High-spin states in ${}^{29}\mathbf{Al}$ and ${}^{27}\mathbf{Mg}$

The structure of ${}^{29}\mathrm{Al}$ and ${}^{27}\mathrm{Mg}$ was investigated using the reactions ${}^{18}\mathrm{O}$(${}^{14}\mathrm{C},p2n$) and ${}^{18}\mathrm{O}$(${}^{14}\mathrm{C},\alpha n$) at 40 MeV. The charged particles were detected and identified with a $\mathrm{\Delta }E-E$ telescope in coincidence with $\gamma$ radiation detected in the Florida State University Compton suppressed $\gamma$ detector array. The level and decay schemes of both nuclei have been expanded at higher spins and excitation energies. The positive-parity states up to 3.5–4.5 MeV agree well with shell model calculations using the USDA interaction. The negative-parity states in ${}^{27}\mathrm{Mg}$ are reproduced relatively well by one-particle–one-hole calculations with the WBP-a interaction. Three ${}^{27}\mathrm{Mg}$ states unbound by 0.4–1.4 MeV to neutron decay were observed to decay radiatively. One of these states had been previously observed to $\gamma$ decay in a ($d,p\gamma$) experiment along with a surprising 16 other neutron unbound states. The competition between neutron and $\gamma$ decay in these states is discussed in terms of angular momentum barriers and spectroscopic factors.

Figure 1

Three different regions of the $\gamma$-ray energy spectrum in coincidence with protons and the 1822 keV $\gamma$ ray from ${}^{29}\mathrm{Al}$. Labeled in black (red) are previously (newly) observed $\gamma$ lines in ${}^{29}\mathrm{Al}$.

Figure 2

Two spectra showing the $\gamma$ spectra in coincidence with the 2276 keV and the 2989 keV $\gamma$ lines from ${}^{29}\mathrm{Al}$. Newly observed states and transitions are shown in red.

Figure 3

Energy level and decay scheme of ${}^{29}\mathrm{Al}$ obtained from the present work. States and decay lines which were previously reported (newly observed in this work) are shown in black (red). The widths of the arrows indicate the $\gamma$ intensities relative to that of the 1753 keV line.

Figure 4

A portion of the $\gamma$-ray energy spectrum in coincidence with protons and the 1696 or 646 keV $\gamma$ rays from ${}^{29}\mathrm{Al}$. Labeled in black (red) are previously (newly) observed $\gamma$ lines.

Figure 5

A comparison of positive-parity excited states in ${}^{27,29}\mathrm{Al}$ up to 5900 keV and shell model calculations for ${}^{29}\mathrm{Al}$ using the USDA interaction in the $1s-0d$ shell. Only states of spin $5/2^{+}$ and higher are shown above 4500 keV. Note that some previously reported states not observed in the present experiment are included for completeness. All parities are positive.

Figure 6

Relative occupancies of the $1s-0d$ orbitals for the lowest four states in ${}^{27,29}\mathrm{Al}$ calculated in the shell model using the USDA interaction. The occupancies are shown relative to the expectations of the extreme single-particle model whose values are shown under the label “Ref”. Note that the reference for ${}^{29}\mathrm{Al}$ contains two neutrons in the $s_{1/2}$ orbital which are not in the ${}^{27}\mathrm{Al}$ reference, leading to the large differences in the figure for $s_{1/2}$ occupancies between these two isotopes, as discussed in the text.

Figure 7

Newly observed positive-parity states in ${}^{29}\mathrm{Al}$ above 5900 keV are compared with USDA shell model predictions. Only states of spin $\ge 7/2^{+}$ are shown among the USDA calculations. Above 7500 keV only states of spin $\ge 9/2^{+}$ are represented.

Figure 8

Energy level and decay scheme of ${}^{27}\mathrm{Mg}$ obtained from the present work. Shown are states and $\gamma$ lines (in keV) that have been previously identified (black) and newly observed (red). The widths of the arrows indicate the $\gamma$ intensities relative to that of the 984 keV line.

Figure 9

Two spectra showing the $\gamma$ spectra in coincidence with the 955 keV and the 1169 keV $\gamma$ lines from ${}^{27}\mathrm{Mg}$. Newly observed states and transitions are shown in red.

Figure 10

Portions of the $\gamma$ spectra in coincidence with the 1288, 2254, and 1698 (inset) keV $\gamma$-rays from ${}^{27}\mathrm{Mg}$. Labeled in black (red) are previously (newly) observed $\gamma$ lines in ${}^{27}\mathrm{Mg}$.

Figure 11

Comparison of positive-parity excited states in ${}^{29}\mathrm{Si}, {}^{27}\mathrm{Mg}$, and shell model calculations for ${}^{27}\mathrm{Mg}$. Positive- (negative-) parity states are shown in black (red). The parities of states are positive unless indicated otherwise. Some previously reported states not observed in the present experiment are included for completeness. The theoretical calculations for positive-parity states use the shell model limited to the $1s-0d$ shell with the USDA interaction. Those for negative-parity states use the WBP-a interaction with one hole (particle) allowed in the $0p$ ($0f-1p$) shell. Only higher spin predicted states are shown at higher excitation energies.