One-neutron removal from ${}^{29}\mathrm{Ne}$: Defining the lower limits of the island of inversion

Background: Very neutron-rich isotopes, including ${}^{30-32}\mathrm{Ne}$, in the vicinity of $N=20$ are known to exhibit ground states dominated by $fp$-shell intruder configurations: the “island of inversion.” Systematics for the Ne-isotopic chain suggest that such configurations may be in strong competition with normal shell-model configurations in the ground state of ${}^{29}\mathrm{Ne}$.

Purpose: A determination of the structure of ${}^{29}\mathrm{Ne}$ is thus important to delineate the extent of the island of inversion and better understand structural evolution in neutron-rich Ne isotopes. This is accomplished here through a combined investigation of nuclear and Coulomb-induced one-neutron removal reactions.

Method: Cross sections for one-neutron removal on carbon and lead targets and the parallel momentum distribution of the ${}^{28}\mathrm{Ne}$ residues from the carbon target are measured at around 240 MeV/nucleon. The measurements are compared with reaction calculations combined with spectroscopic information from SDPF-M shell-model wave functions.

Results: The deduced width of the inclusive parallel momentum distribution, 98(12) MeV/$c$ (FWHM), suggests that the ground state of ${}^{29}\mathrm{Ne}$ has a spin parity of $3/2^{-}$. Detailed comparisons of the measured inclusive and partial cross sections of the two targets and the parallel momentum distribution of the carbon target with reaction calculations, combined with spectroscopic information from large-scale shell-model calculations, are all consistent with a $3/2^{-}$ spin-parity assignment.

Conclusions: The results indicate that ${}^{29}\mathrm{Ne}$ lies within the island of inversion and that the ground state of ${}^{29}\mathrm{Ne}$ is dominated by a ${}^{28}\mathrm{Ne}\left(0_1^{+}\right)\otimes 2p_{3/2}$ neutron configuration. Combined with recently measured interaction cross sections, it is concluded that ${}^{29}\mathrm{Ne}$ may exhibit a moderately developed halo-like distribution.

Figure 1

Measured $\gamma$-ray energy spectra in coincidence with ${}^{28}\mathrm{Ne}$ residues following $1n$ removal from ${}^{29}\mathrm{Ne}$ on C (a) and Pb (b) targets. Solid (red) lines show the fits to the spectra based on the simulated detector response functions [dotted (red) lines] and exponential backgrounds [dashed (red) lines]. The inset in (a) is discussed in the text.

Figure 2

Measured ${}^{28}\mathrm{Ne}$ inclusive longitudinal momentum distribution following neutron removal reactions on the carbon target. The solid line is a fit to the data, for momenta between $\pm 100$ MeV/$c$, using a Lorentzian function convoluted with a Gaussian experimental resolution with $\sigma =22$ MeV/$c$.

Figure 3

Fractions of the $0\hslash \omega$ (black circles), $2\hslash \omega$ [(red) squares], and $4\hslash \omega$ [(blue) diamonds] configurations in the ground states of the Ne isotopes, as given by the SDPF-M [15] SM calculations. For ${}^{29}\mathrm{Ne}$, the calculation is for the $3/2^{+}$ SM ground state. For the $3/2^{-}$ state, which is found here to be the ${}^{29}\mathrm{Ne}$ ground state, the (1+3)$\hslash \omega$ configuration is dominant (Sec. 5).

Figure 4

Low-lying shell-model states of ${}^{27,29,31}\mathrm{Ne}$ with spin parities $3/2^{+},3/2^{-},7/2^{-}$, and $1/2^{+}$ calculated with the SDPF-M interaction. The relative positions of the $3/2^{+}$ and $3/2^{-}$ states are highlighted. The experimental energy level scheme of ${}^{27}\mathrm{Ne}$ is based on Refs. [18, 19, 20, 21]. For ${}^{29}\mathrm{Ne}$, the experimental level scheme is based on Ref. [22]. For ${}^{31}\mathrm{Ne}$, the ground-state spin parity of $3/2^{-}$ and separation energy of $0.{15}_{-0.10}^{+0.16}$ MeV were obtained from an analysis of Coulomb and nuclear breakup reactions [11]. The experimental separation energies of ${}^{27,29}\mathrm{Ne}$ are taken from Ref. [29].

Figure 5

Measured inclusive momentum distribution of ${}^{28}\mathrm{Ne}$ residues after reactions on the carbon target are compared with absolute theoretical calculations based on the ${}^{29}\mathrm{Ne}\left(J^{\pi }\right)$ SM states with (a) $J^{\pi }=3/2^{+}$, (b) $J^{\pi }=3/2^{-}$, (c) $J^{\pi }=7/2^{-}$, and (d) $J^{\pi }=1/2^{+}$. The summed contributions to the calculated inclusive momentum distributions from neutron removal (overlap) components with each $\ell$ value are also shown (see legend).

Figure 6

$C^{2}S$ deduced from the ratios of the measured and calculated ${}^{28}\mathrm{Ne}$ ground-state partial cross sections on the C target (blue hatched areas) and Coulomb breakup (red hatched areas) on the Pb target as a function of the assumed $S_n$ and $J^{\pi }$ of ${}^{29}\mathrm{Ne}$. The green hatched area shows the value and $1\sigma$ error on the empirical $S_n$. Calculations are shown for (a) $3/2^{+},{}^{28}\mathrm{Ne}\left(0_1^{+}\right)\otimes 1d_{3/2}$; (b) $3/2^{-},{}^{28}\mathrm{Ne}\left(0_1^{+}\right)\otimes 2p_{3/2}$; (c) $7/2^{-},{}^{28}\mathrm{Ne}\left(0_1^{+}\right)\otimes 1f_{7/2}$; and (d) $1/2^{+},{}^{28}\mathrm{Ne}\left(0_1^{+}\right)\otimes 2s_{1/2}{}^{29}\mathrm{Ne}$ ground-state configurations. The filled black circle in each panel shows the theoretical ${}^{29}\mathrm{Ne}$ ground state–to– ${}^{28}\mathrm{Ne}$ ground state SM spectroscopic factor, ${[A/(A-1)]}^{N_{\mathrm{osc}}}{C}^{2}S$, for each $J^{\pi }$.

Figure 7

Neutron single-particle levels in a deformed Woods-Saxon well as a function of the quadrupole deformation parameter $\beta$. The depth, diffuseness, and radius of the potential (for $A=28$) are $-41.0$ MeV, 0.67 fm, and 3.856 fm, respectively. Positive- and negative-parity levels are plotted as solid and dashed curves, respectively. The asymptotic quantum numbers $\left[N{n}_z\lambda \mathrm{\Omega }\right]$ are also shown.