Onset of collectivity for argon isotopes close to $N=32$

The shell closure at $N=32$ has been investigated by a first spectroscopy of the $N=31$ nucleus ${}^{49}\mathrm{Ar}$ at the Radioactive Isotope Beam Factory. Using the ${}^{50}\mathrm{Ar}(p,pn)$ reaction channel in inverse kinematics, ${}^{50}\mathrm{Ar}$ projectiles at 217 MeV/nucleon impinged on a 150 mm long liquid hydrogen target, part of the MINOS device. Prompt deexcitation $\gamma$ rays were measured with the NaI(Tl) array ${\mathrm{DALI}2}^{+}$. Reaction products were analyzed with the SAMURAI spectrometer, which allowed the measurement of the momentum distributions and angular momentum transfer. Data were compared to state-of-the-art theoretical predictions, including shell-model, energy-density functional, and ab initio calculations. An onset of collectivity is suggested besides the spherical configuration typical of a closed shell nucleus, such as for ${}^{52}\mathrm{Ca}$.

Figure 1

Particle identification with the mass over charge ratio $A/Q$ and atomic number $Z$. Left: beam particle identification at BigRIPS before the target. Right: residue particle identification downstream the secondary target from the large acceptance SAMURAI spectrometer. ${}^{50}\mathrm{Ar}$ and ${}^{49}\mathrm{Ar}$ in front and behind the MINOS secondary target are shown by the red ellipses.

Figure 2

Doppler-corrected $\gamma$-ray spectra of ${}^{49}\mathrm{Ar}$ obtained from (a) one-neutron knockout ${}^{50}\mathrm{Ar}(p,pn)$, (b) the more complex ${}^{51}\mathrm{K}(p,2pn)$ reaction, and (c) inelastic scattering ${}^{49}\mathrm{Ar}(p,p^{\prime })$. Spectra in (a) and (b) are obtained after subtraction of a low-energy bremsstrahlung component (see text). Experimental data (points) are fitted by a combination (black line) of five simulated ${\mathrm{DALI}2}^{+}$ response functions (red continuous lines) and a two-component exponential background (red dashed line).

Figure 3

Doppler-corrected $\gamma$-ray spectra of ${}^{49}\mathrm{Ar}$ obtained from the one-neutron knockout ${}^{50}\mathrm{Ar}(p,pn)$ (a) gated by the [1180,1320] range in Fig. 2, which maximizes the ratio of the response function corresponding to the 1266 keV transition over other transitions; (b) gated by the energy ranges just below and above, which maximizes the background due to other transitions.

Figure 4

Momentum distributions of ${}^{49}\mathrm{Ar}$ ejectiles following the one-neutron knockout reaction: (a) and (b) PMD in coincidence with the 198 and 1340 keV transitions measured in ${\mathrm{DALI}2}^{+}$; (c) and (d) TMD in coincidence with the 198 and 1340 keV transitions. Data are compared to calculations with the TC [47] and DWIA [48] methods for $\ell =1$ and $\ell =3$ waves after convolution with the experimental resolution.

Figure 5

Level scheme of ${}^{49}\mathrm{Ar}$ with excitation energies expressed in keV. Experimental results (right) are obtained from the analyses of Fig. 2. They are compared to the theoretical calculations developed in the text: from right to left, shell-model calculations performed with the ${\mathrm{SDPF}-\mathrm{MU}}_s$ and the original SDPF-MU interactions, energy-density functional calculations including states obtained from the quasiparticle random phase approximation (QRPA, dashed lines), IMSRG calculation with the EM 1.8/2.0 interaction, and GGF calculation with the $NN+3N$(lnl) interaction; ${}^{50}\mathrm{Ar}$ is shown on the right side with the latest $E\left(2_1^{+}\right)$ value taken from [29].

Figure 6

Spectroscopic factor $\left|\right|{\langle }^{A-1}X+n{\parallel }^{A}X\rangle {\left|\right|}^2$ distributions for (a) $1/2^{-}$, (b) $3/2^{-}$, and (c) $7/2^{-}$ states in ${}^{49}\mathrm{Ar}$ (red) and ${}^{51}\mathrm{Ca}$ (blue) obtained in the shell-model calculation with the SDPF-MUs interaction [46]. The dashed line corresponds to the maximal occupancy $2j+1$ of the corresponding neutron orbitals $\nu 1p_{3/2}$ and $\nu 0f_{7/2}$ in an independent particle model (IPM).

Figure 7

Potential energy surfaces energy $E_{\mathrm{HFB}}$ versus the quadrupole deformation parameter $\beta$ for argon (a) and calcium (b) isotopes obtained from HFB calculations based on the D1M parametrization [55] of the Gogny effective interaction [56]. The curves are shifted by 2 MeV from each other in order to allow superposition. (c) HFB $+$ blocking calculations (see text) for the lowest-lying states of ${}^{49}\mathrm{Ar}$ at a given spin-parity $1/2^{-}$, $3/2^{-}$, $5/2^{-}$, $7/2^{-}$, and $9/2^{+}$.

Figure 8

Energy of the proton (left) and neutron (right) orbitals versus the quadrupole deformation $\beta$ parameter in ${}^{50}\mathrm{Ar}$ obtained from Hartree-Fock-Bogoliubov (HFB) calculations based on the D1M parametrization [55] of the Gogny effective interaction [56]. The orbitals discussed in the text are labeled with the usual Nilsson parameters $K[N,n_z,\mathrm{\Lambda }]$. The black dots stand for the Fermi level. The red arrow is placed at $\beta =-0.15$.