Excited intruder states in ${}^{32}\mathrm{Mg}$

The low energy level structure of $N=20$ ${}^{32}\mathrm{Mg}$ obtained via β-delayed γ spectroscopy is reported. The level structure of ${}^{32}\mathrm{Mg}$ is found to be completely dominated by intruders. An inversion between the 1p-1h and 3p-3h states is observed for the negative parity states, similar to the 0p-0h and 2p-2h inversion for the positive parity states in these $N~20$ nuclei. The intruder excited states, both positive and negative parity, are reasonably explained by Monte Carlo shell model calculations, which suggest a shrinking $N=20$ shell gap with decreasing $Z$.

Figure 1

Systematics of the $2_1^{+}$ energies in even-even neutron-rich Mg and Si isotopes (for $N=14\text{−}24$). The data are from http://www.nndc.bnl.gov/ensdf/.

Figure 2

Excited states of ${}^{32}\mathrm{Mg}$ observed in various experiments: (a,b) β decay of ${}^{32}\mathrm{Na}$ [18, 19], (c) β-delayed neutron emission from ${}^{33}\mathrm{Na}$ [20], (d) in-flight spectroscopy following fragmentation at GANIL [21], (e) two-proton knockout from ${}^{34}\mathrm{Si}$ at MSU [22], (f) intermediate energy Coulomb excitation at MSU [4], (g) nuclear inelastic scattering [23], and (h) proton inelastic scattering in inverse kinematics at RIKEN [24].

Figure 3

Two-dimensional particle identification plot of energy loss ($\Delta E$) vs time-of-flight (Tof) for implantations that have a correlated β decay. The ${}^{32,31}\mathrm{Na}$ groups were the strongest with the 2% momentum acceptance setting of the A1900. The other nuclides of the cocktail secondary beam were ${}^{30}\mathrm{Ne}$ and ${}^{33}\mathrm{Mg}$.

Figure 4

Decay curve of the ${}^{32}\mathrm{Na}$ implants. The components of the fit that lead to a half-life determination of 13.1 (5) ms are: 1, ${}^{32}\mathrm{Na}$ decay; 2, ${}^{32}\mathrm{Mg}$ decay [95 (16) ms]; 3, ${}^{32}\mathrm{Al}$ decay [33 (4) ms]; 4, ${}^{31}\mathrm{Mg}$ decay [230 (20) ms]; and 5, ${}^{30}\mathrm{Mg}$ decay [335 (17) ms]. ${}^{31}\mathrm{Mg}$ and ${}^{30}\mathrm{Mg}$ result from β-delayed $1n$ and $2n$ emissions, respectively.

Figure 5

Decay time spectra for the 885 keV γ line in ${}^{32}\mathrm{Mg}$. The result of an exponential fit with a constant background gives a half-life of 11.5 (12) ms.

Figure 6

A partial β-delayed γ-ray spectrum for events coming within the first 60 ms after a ${}^{32}\mathrm{Na}$ implantation, showing the important transitions in ${}^{32}\mathrm{Mg}$. The 485, 1666, 2269, and 3935 keV transitions with small intensities cannot be seen in this scale. γ rays from daughter and granddaughter activities are also indicated.

Figure 7

Apparent β-feeding intensities for the excited levels in ${}^{32}\mathrm{Mg}$ observed in the present work. Intensity of the ground state was calculated using $P_{1n}$ of $24(7)\%$ and $P_{2n}$ of $8(2)\%$ from Ref. [18]. The apparent log $\mathit{ft}$ values were calculated using the measured absolute intensities, half-life of 13.1 (5) ms, and $Q_{\beta }$ value of 20019(357) keV [27] according to Ref. [31]. The proposed spin and parity assignments for the experimental levels are indicated on the left. Predictions of the MCSM calculations with the SDPF-M interaction are also shown. For MCSM, positive parity state levels above $0_2^{+}$ are not shown for clarity. The negative parity states are labeled as ${\pi }^{-}$. All energies are in keV.

Figure 8

(Top) Ratio of the energy of the $4_1^{+}$ and $2_1^{+}$ states ($R4$) for neutron-rich Mg isotopes, which is an indicator of the nature of collectivity of the isotope. (Bottom) Correlations between the measured ratio $R4$ with measured $B(E2)$ values for even-even Mg isotopes. ${}^{30}\mathrm{Mg}$ is omitted as the $4^{+}$ state is not known experimentally. The data are from http://www.nndc.bnl.gov/ensdf/.

Figure 9

The experimental and calculated $B$(GT) strength in the ${\beta }^{-}$ decay of ${}^{32}\mathrm{Na}$. The B(GT) was estimated in the MCSM calculations (histogram) by assuming a $J^{\pi }=3^{-}$ for the ground state of ${}^{32}\mathrm{Na}$ with a 2p-2h configuration and is scaled down by the quenching factor 0.7 [33].