Half-life measurements of several states in ${}^{95,97}\mathrm{Sr},{}^{97,100,104}\mathrm{Zr},{}^{106}\mathrm{Mo}$, and ${}^{148}\mathrm{Ce}$

Half-lives $T_{1/2}$ of states in ${}^{95,97}\mathrm{Sr}$, ${}^{97,100,104}\mathrm{Zr}$, ${}^{106}\mathrm{Mo}$, and ${}^{148}\mathrm{Ce}$, which decay by delayed γ transitions, were determined by using a new time-gated triple γ coincidence method. Transition energy dependent effects such as time walks, time jitters, amplitude walks, and possible timing fluctuations of Ge detectors that contribute to the width of the time window were taken into consideration by comparing prompt and delayed cascades with similar transition energies. It is shown that the normalized triple γ coincidence counts of two prompt cascades with similar transition energies are similar. Also, it is observed that the real triple γ coincidence counts in the prompt cascades change systematically with the widths of the coincidence time window and the transition energies. Half-lives of states in ${}^{100,104}\mathrm{Zr}$ were measured for the first time. The half-lives of states in the delayed cascades were determined by using the prompt cascades with transition energies similar to those in delayed cascades. The half-life of the 2${}^{+}$ state in ${}^{104}\mathrm{Zr}$ is measured to be 2.0(3) ns. The B(E2$;2^{+}\to 0^{+}$)($e^2{b}^2$) value and quadrupole deformation ${\beta }_2$ are 0.40(6) ($e^2{b}^2$) and 0.47(7), respectively. ${}^{104}\mathrm{Zr}$ has the most deformed 2${}^{+}$ state among medium and heavy even-even nuclei, except for ${}^{102}\mathrm{Sr}$. This method is only approximately valid, but it is believed to be generally within 10% of the true value.

Figure 1

Delayed and prompt cascades. Double gates are set on ${\gamma }_3$ and ${\gamma }_1$ to get the triple coincident counts of ${\gamma }_2$. The state with the half-life can be either the second or third one in the delayed cascade.

Figure 2

N1 normalization factors obtained from several prompt cascades normalized to the coincident counts at the time window of 500 ns. More counts at the 48 ns time window and fewer counts at the 100 ns time window observed for all the prompt cascades are caused mainly by the time-window-dependent total count difference of each time-gated cube. Half-lives of the states in these prompt cascades (except the low-energy cascade in ${}^{111}\mathrm{Ru}$) are less than a few hundred ps [3]. The ${}^{111}\mathrm{Ru}$ cascade with half-lives of 14 ns and 5 ns [3] for the states within the cascade is included to show that the timing effects are much larger for low-energy transitions.

Figure 3

Normalization factors n showing the timing effects dependent on the triple transition energies of several prompt cascades. These are normalized to the prompt cascade 1750.0- 1106.7-915.0 in ${}^{96}\mathrm{Zr}$. Note that the more counts at 48 ns and the fewer counts at 100 ns seen in the N1 plot (Fig. 2) are removed in this n plot.

Figure 4

Time-gated coincident spectra with double gates on 248.6 and 400.7 keV transitions for the prompt cascade consisting of 248.6 (6${}^{+}$$\to 4^{+}$), 328.2 (8${}^{+}$$\to 6^{+}$), and 400.7 (10${}^{+}$$\to 8^{+}$) keV transitions in ${}^{154}\mathrm{Nd}$ and on 247.4 and 389.9 keV transitions for the prompt cascade of 247.4 (6${}^{+}$$\to 4^{+}$), 322.2 (8${}^{+}$$\to 6^{+}$), and 389.9 (10${}^{+}$$\to 8^{+}$) keV transitions in ${}^{152}\mathrm{Nd}$.

Figure 5

Normalized count N vs coincident time window for prompt cascade 248.6-328.2-400.7 keV in ${}^{154}\mathrm{Nd}$. N values are essentially constant as expected for a prompt cascade with half-life of the order of ps. N1 values obtained from the prompt cascade 247.4-322.2-389.9 keV in ${}^{152}\mathrm{Nd}$ are used.

Figure 6

Partial level schemes of ${}^{95,97}\mathrm{Sr}$, ${}^{104}\mathrm{Zr}$, and ${}^{106}\mathrm{Mo}$.

Figure 7

Partial level schemes of ${}^{97,100}\mathrm{Zr}$ and ${}^{148}\mathrm{Ce}$.

Figure 8

Time-gated coincident spectra with double-gates on 167.0 and 522.0 keV transitions for the delayed cascade 167.0-140.8-522.0 keV and on 522.0 and 239.6 keV transitions for the delayed cascade 522.0-205.6-239.6 keV in ${}^{97}\mathrm{Sr}$. Marked peaks belong to ${}^{97}\mathrm{Sr}$.

Figure 9

Normalized count N vs coincident time window in ${}^{97}\mathrm{Sr}$.

Figure 10

Time-gated coincident spectra with double gates on 1103.4 and 594.3 keV transitions for the delayed cascade 1103.4 > 161.5-594.3 keV in ${}^{97}\mathrm{Zr}$, and on 682.4, and 427.1 keV transitions for the delayed cascade 204.0-682.4 > 427.1 keV in ${}^{95}\mathrm{Sr}$.

Figure 11

Normalized count N vs coincident time window in ${}^{97}\mathrm{Zr}$ and ${}^{95}\mathrm{Sr}$. Half-lives are for the 1264.9 keV state in ${}^{97}\mathrm{Zr}$ and 556.0 keV state in ${}^{95}\mathrm{Sr}$.

Figure 12

Time-gated coincident spectra with double gates on 845.1 and 275.6 keV transitions for the delayed cascade 845.1-219.5-275.6 in ${}^{100}\mathrm{Zr}$, and on 140.3 and 473.3 keV transitions for the delayed cascade 140.3-312.5-473.3 in ${}^{104}\mathrm{Zr}$.

Figure 13

Normalized count N vs coincident time window in ${}^{100}\mathrm{Zr}$ and ${}^{104}\mathrm{Zr}$. Half-lives are for the 2259.8 state in ${}^{100}\mathrm{Zr}$ and 140.3 keV state in ${}^{104}\mathrm{Zr}$.

Figure 14

Time-gated coincident spectra with double gates on 171.8 and 545.4 keV transitions for the delayed cascade 171.8-350.8-545.4 in ${}^{106}\mathrm{Mo}$.

Figure 15

Normalized count N vs coincident time window in ${}^{106}\mathrm{Mo}$. Half-life is for 171.8 keV state in ${}^{106}\mathrm{Mo}$.

Figure 16

Time-gated coincident spectra with double gates on 158.5 and 386.2 keV transitions for the delayed cascade consisting of 158.5, 294.9 and 386.2 keV transitions in ${}^{148}\mathrm{Ce}$.

Figure 17

Normalized count N vs coincident time window in ${}^{148}\mathrm{Ce}$. Half-life is for 158.5 keV state in ${}^{148}\mathrm{Ce}$.

Figure 18

Quadrupole deformation ${\beta }_2$ vs proton number Z. The ${\beta }_2$ value of ${}^{102}\mathrm{Sr}$ [0.50(10)] is obtained from the previously known half-life of 3.0(12) ns [5]. ${\beta }_2$ values in other nuclei except ${}^{102}\mathrm{Sr}$, ${}^{104}\mathrm{Zr}$, and ${}^{106}\mathrm{Mo}$ are obtained from Ref. 4. ${\beta }_2$ values of ${}^{104}\mathrm{Zr}$, and ${}^{106}\mathrm{Mo}$ are added from the present work.