Total absorption spectroscopy of the $\beta$ decay of ${}^{101,102}\mathrm{Zr}$ and ${}^{109}\mathrm{Tc}$

The $\beta$ decay of ${}^{101,102}\mathrm{Zr}$ and ${}^{109}\mathrm{Tc}$ was studied using the technique of total absorption spectroscopy. The experiment was performed at the National Superconducting Cyclotron Laboratory using the Summing NaI(Tl) (SuN) detector in the first-ever application of total absorption spectroscopy with a fast beam produced via projectile fragmentation. The $\beta$-decay feeding intensity and Gamow-Teller transition strength distributions were extracted for these three decays. The extracted distributions were compared to three different quasiparticle random-phase approximation (QRPA) models based on different mean-field potentials. A comparison with calculations from one of the QRPA models was performed to learn about the ground-state shape of the parent nucleus. For ${}^{101}\mathrm{Zr}$ and ${}^{102}\mathrm{Zr}$, calculations assuming a pure shape configuration (oblate or prolate) were not able to reproduce the extracted distributions. These results may indicate that some type of mixture between oblate and prolate shapes is necessary to reproduce the extracted distributions. For ${}^{109}\mathrm{Tc}$, a comparison of the extracted distributions with QRPA calculations suggests a dominant oblate configuration. The other two QRPA models are commonly used to provide $\beta$-decay properties in $r$-process network calculations. This work shows the importance of making comparisons between the experimental and theoretical $\beta$-decay distributions, rather than just half-lives and $\beta$-delayed neutron emission probabilities, as close to the $r$-process path as possible.

Figure 1

Comparison of experimental (black, solid line) and reconstructed (blue, solid line) spectra from the $\beta$ decay of ${}^{101}\mathrm{Zr}$ for the (a) TAS spectrum, (b) sum-of-segments spectrum, and (c) multiplicity spectrum. The experimental spectra were obtained by correlating decay events to ${}^{101}\mathrm{Zr}$ implantations with a correlation time window of 1 s. Contamination from random correlations and the decay of the daughter has been subtracted from the experimental spectra. The ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{101}\mathrm{Zr}$ is 5726 keV [72].

Figure 2

Comparison of experimental (black, solid line) and reconstructed (blue, solid line) spectra from the $\beta$ decay of ${}^{102}\mathrm{Zr}$ for the (a) TAS spectrum, (b) sum-of-segments spectrum, and (c) multiplicity spectrum. The experimental spectra were obtained by correlating decay events to ${}^{102}\mathrm{Zr}$ implantations with a correlation time window of 1 s. Contamination from random correlations and the decay of the daughter has been subtracted from the experimental spectra. There is a label for the ground-state to ground-state $Q$ value in the TAS spectrum for the $\beta$ decay of ${}^{102}\mathrm{Zr}$ at 4717 keV [72].

Figure 3

Comparison of experimental (black, solid line) and reconstructed (blue, solid line) spectra from the $\beta$ decay of ${}^{109}\mathrm{Tc}$ for the (a) TAS spectrum, (b) sum-of-segments spectrum, and (c) multiplicity spectrum. The experimental spectra were obtained by correlating decay events to ${}^{109}\mathrm{Tc}$ implantations with a correlation time window of 1 s. Contamination from random correlations has been subtracted from the experimental spectra. The ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{109}\mathrm{Tc}$ is 6456 keV [72].

Figure 4

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$ decay of ${}^{101}\mathrm{Zr}$ as a function of excitation energy in the daughter ${}^{101}\mathrm{Nb}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA calculations assuming the ground state of the parent is oblate (red, dashed line) and prolate (blue, dotted line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{101}\mathrm{Zr}$ at 5726 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.

Figure 5

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$ decay of ${}^{102}\mathrm{Zr}$ as a function of excitation energy in the daughter ${}^{102}\mathrm{Nb}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA calculations assuming the ground state of the parent is oblate (red, dashed line) and prolate (blue, dotted line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{102}\mathrm{Zr}$ at 4717 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.

Figure 6

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$-decay of ${}^{109}\mathrm{Tc}$ as a function of excitation energy in the daughter ${}^{109}\mathrm{Ru}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA calculations assuming the ground state of the parent is oblate (red, dashed line) and prolate (blue, dotted line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{109}\mathrm{Tc}$ at 6456 keV [72]. There is an arrow indicating the one-neutron separation energy $S_n$ of the daughter ${}^{109}\mathrm{Ru}$ at 5148 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.

Figure 7

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$ decay of ${}^{101}\mathrm{Zr}$ as a function of excitation energy in the daughter ${}^{101}\mathrm{Nb}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA 2 (cyan, dash-dotted line) and QRPA 3 (green, dotted line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{101}\mathrm{Zr}$ at 5726 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.

Figure 8

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$ decay of ${}^{102}\mathrm{Zr}$ as a function of excitation energy in the daughter ${}^{102}\mathrm{Nb}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA 2 (cyan, dash-dotted line) and QRPA 3 (green, dotted line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{102}\mathrm{Zr}$ at 4717 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.

Figure 9

(a) Cumulative $\beta$-decay feeding intensity and (b) cumulative $B$(GT) for the $\beta$ decay of ${}^{109}\mathrm{Tc}$ as a function of excitation energy in the daughter ${}^{109}\mathrm{Ru}$. The present work (black, solid line, with uncertainty in orange shading) is compared to QRPA 2 (cyan, dash-dotted line) and QRPA 3 (green, dotted line and purple, dashed line). There is an arrow indicating the ground-state to ground-state $Q$ value for the $\beta$ decay of ${}^{109}\mathrm{Tc}$ at 6456 keV [72]. There is an arrow indicating the one-neutron separation energy $S_n$ of the daughter ${}^{109}\mathrm{Ru}$ at 5148 keV [72]. The half-lives $T_{1/2}$ and quadrupole deformation parameters ${\beta }_2$ are provided in parentheses.