectrometer LOHENGRIN at the Institut Laue-Langevin in Grenoble, France. Experimental values are compared to two different calculations in the framework of the interacting boson-fermion model and discussed in the context of shape coexistence.

Figure 1

(a) PRD curve determined from ${}^{152}\mathrm{Eu}$, ${}^{185}\mathrm{Os}$, and ${}^{187}\mathrm{W}$ sources and using Eq. (4) as fit function. Known lifetimes for the data points are taken from [38, 39]. (b) Fit residuals of the PRD curve. The $1\sigma$ uncertainty band is plotted in red.

Figure 2

Full projections of ${\mathrm{LaBr}}_3$(Ce)-${\mathrm{LaBr}}_3$(Ce) (black) and ${\mathrm{LaBr}}_3$(Ce)-HPGe (red) twofold coincidences without any energy conditions applied and within a $1\mu \mathrm{s}$ coincidence window. Relevant transitions [38] for the determination of lifetimes in the ${}^{99}\mathrm{Zr}$ and ${}^{99}\mathrm{Nb}$ nuclei are marked in green and blue, respectively. The peaks that are not marked mostly stem from the $A=85$, 94, and 104 masses which have a similar $A/q$ ratio.

Figure 3

Partial energy level scheme after $\beta$ decay for both nuclei, ${}^{99}\mathrm{Nb}$ and ${}^{99}\mathrm{Zr}$, respectively [38]. The scheme only contains transitions used to determine the lifetimes of this work.

Figure 4

(a) Energy spectra from HPGe and ${\mathrm{LaBr}}_3$(Ce) detectors showing the 546.1 keV feeding transition of the ($5/2_1{)}^{+}$ state in ${}^{99}\mathrm{Nb}$, gated on the ($5/2_1{)}^{+}\to 9/2_{\text{g.s.}}^{+}$ (469.1 keV) transition in a spectrum measured by another ${\mathrm{LaBr}}_3$(Ce) detector. (b) Energy spectra from HPGe and ${\mathrm{LaBr}}_3$(Ce) detectors showing the 469.1 keV decaying transition of the ($5/2_1{)}^{+}$ state in ${}^{99}\mathrm{Nb}$, gated on the ($3/2_3{)}^{+}\to {(5/2_1)}^{+}$ (546.1 keV) transition in a spectrum measured by another ${\mathrm{LaBr}}_3$(Ce) detector. (c) Interpolated Compton background time response of the feeding transition. Data points in red [also labeled in the corresponding energy spectrum (a)] are used for the fitted curve. (d) Interpolated Compton background time response of the decaying transition. Data points in red [also labeled in the corresponding energy spectrum (b)] are used for the fitted curve. (e) Slope and convolution (f) method for the delayed time distribution of the ${(5/2_1)}^{+}$ state using gates on the ${(3/2_3)}^{+}\to {(5/2_1)}^{+}$ feeding transition at 546.1 keV and the ${(5/2_1)}^{+}\to 9/2_{\text{g.s.}}^{+}$ decaying transition at 469.1 keV. The antidelayed distribution was mirrored and summed up to increase statistics. The dashed lines in (e) represent the fit interval for the slope method. (g) Delayed and antidelayed time distribution for the ($5/2_1{)}^{+}$ state using ${\mathrm{LaBr}}_3$(Ce) gates on the ($3/2_3{)}^{+}\to {(5/2_1)}^{+}$ feeding transition at 546.1 keV and on the ($5/2_1{)}^{+}\to 9/2_{\text{g.s.}}^{+}$ decaying transition at 469.1 keV.

Figure 5

Experimental [38] vs theoretical low energy level scheme of ${}^{99}\mathrm{Nb}$ using IBFM-CM calculations. Positive (left) and negative parity (right) states are shown. Theoretically calculated states of the $K=1/2_3^{-}$ band originating at 0.745 MeV are omitted for better clarity.

Figure 6

Experimental [38] vs theoretical low energy level scheme of ${}^{99}\mathrm{Zr}$ using SCMF-IBFM calculations. Here, only a selected choice of theoretical energy levels are displayed for better clarity.