Observations of the Gamow-Teller resonance in the rare-earth nuclei above ${}^{146}\mathrm{Gd}$ populated in $\beta$ decay

The rare-earth region of the nuclear table around the quasi-doubly magic nucleus ${}^{146}\text{Gd}$ is one of the very few places in which the Gamow-Teller (GT) resonance can be populated in $\beta$ decay. The appropriate technique to study such a phenomenon is total absorption spectroscopy, thanks to which one can measure the $B$(GT) distribution in $\beta$-decay experiments even when it is very fragmented and lies at high excitation energy in the daughter nucleus. Results on the GT resonance measured in the $\beta$ decay of the odd-$Z, N=83$ nuclei ${}^{148}\text{Tb}, {}^{150}\text{Ho}$, and ${}^{152}\text{Tm}$ are presented in this work and compared with shell-model calculations. The tail of the resonance is clearly observed up to the limit imposed by the $Q$ value. This observation is important in the context of the understanding of the “quenching” of the GT strength.

Figure 1

Extreme single-particle representation of the configuration of the two isomers in the odd-$Z, N=83$ isotopes above ${}^{146}\text{Gd}$ and their allowed GT decay. Panel (a) represents the low-spin isomer and panel (b) the high-spin one. The shaded region represents the occupation of proton pairs that may cross the gap at $Z=64$ and the neutron occupation.

Figure 2

Total absorption spectrometer at the GSI on-line mass separator (a). Simulated total and photo-peak efficiency for individual $\gamma$ rays at several energies (b). Note that in the ${\beta }^{+}$/EC decays of interest the $\gamma$ multiplicity is, in general, larger than 1, which makes the total efficiency close to 1 for most of the cases.

Figure 3

Direct spectra obtained in the ${}^{152}\text{Tm} 2^{-}$ decay measurement in the TAS (a) and in the x-ray detector (b). The shaded regions represent the gates used in the analysis (see text).

Figure 4

(a) The TAS spectrum obtained by setting gates on the characteristic Er x rays in the $\underset{2^{-}}{{}^{152}\text{Tm}}$ measurement is shown in black, and the spectrum of the relevant contaminants is shown in gray; see text. (b) The resulting TAS spectrum of $\underset{2^{-}}{{}^{152}\text{Tm}}$ after the subtraction of the contaminants.

Figure 5

Simulation of the $\beta$ decay of ${}^{24}\mathrm{Na}$ (dashed black line) overlaid to the measured ${}^{24}\mathrm{Na}$ source (gray shade). The counts beyond the $Q_{\beta }$ value correspond to pileup events.

Figure 6

(a) Experimental spectrum measured for the ${}^{152}\text{Tm} 2^{-}$ EC decay (gray shade). Overlaid, there is the recalculated spectrum using the results after the analysis and the response function (dashed line). (b) Resulting intensity distribution $I_{\beta }\left(E\right)$ after unfolding the data. (c) ${}^{152}\text{Tm} 2^{-} \beta$-decay $B$(GT) distribution. The gray shading represents the uncertainty.

Figure 7

End point of the EC-decay spectrum of $\underset{9^{+}}{{}^{152}\text{Tm}}$ measured with the TAS. The spectrum represents the square root of the number of counts as a function of the energy as done in Ref. [41]. The solid line is a linear fit within the range 7000 to 8500 keV. The dashed line is just to guide the eye to the crossing point with the 0.

Figure 8

GT strength distribution in the $\beta$ decay of the odd-$Z, N=83$ nuclei above ${}^{146}\text{Gd}$ pertinent to the present discussion. The left column (a),(c),(e) corresponds to the $2^{-}$ isomer and the right column (b),(d),(f) to the $9^{+}$ isomer. From the bottom to the top we have first the decay of ${}^{148}\text{Tb}$, which covers the cases with 0 (e) and 1 (f) proton in the $h_{11/2}$, then the decay of ${}^{150}\text{Ho}$, corresponding to the cases with 2 (c) and 3 (d) protons and at the top ${}^{152}\text{Tm}$, covering the cases with 4 (a) and 5 (b) protons in the $h_{11/2}$. The shading at the right-hand side of each graph represents the region beyond the $Q_{\mathrm{EC}}$ value which is inaccessible in the decay. The circles at the top of each graph represent schematically the number of protons above the $Z=64$ gap involved in the decay in an extreme single-particle approximation.

Figure 9

Evolution of the total $B$(GT) as a function of the occupancy number of the proton orbital $h_{11/2}$. The results from this work (gray squares) are compared with the theoretical estimates of Ref. [53] (black bars).

Figure 10

GT strength distribution for the low-spin isomer of the odd-$Z, N=83$ nuclei above ${}^{146}\text{Gd}$. The results from the TAS measurement (black/gray) are compared with a shell-model calculation (red).

Figure 11

Same as Fig. 10 but for the high-spin isomers.