$\beta$ decay and isomeric properties of neutron-rich Ca and Sc isotopes

The isomeric and $\beta$-decay properties of neutron-rich ${}^{53-57}\mathrm{Sc}$ and ${}^{53,54}\mathrm{Ca}$ nuclei near neutron number $N=32$ are reported, and the low-energy level schemes of ${}^{53,54,56}\mathrm{Sc}$ and ${}^{53-57}\mathrm{Ti}$ are presented. The low-energy level structures of the ${}_{21}\mathrm{Sc}$ isotopes are discussed in terms of the coupling of the valence $1f_{7/2}$ proton to states in the corresponding ${}_{20}\mathrm{Ca}$ cores. Implications with respect to the robustness of the $N=32$ subshell closure are discussed, as well as the repercussions for a possible $N=34$ subshell closure.

Figure 1

The region of the chart of the nuclides under consideration in the present work. Black squares represent stable nuclei, while nuclei for which low-energy levels were identified in the present work from the $\beta$ decay of parent nuclei are highlighted by a thick black border. Nuclei for which $\mu$s isomeric states permitted access to low-energy levels are shaded. Ground-state spins and parities are included where known, and all even-even nuclides have ground state $J^{\pi }=0^{+}$.

Figure 2

Particle identification spectrum obtained from fragment energy loss in PIN1 versus time of flight. A1900 magnetic rigidity settings of $B{\rho }_{1,2}=4.103$ Tm and $B{\rho }_{3,4}=4.030$ Tm were used to produce the observed cocktail beam.

Figure 3

(a) $\beta$-delayed $\gamma$-ray spectrum for ${}^{53}\mathrm{Ca}$ in the range of 0–3 MeV. The spectrum includes events within the first 5 s following a ${}^{53}\mathrm{Ca}$ implantation event, in detector pixels in which the average time between implantations was $⩾100$ s. The 2109-keV transition is the sole $\gamma$ ray observed. (b) Decay curve for ${}^{53}\mathrm{Ca}$ using a 5-s correlation time, considering all DSSD pixels, with the additional requirement of a coincident 2109-keV $\gamma$ ray. The curve was fitted with a single exponential decay.

Figure 4

(a) $\beta$-delayed $\gamma$-ray spectrum for ${}^{54}\mathrm{Ca}$ in the range of 0–1.8 MeV. The spectrum includes events within the first 1 s following a ${}^{54}\mathrm{Ca}$ implantation. Transitions are marked by their energy in keV. (b) Decay curve for ${}^{54}\mathrm{Ca}$-correlated $\beta$-decay events occurring within 1 s of a ${}^{54}\mathrm{Ca}$ implantation, with a requirement of a coincident 247-keV $\gamma$ ray. The curve was fitted with a single exponential decay and a constant background.

Figure 5

$\beta$-delayed $\gamma$-ray spectra (left column) and $\gamma$-gated half-life curves (right column) for (a, b) ${}^{53}\mathrm{Sc}$, (c, d) ${}^{54}\mathrm{Sc}$, (e, f) ${}^{55}\mathrm{Sc}$, (g, h) ${}^{56}\mathrm{Sc}$, and (i, j) ${}^{57}\mathrm{Sc}$. The $\beta$-delayed $\gamma$-ray spectra cover transitions in the range 0–2 MeV. The conditions under which individual spectra were obtained are discussed in the text. Observed transitions assigned to the decay of the Sc isotopes are marked by their energy in keV. Transitions in the decay of the $\beta$ daughters are marked by a filled circle, while transitions in decays of the $\beta$ granddaughters are marked by a hollow square. In (c) and (g), the peak at 83 keV corresponds to a background transition in the $\beta$ decay of ${}^{56}\mathrm{Cr}$. The half-life curves made use of correlation times specified in the text and required a coincident $\gamma$ ray (marked in the corresponding $\gamma$ spectrum by a shaded triangle). Data in all cases were fitted with a single exponential decay and a constant background, where such a contribution was nonzero.

Figure 6

Proposed decay scheme for the $\beta$ decay of ${}^{53}\mathrm{Sc}$ to states in ${}^{53}\mathrm{Ti}$. The energy of each state is given in keV. The number in brackets following the $\gamma$-ray energy is the absolute $\gamma$-ray intensity. The decay $Q$ value, $Q_{\beta }$, was deduced from data in Ref. [31].

Figure 7

$\gamma$$\gamma$ coincidence spectra gated on the (a) 292-keV, (b) 340-keV, (c) 413-keV, (d) 629-keV, and (e) 1576-keV transitions in coincidence with ${}^{53}\mathrm{Sc}$-correlated $\beta$-decay events. $\gamma$ rays are marked by their energy in keV, the number in square brackets following the energy is the number of counts in the peak. These coincident spectra include data within a 10 s correlation time for implants collected over the entire surface of the DSSD.

Figure 8

Proposed decay scheme for ${}^{54}\mathrm{Sc}$ to states in ${}^{54}\mathrm{Ti}$. The energy of each state is given in keV. The number in brackets following the $\gamma$-ray decay energy is the absolute $\gamma$-ray intensity. The $Q_{\beta }$ value was deduced from data in Ref. [31].

Figure 9

(a) $\gamma$-ray spectrum collected within a 20-$\mu$s window following a ${}^{54}\mathrm{Sc}$ implant. The 110-keV isomeric transition observed here was previously reported in Ref. [32], and confirmed in Ref. [18]. (b) Time dependence of the 110-keV transition. The decay curve was fitted with a single exponential decay to yield a half-life of 2.77 $\pm$ 0.02 $\mu$s.

Figure 10

Decay scheme for ${}^{55}\mathrm{Sc}$ to states in ${}^{55}\mathrm{Ti}$.

Figure 11

Proposed level scheme for ${}^{56}\mathrm{Sc}$, following the $\gamma$ decay of the isomeric transition at 775 keV and levels in ${}^{55,56}\mathrm{Ti}$ populated following $\beta$-decay of ${}^{56}\mathrm{Sc}$. The number in brackets following the isomeric $\gamma$-ray energies are the relative $\gamma$ intensities. The numbers following the $\beta$-delayed $\gamma$-ray energies are the absolute $\gamma$-ray intensities. The relative energies of the two $\beta$-decaying states are not known. The energy of the higher-spin $\beta$-decaying state, denoted by “X” may be negative. $Q_{\beta }$ for this decay is $13.7\pm 0.7$ MeV [31].

Figure 12

(a) The prompt $\gamma$-ray spectrum collected within the first 20 $\mu$s following a ${}^{56}\mathrm{Sc}$ implant. The $\gamma$ rays assigned to the isomer decay in ${}^{56}\mathrm{Sc}$ are marked by their energies in keV. The additional peak visible in the spectrum at 110 keV is contamination from the isomer decay of ${}^{54}\mathrm{Sc}$. (b) A plot of $\gamma$-ray energy as a function of time elapsed after the corresponding ${}^{56}\mathrm{Sc}$ implantation event. The five isomer $\gamma$ lines are visible, decaying with comparable lifetimes. (c) A projection of (b) onto the time axis, gated on the five identified $\gamma$-ray transitions. The resultant decay curve was fitted with a single exponential decay and constant background.

Figure 13

$\gamma$$\gamma$ coincidence gates for the (a) 48-keV, (b) 140-keV, (c) 188-keV, (d) 587-keV, and (e) 727-keV transitions in the 20-$\mu$s time window following a ${}^{56}\mathrm{Sc}$ implant. $\gamma$ rays are marked by their energy in keV and the number in square brackets is the number of counts in the peak.

Figure 14

Decay curve for ${}^{56}\mathrm{Sc}$-correlated $\beta$ decays considering only ${}^{56}\mathrm{Sc}$ implants coincident with identified isomeric $\gamma$-ray transitions. The decay curve is fitted with a single exponential decay and a constant background, and includes contributions from the growth and decay of the $\beta$-decay daughter (${}^{56}\mathrm{Ti}$, $T_{1/2}=200\pm 5$ ms [14]) and granddaughter (${}^{56}\mathrm{V}$, $T_{1/2}=216\pm 4$ ms [35]).

Figure 15

The comparison of the known levels in ${}^{53}\mathrm{Sc}$ [24, 37] to states in ${}^{52}\mathrm{Ca}$ suggests that ${}^{53}\mathrm{Sc}$ is accurately described by weak coupling of the odd $\pi 1f_{7/2}$ proton to the ${}^{52}\mathrm{Ca}$ core.

Figure 16

Experimentally determined levels below 3 MeV for the odd-odd, even-$A$ (a) ${}^{50}\mathrm{Sc}$, (b) ${}^{52}\mathrm{Sc}$, (c) ${}^{54}\mathrm{Sc}$, and (d) ${}^{56}\mathrm{Sc}$ isotopes. Level energies are labeled in keV. Theoretical predictions using the GXPF1 shell-model interaction are shown where available.

Figure 17

Experimentally determined levels below 4 MeV for odd-$A$ ${}^{53,55,57}\mathrm{Ti}$ isotopes.