Low spin spectroscopy of neutron-rich ${}^{43,44,45}\mathrm{Cl}$ via ${\beta }^{-}$ and $\beta n$ decay

In this article, ${\beta }^{-}$ decay studies of neutron-rich isotopes ${}^{43,45}\mathrm{S}$ performed at the National Superconducting Cyclotron Laboratory are reported. $\beta$-delayed $\gamma$ transitions were detected by an array of 16 clover detectors surrounding the Beta Counting Station, which consists of a $40\times 40$ double-sided silicon strip detector followed by a single-sided silicon strip detector. $\beta$-decay half-lives were extracted for ${}^{43,45}\mathrm{S}$ by correlating implants and decays in the pixelated implant detector and by considering further coincidences with $\gamma$ transitions in the daughter nuclei. The level structures of ${}^{43,45}\mathrm{Cl}$ are expanded by the addition of 20 and 8 new $\gamma$ transitions in ${}^{43}\mathrm{Cl}$ and ${}^{45}\mathrm{Cl}$ respectively, and core-excited negative-parity states were observed in both nuclei for the first time. For ${}^{45}\mathrm{S}$, a large fraction of the $\beta$-decay strength was observed feeding neutron-unbound states in ${}^{45}\mathrm{Cl}$, which, decaying by delayed neutrons, populated excited states in the $\beta 1n$ daughter, ${}^{44}\mathrm{Cl}$. Experimental observations were compared to detailed shell-model calculations using the SDPFSDG-MU interaction to highlight the role of the diminished $N=28$ neutron shell gap and the near degeneracy of the proton $s_{1/2}$ and $d_{3/2}$ orbitals in the structure of the neutron-rich Cl isotopes. The current work also provides further support to a ground-state spin-parity assignment of $3/2^{+}$ in ${}^{45}\mathrm{Cl}$.

Figure 1

Top: $\beta$-delayed $\gamma$ transitions in ${}^{43}\mathrm{Cl}$ for a correlation time window of 200 ms ($\approx 1T_{1/2}$) after subtracting a background spectrum generated from a 1000 ms correlation window. Bottom: Similarly, $\beta$-delayed $\gamma$ transitions in ${}^{45}\mathrm{Cl}$ for a correlation window of 100 ms ($\approx 1T_{1/2}$) after subtracting a background spectrum generated from a 1000 ms correlation window. For both, the strong transitions are labeled, while the weaker ones are displayed in the coincidence spectra (Figs. 4 and 7). Transitions marked with an asterisk in the bottom panel are in the $\beta 1n$ daughter, ${}^{44}\mathrm{Cl}$.

Figure 2

(a) Decay curve for ${}^{43}\mathrm{S}$ from $\beta$-correlated implants within a grid of 9 pixels in the DSSD using a 2-s correlation time, along with the fit used to extract the half-life and the initial activity. Components of the fit are (i) exponential decay of the parent, ${}^{43}\mathrm{S}$, (ii) exponential growth and decay of the daughter nuclei, ${}^{43}\mathrm{Cl}$ ($\beta 0n$) and${}^{42}\mathrm{Cl}$ ($\beta 1n$), and (iii) exponential background. Known half-lives were used for the daughter nuclides [34]. The half-life extracted is 256(5) ms, in agreement with the evaluated value, 265(15) ms. (b) Decay curve gated by the 329- and 879-keV transitions, the two lowest and strongest transitions in the daughter ${}^{43}\mathrm{Cl}$ (see Figs. 1 and 3). The half-life extracted using an exponential fit with a constant background is 250.2(25) ms.

Figure 3

Partial level scheme of ${}^{43}\mathrm{Cl}$ following the ${\beta }^{-}$ decay of ${}^{43}\mathrm{S}$ ($T_{1/2}=250.2\left(25\right)$ ms and $Q_{{\beta }^{-}}=11.960\left(60\right)$ MeV [31]). The transitions marked in black were known before this work, whereas red indicates the new transitions added in this work. The absolute branching for each level was calculated using the measured yields in the $\gamma$ transitions feeding in and out of that state, measured $\gamma$ detection efficiency and total number of implants obtained from the fit to the decay curve. Using the $P_n$ value from Refs. [20, 22] of 40(10)%, the feeding to the ground state can be estimated as 13(11)% (not noted in the level scheme as $P_n$ could not be measured for ${}^{43}\mathrm{S}$ in this work). $logft$ values were calculated using the $logft$ calculator [30]. Alongside are the predictions of the shell-model calculations using the SDPFSDG-MU interaction [29]. The positive-parity states represent 0p0h excitations, while the negative-parity states are 1p1h excitations across a major shell gap. For protons it will be between $sd$ and $pf$ shells while neutrons can be excited from the $sd$ to the $pf$ shells as well as from $pf$ to $sdg$ shells. Only selected $1/2^{-}$ (green), $3/2^{-}$ (magenta), and $5/2^{-}$ (blue) states (with $logft <$ 6.00 and $E^{*}<6$ MeV) along with the predicted $logft$ values are shown.

Figure 4

(a)–(b) $\gamma$ transitions in ${}^{43}\mathrm{Cl}$ observed in coincidence with the 329-keV $\gamma$ transition which deexcites the $3/2_1^{+}$ state to the ground state. The inset of (b) shows the high-energy $\gamma$ transitions. (c) Spectrum showing the $\gamma$ transitions coincident with the 879-keV transition. (d)–(e) the 329-keV transition is seen in coincidence with the high-lying 4744- and 5280-keV transitions.

Figure 5

(a) Decay curve for ${}^{45}\mathrm{S}$ from $\beta$-correlated implants within a grid of 9 pixels in the DSSD using a correlation window of 1 s along with the fit used to extract the half-life and the initial activity. Components of the fit are (i) exponential decay of the parent, ${}^{45}\mathrm{S}$, (ii) exponential growth and decay of the daughter nuclei, ${}^{45}\mathrm{Cl}$ ($\beta 0n$) and ${}^{44}\mathrm{Cl}$ ($\beta$ 1n), and (iii) constant background. Known half-lives were used for the daughter nuclides [16, 22, 34]. (b) Decay curve gated by the 132-keV transition, which represents the $1/2_1^{+}\to 3/2^{+}\left(gs\right)$ transition in daughter ${}^{45}\mathrm{Cl}$. The extracted half-life values are 69(1) and 74(5) ms from the two different conditions.

Figure 6

Partial level scheme of ${}^{45}\mathrm{Cl}$ following $\beta$ decay of ${}^{45}\mathrm{S}$ ($T_{1/2}$ = 69(1) ms and $Q_{{\beta }^{-}}=14.92\left(33\right)$ MeV [31]). The transitions marked in black were known before, whereas red indicates the new transitions observed in this study. The absolute branching for each level was calculated similarly to that for ${}^{43}\mathrm{S}$ decay. As the intensity of the 1949-keV transition could not be determined, the feeding of the 1949-keV level is tentative (*). Based on our measurements, the ground-state feeding is consistent with zero. SM calculations similar to those for ${}^{43}\mathrm{Cl}$ are shown alongside. Positive parity states (0p0h) with spins of $1/2, 3/2, 5/2$, and $7/2$ below 3.5 MeV are shown with different colors identifying the spin values, similar to Fig. 3. A few representative negative-parity states (1p1h excitations in the calculations) are also shown. Only spins $1/2, 3/2$, and $5/2$ with $logft$ values below 6.00 in the energy range of the experimental states (above 3400 keV) are displayed for clarity. The complete list can be seen in Table 4.

Figure 7

Spectra displaying the coincidences observed between the $\gamma$ transitions in ${}^{45}\mathrm{Cl}$. (a) The 1020- and 1462- keV transitions are shown in the 929-keV gate. (b) Coincidences observed between the 1619- and 1081-keV transitions. (c)–(d) The 132-keV transition is seen in the gates of the transitions at 4596-, 5028-, 5118-, and 5229 keV. The $y$ scales for the 5028- and 5229-keV gates were shifted upwards by 10 and 20 counts respectively for clarity of display. (e) The 5028-, 5118-, and 5229-keV transitions are seen in the 132-keV gate. (f) The gate on the 511-keV $\gamma$ transition from pair production in the detector displays the single (SE) and double escape (DE) peaks of the high-energy $\gamma$ transitions as noted.

Figure 8

Partial level scheme of the $\beta$-delayed neutron daughter ${}^{44}\mathrm{Cl}$. The number in italics (magenta) alongside the energy of the transition (in keV) represents the relative intensity, with the 518-keV transition taken as 100%. Comparison with shell-model calculations (shown on the right) and the decay patterns have been used to suggest tentative spin-parities of the excited states.

Figure 9

Comparison of the low-lying level structure of odd-$A$ Cl isotopes from $N=22$ to $N=32$. The data for ${}^{43,45}\mathrm{Cl}$ is from the current data set, while those of the other isotopes are from published work [34]. Though some of the spin-parity assignments are tentative, we did not put them in parentheses for ease of comparison. The point to emphasize here is the strong decay branch for the $5/2^{+}$ states to the $3/2_1^{+}$ state and not to the $1/2^{+}$ state. The only deviation is for ${}^{39}\mathrm{Cl}$ where both the branches from the $5/2_2^{+}$ state have comparable strength. This is also supported by shell-model calculations, as shown in Table 3.

Figure 10

The energy difference between the first $3/2^{+}$ and $1/2^{+}$ states (one of them is the ground state) in odd-$A$ Cl and K isotopes with neutron numbers from 20 to 32, as observed in experiments, is shown by the solid symbols connected by thin dashed lines (magenta for Cl and green for K). An inversion of the ground-state $J^{\pi }$ is seen for both Cl and K for certain neutron numbers. The data for ${}^{43,45}\mathrm{Cl}$ is from the current data set, while data for other isotopes are from published work [34]. The solid lines are the corresponding energy differences between the $3/2_1^{+}$ and $1/2_1^{+}$ states from the shell-model calculations for the Cl (magenta) and K (green) isotopes.

Figure 11

The predicted occupancies of the proton $s_{1/2}$ and $d_{3/2}$ orbitals and neutron $f_{7/2}$ and $p_{3/2}$ orbitals for the first four excited states in odd-$A$ Cl isotopes are displayed in the top panel. These are the orbitals where the valence nucleons would reside in these isotopes. The top panel shows the occupancies for the ground state (solid lines) and first excited state (dashed line). For the ground state and the first excited state, the dominant occupancy of the proton toggles between the $0d_{3/2}$ and $1s_{1/2}$ orbitals for these isotopes which leads to the determination of the ground state in the calculations. The energy difference calculated between the $3/2_1^{+}$ and $1/2_1^{+}$ states ($\mathrm{\Delta }$) (in keV) from the shell-model calculations is also shown, where the negative sign indicates a $3/2^{+}$ ground state. The bottom panel displays the same for the $5/2_1^{+}$ state (solid line) and $3/2_2^{+}$ state (dashed line).

Figure 12

The first 15 negative-parity states calculated for ${}^{43}\mathrm{Cl}$ and ${}^{45}\mathrm{Cl}$ using the SDPFSDG-MU interaction are shown. The dashed lines are for spins $7/2^{-}$ and higher, which will not be populated in allowed GT decays, while the solid lines show the lower spins. Excitation energy of the states is given in keV and the spin value as $2J$ (in parentheses) is displayed alongside. The solid symbols represent the experimental states with proposed negative parity in the two cases. For ${}^{43}\mathrm{Cl}$, the $1/2^{-},3/2^{-},5/2^{-}$ states are matched by colors consistent with what is shown in Fig. 3. For ${}^{45}\mathrm{Cl}$, no spin values have been assigned for the negative-parity states and all are shown in black. See text for further discussion.