Development of shell closures at $N=32,34$. I. $\beta$ decay of neutron-rich Sc isotopes

Details regarding the $\beta$-decay properties of ${}^{54,55,56}\mathrm{Sc}$ are reported and compared with shell model predictions. The low-energy level structures of even-even ${}^{54,56}\mathrm{Ti}$ are presented, and the systematic variation of the energy of the first excited $2_1^{+}$ state is discussed in light of proposed shell closures at $N=32,34$ for the neutron-rich $\mathrm{Ti}$ isotopes.

Figure 1

Systematic variation of $E\left(2_1^{+}\right)$ and $E\left(4_1^{+}\right)$ for the $N=32$ isotones.

Figure 2

$\beta$-delayed $\gamma$-ray spectra for ${}^{54}\mathrm{Sc}$ in the range $0–2\mathrm{MeV}$. The spectra include events within the first (a) $10\mathrm{s}$ and (b) $1\mathrm{s}$ after a ${}^{54}\mathrm{Sc}$ implant. The peaks labeled by energy have been identified as transitions in ${}^{54}\mathrm{Ti}$ following the decay of ${}^{54}\mathrm{Sc}$.

Figure 3

Decay curve for ${}^{54}\mathrm{Sc}$. Data were fitted with a single-exponential decay and the exponential growth and decay of the short-lived daughter ${}^{54}\mathrm{Ti}$. An exponential background is also considered in the fit. See text for details.

Figure 4

Proposed level scheme for ${}^{54}\mathrm{Ti}$ populated following the $\beta$ decay of ${}^{54}\mathrm{Sc}$. The number in brackets following the $\gamma$-ray-decay energy is the absolute $\gamma$-ray intensity in percent. The $Q_{\beta }$ value was deduced from data in Ref. 19.

Figure 5

$\gamma$-ray spectrum collected within a $20\text{−}\mu \mathrm{s}$ time window after a ${}^{54}\mathrm{Sc}$ implant. The $110\text{−}\mathrm{keV}$ isomeric transition was previously reported in Ref. 18.

Figure 6

(a) Decay curve for ${}^{55}\mathrm{Sc}$. Data were fitted with a single-exponential decay and the exponential growth and decay of the short-lived daughter ${}^{55}\mathrm{Ti}$. An exponential background is also considered in the fit. (b) $\beta$-delayed $\gamma$-ray spectrum for ${}^{55}\mathrm{Sc}$ in the range $0–1.0\mathrm{MeV}$. A gate was placed on the decay curve to include only events within the first second of a ${}^{55}\mathrm{Sc}$ implant.

Figure 7

$\beta$-delayed $\gamma$-ray spectrum for ${}^{56}\mathrm{Sc}$ in the range $0–2\mathrm{MeV}$. This spectrum includes events within the first second after a ${}^{56}\mathrm{Sc}$ implant.

Figure 8

Decay curves for ${}^{56}\mathrm{Sc}$, showing (a) fragment-$\beta$ correlations only, where the data were fitted with an exponential decay from the ${}^{56}\mathrm{Sc}$ ground state and isomeric state, with weights of 83% and 20%, respectively, and ${}^{56}\mathrm{Ti}$ and ${}^{56}\mathrm{V}$ growth and decay with a linear background; (b) fragment-$\beta$ correlations with an additional requirement of a $1129\text{−}\mathrm{keV}$ $\gamma$ ray in coincidence; (c) fragment-$\beta$ correlations with an additional requirement of a $690\text{−}\mathrm{keV}$ coincident $\gamma$ ray; and (d) fragment-$\beta$ correlations with an additional requirement of the presence of a $1161\text{−}\mathrm{keV}$ $\gamma$ ray. The curves shown in (b), (c), and (d) were fitted with a single exponential and constant background.

Figure 9

$\gamma$-ray spectrum collected within a $20\text{−}\mu \mathrm{s}$ time window following a ${}^{56}\mathrm{Sc}$ implant. The $587\text{−}\mathrm{keV}$ transition is a possible doublet.

Figure 10

Proposed level scheme for ${}^{56}\mathrm{Ti}$ populated following the $\beta$ decay of ${}^{56}\mathrm{Sc}$. The decay energies are the adopted values taken from a weighted average of the $\beta$-decay and in-beam experiments discussed in the text. The number in brackets following the $\gamma$-ray-decay energy is the absolute $\gamma$-ray intensity in percent. The $Q_{\beta }$ value was deduced from data in Ref. 19. A possible $\beta$-delayed neutron branch precludes the determination of $\beta$-branching ratios to ${}^{56}\mathrm{Ti}$ excited states.

Figure 11

$\gamma$ rays in coincidence with the (a) $690\text{−}\mathrm{keV}$ and (b) $1129\text{−}\mathrm{keV}$ $\gamma$-ray transitions following ${}^{56}\mathrm{Sc}$ $\beta$ decay.

Figure 12

Low-energy levels of ${}^{54,56}\mathrm{Sc}$ calculated in the full $pf$-shell model space using the GXPF1 interaction.

Figure 13

Spin and parities for selected ${}_{23}\mathrm{V}$ and ${}_{21}\mathrm{Sc}$ isotopes with schematic neutron single-particle levels. Energy spacings are not to scale.