How Robust is the N = 34 Subshell Closure? First Spectroscopy of $^{52}$Ar

The first $\gamma$-ray spectroscopy of $^{52}$Ar, with the neutron number N = 34, was measured using the $^{53}$K(p,2p) one-proton removal reaction at $\sim$210 MeV/u at the RIBF facility. The 2$^{+}_{1}$ excitation energy is found at 1656(18) keV, the highest among the Ar isotopes with N $>$ 20. This result is the first experimental signature of the persistence of the N = 34 subshell closure beyond $^{54}$Ca, i.e., below the magic proton number Z = 20. Shell-model calculations with phenomenological and chiral-effective-field-theory interactions both reproduce the measured 2$^{+}_{1}$ systematics of neutron-rich Ar isotopes, and support a N = 34 subshell closure in $^{52}$Ar.

The first γ-ray spectroscopy of 52 Ar, with the neutron number N = 34, was measured using the 53 K(p,2p) one-proton removal reaction at ∼210 MeV/u at the RIBF facility. The 2 + 1 excitation energy is found at 1656 (18) keV, the highest among the Ar isotopes with N > 20. This result is the first experimental signature of the persistence of the N = 34 subshell closure beyond 54 Ca, i.e., below the magic proton number Z = 20. Shell-model calculations with phenomenological and chiraleffective-field-theory interactions both reproduce the measured 2 + 1 systematics of neutron-rich Ar isotopes, and support a N = 34 subshell closure in 52 Ar.

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In the shell model description of atomic nuclei, magic numbers of nucleons correspond to fully occupied energy shells below the Fermi surface [1], and present the backbone of our understanding of nuclei. Scientific advances over the past decades have shown that the sequence of magic numbers established for stable nuclei-2, 8, 20, 28, 50, 82, 126-is not universal across the nuclear landscape [2]. A few prominent examples are the breakdown of the conventional N = 20, 28 magic numbers [3][4][5] and the emergence of a new N = 16 magic number [6,7] in neutron-rich nuclei. Considerable efforts have been spent to unfold the driving forces behind such shell evolution. In particular, the spin-isospin terms of the monopole part of the effective nucleon-nucleon interactions [8,9], as well as three-nucleon forces [10,11] have been proposed to play a dominant role.
For rare isotopes, the first 2 + excitation energy [E(2 + 1 )] in even-even nuclei is often the first observable accessible to experiment to characterize shell effects. In a simplified shell model picture, a high 2 + 1 excitation energy is interpreted as resulting from the excitation of nucleons across a large shell gap [12].
Recently, neutron-rich pf-shell nuclei have received much attention on both experimental and theoretical fronts with the possible appearance of new subshell closures at N = 32 and 34. A sizable N = 32 subshell closure has been reported in the region from Ar to Cr isotopes based on E(2 + 1 ) [13][14][15][16], reduced transition probabilities B(E2; 0 + 1 →2 + 1 ) [17,18], and mass [19][20][21] measurements, although some ambiguity remains due to the newly measured large charge radii of neutron-rich Ca isotopes [22], the masses of 51−55 Ti [23], and the low E(2 + 1 ) in 50 Ar [16]. On the other hand, the N = 34 subshell closure has been so far suggested only in 54 Ca [24,25]. In the Ti and Cr isotopes, the systematics of E(2 + 1 ) [26,27] and B(E2; 0 + 1 →2 + 1 ) [17,18] show no local maximum and minimum at N = 34. The measured lowlying structure of 55 Sc [28] was interpreted as indicating a rapid weakening of the N = 34 subshell closure in pf-shell nuclei at atomic number Z > 20. The E(2 + 1 ) of 54 Ca was measured to be 2043 (19) keV, ∼0.5 MeV lower than its even-even neighbor 52 Ca [24]. Despite this lower 2 + 1 excitation energy, 54 Ca was concluded to be a doubly magic nucleus from a phenomenological shellmodel interpretation [24], whereas ab initio coupledcluster calculations indicated a weak N = 34 subshell closure [29]. Very recently, the mass measurements of 55−57 Ca [25] confirmed the picture of a subshell closure at N = 34 in Ca isotopes. Until now, the region below Z = 20 was unexplored. It is still an open question how the N = 34 subshell evolves below Z = 20 towards more neutron-rich systems, such as 52 Ar.
The heaviest Ar isotope with known spectroscopic information so far is 50 Ar [16]. Phenomenological shellmodel calculations [24,30] reproducing the available E(2 + 1 ) data for neutron-rich Ar isotopes predict a relatively high-lying 2 + 1 state in 52 Ar, and suggest that the N = 34 subshell closure in 52 Ar is stronger than the one reported for 54 Ca [16]. In the present Letter, we report on the first spectroscopy of 52 Ar, the most neutron-rich even-even N = 34 isotone accessible today and possibly for the next decades. A clear enhancement of E(2 + 1 ) at N = 34 is found, supporting the persistence of the N = 34 magic number in Z < 20 nuclei.
The experiment was carried out at the Radioactive Isotope Beam Factory (RIBF), operated by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo. Radioactive nuclei were produced by fragmentation of a 345 MeV/u 70 Zn primary beam with an average beam intensity of ∼240 pnA on a 10-mm- thick rotating Be target. The secondary beam cocktail, magnetically centered on 53 K, was identified event-byevent using the magnetic rigidity (Bρ), energy loss (∆E) and time-of-flight (TOF) information [31] in the BigRIPS two-stage fragment separator [32]. The intensity and purity of the 53 K beam were ∼1.0 particle per second and ∼0.5%, respectively.
The secondary beam impinged on a 151(1)-mm-thick liquid hydrogen (LH 2 ) target with a density of 73 kg/m 3 to induce one-proton knockout reactions. Two multiwire drift chambers [33], located upstream of the LH 2 target, were used to measure the trajectories of the incoming projectiles. The kinetic energy of the 53 K beam at the entrance of the target was ∼245 MeV/u. Its energy loss in the LH 2 target was approximately 70 MeV/u. The LH 2 target was surrounded by a 300-mm-long time projection chamber (TPC), constituting the MINOS device [34]. The tracks of the recoil protons were recorded by the TPC to reconstruct the reaction vertex [35]. The MINOS efficiency to detect at least one of the two protons was measured to be 92(3)%. The vertex resolution was estimated to be 4 mm (FWHM) [35]. The determination of the reaction vertices allowed precise Doppler correction of the de-excitation γ rays from the reaction residues.
The DALI2+ [36] high-efficiency γ-ray spectrometer surrounded the MINOS device to detect in-flight deexcitation γ rays from 52 Ar. It consisted of 226 NaI(Tl) crystals and covered polar angles from 15 • to 118 • with respect to the center of the LH 2 target. Add-back analysis was applied for events with γ-ray multiplicity M γ > 1 when the centers of hit detectors were less than 20 cm apart. For 1 MeV γ rays emitted from nuclei moving at 60% of the velocity of light, the photopeak efficiency and energy resolution after add-back analysis were 30% and 11% (FWHM), respectively. The whole array was calibrated using 133 Ba, 137 Cs, 60 Co, and 88 Y sources leading to an energy calibration uncertainty of 4 keV, and showed a good linearity from 356 keV to 1836 keV.
Downstream the LH 2 target, reaction residues were transported to the SAMURAI spectrometer [33] and identified with the Bρ-∆E-TOF method.
The Bρ of charged fragments passing through the SAMURAI magnet with a central magnetic field of 2.7 T was reconstructed using two multiwire drift chambers placed upstream and downstream the magnet [33]. The ∆E and TOF information were provided by a 24-element plastic scintillator hodoscope. Figure 1 shows the particle identification of fragments with the selection of 53 K identified at BigRIPS. A 6.6 σ separation in Z and a 9.1 σ separation in mass number, A, for Ar isotopes were achieved. Over the data taking of seven days, 438 counts of 52 Ar were obtained from the 53 K(p, 2p) 52 Ar reactions, in which the kinematics of protons measured by MINOS supported a quasi-free scattering reaction mechanism. The reaction loss of 53 K in materials along the beam and fragment trajectories was determined by measuring the unreacted 53 K, and the inclusive cross section was measured to be 1.9(1) mb.
The Doppler-shift corrected γ-ray energy spectrum of 52 Ar following the 53 K(p,2p) reaction is shown in Fig. 2. A clear peak is present in the range of 1500-1800 keV, while three structures are visible in the range of 600-900, 1000-1300 and 2000-2500 keV. In order to quantify the significance level of these peaks, we performed the likelihood ratio test by fitting the spectrum of 52 Ar using the GEANT4 [37] simulated response functions on top of a double exponential background. Given the low statistics of the γ-ray spectrum of 52 Ar, a Poisson distribution was adopted to describe the fluctuations of each bin, and the background line shape was constrained by the measured γ-ray spectrum in coincidence with 50 Ar following the 51 K(p,2p) reaction. As a result, a significance level of 5 standard deviations (σ) was obtained for the 1656(18) keV transition. The 2295(39) keV γ line was found to have a significance of 3 σ, while the other two structures in the range of 600-900 and 1000-1300 keV both had a significance level of less than 1 σ and are therefore not considered in the following analysis. Note that the errors of the deduced γ-ray energies shown above include both statistical and systematic uncertainties. The former dominates and the latter mainly originates from the energy calibration uncertainty. Lifetime (τ γ ) effects of the excited states on the deduced γ-ray energies are expected to be negligible, since Raman's global systematics [38] suggests τ γ < 2 ps for the two excited states measured in 52 Ar.
Based on the measured γ-ray intensities, the 1656 keV transition is attributed to a direct decay to the ground state. The low statistics do not allow to conclude any (non) coincidence between the 1656 and 2295 keV transitions from γ-γ correlations, but the cascade scenario is very unlikely due to the expected low neutron separation energy (S n ) of 52 Ar. The recent precision mass measurement gives S n = 3840(70) keV for 54 Ca [19]. Being more exotic, 52 Ar is expected to have a significantly lower S n . The 2016 Atomic Mass Evaluation [39] gives an estimation S n = 2660(850) keV for 52 Ar, and excludes the coincidence scenario. The proposed energy level scheme of 52 Ar is presented in the inset of Fig.  2. The measured partial cross sections to the 1656 and 2295 keV states are 0.9(2) and 0.4(1) mb, respectively. Assuming no population to other excited states, the cross section to the ground state is deduced to be 0.7(2) mb via subtraction from the inclusive cross section. The quoted uncertainties are dominated by statistical errors, while the systematic uncertainties mainly arise from the estimation of MINOS efficiency. All the experimental results are summarized in Table I. The 1656 keV state with the higher population is assigned to be 2 + 1 . The 2295 keV state decaying directly to the ground state is assigned as 2 + 2 . Further discussions about these spin-parity assignments are given later based on the comparison between experimental partial cross sections and theoretical calculations. Figure 3 displays the energy of the 2 + 1 state deduced for 52 Ar together with values for lighter Ar isotopes [40]. Notably, the measured E(2 + 1 ) = 1656(18) keV for 52 Ar is found to be the highest among the Ar isotopes with N > 20. It is larger than the E(2 + 1 ) = 1577(1) keV [41] for 46 Ar which reflects the conventional N = 28 shell closure. Moreover, the measured systematics of E(2 + 1 ) along the Ar isotopic chain is characterized by a pronounced enhancement at N = 34 relative to its N = 32 even-even neighbor, unlike the trend observed for Ca, Ti and Cr isotopes in which a decrease is seen from N = 32 to 34. The present work offers the first experimental signature of the N = 34 subshell closure in Ar isotopes.
By employing a double-charge exchange equation-of-motion (DCE-EOM) coupled-cluster technique, the E(2 + 1 ) states in 40,48,52 Ar can be obtained from generalized excitations of the ground states of the closed (sub-)shell nuclei 40,48,52 Ca, while the E(2 + 1 ) state in 44 Ar is obtained from excitations of the 44 S ground state, respectively. The E(2 + 1 ) states in 46,50,52 Ar are also computed using the two-particleremoved equation-of-motion coupled-cluster method [54] (denoted by 2PR-EOM).
In this work, we employ the DCE-EOM coupled-cluster calculations with particle-hole excitations truncated at the singles, doubles, and approximate triples level (CCSDT-3) [55], while the 2PR-EOM coupled-cluster calculations are truncated at the three-hole-one-particle excitation level using CCSD and CCSDT-3 for the ground states of 48,52,54 Ca. Theoretical uncertainties in coupled-cluster calculations are estimated by comparing results with and without triples excitations. In addition, we also compare our results to large scale shell-model calculations with the phenomenological SDPF-MU effective interaction [56]. Note that the original SDPF-MU Hamiltonian was modified using recent experimental data on exotic Ca [24] and K [57] isotopes. The pf-shell part of the new interaction is the GXPF1Br Hamiltonian and details of the modifications are given in Ref. [30].
Theoretical (p,2p) cross sections to different final states of 52 Ar are computed with spectroscopic factors calculated with the VS-IMSRG method using the 1.8/2.0 (EM) interaction and single-particle cross sections (σ sp ) calculated using the Glauber theory as described in Ref. [58]. The input of the σ sp calculations are the nucleonnucleon cross sections, using the parametrization from Ref. [59], and the nuclear ground-state densities deduced from a mean-field Hartree-Fock-Bogoliubov calculation using the SLy4 interaction. The involved single-particle states are calculated using a Woods-Saxon potential including the Coulomb and spin-orbit terms with parameters chosen to reproduce the proton separation energies. The range of the Woods-Saxon potential was taken as R = r 0 (A − 1) 1/3 fm with r 0 = 1.25 fm, and the  52 Ar reaction in comparison with theoretical calculations. Predicted excitation energies (Ex), J π , and spectroscopic factors (C 2 S th ) associated with the removed protons from different orbits (lj) were obtained using the VS-IMSRG method predicting a 53 K(3/2 + ) ground state. Theoretical partial cross sections (σ th ) were computed using the C 2 S th values and beam-energy-weighted average single-particle cross sections ( σsp ).

Experiment
Theory  52 Ar agree well with the predictions for the 2 + 1 state at 1849 keV and the 2 + 2 state at 2367 keV, respectively. The ratio of the experimental cross section to the theoretical prediction is in line with the systematic reduction factor reported from (e,e p) measurements on stable targets [60] and from (p,2p) reactions on oxygen isotopes [61,62]. The good agreement between experiment and theory not only supports the spin-parity assignment, but also indicates that the adopted VS-IMSRG approach provides a satisfactory description of the structure of 52 Ar with the 1.8/2.0 (EM) interaction.
We now discuss the systematics of E(2 + 1 ) in Ar isotopes. As seen in Fig. 3, the phenomenological shellmodel calculations with the original and modified SDPF-MU interaction and the VS-IMSRG calculations with the 1.8/2.0 (EM) interaction reproduce the steep rise of E(2 + 1 ) from 50 Ar to 52 Ar. The modified SDPF-MU calculations provide the best overall description of the experimental data along the Ar isotopic chain including the E(2 + 1 ) of 52 Ar. The VS-IMSRG approach using the 1.8/2.0 (EM) interaction reasonably reproduces the measured E(2 + 1 ) in neutron-rich Ar isotopes, though an overprediction is seen between N = 28 and 34. The dependence of the ab initio calculations on the initial NN and 3N forces is illustrated by the VS-IMSRG calculations with the N 2 LO sat Hamiltonian. Compared to results with the 1.8/2.0 (EM) interaction, calculations with the N 2 LO sat interaction systematically underpredict the data, despite a better agreement for the E(2 + 1 ) at N = 28 and 30. The DCE-EOM calculations with the 1.8/2.0 (EM) interaction reproduce the E(2 + 1 ) in 44,48 Ar within the estimated uncertainties, but underestimate the E(2 + 1 ) in 52 Ar by ∼600 keV. For 40 Ar, which is characterized by deformation and shape co-existence [63], all considered calculations underestimate its E(2 + 1 ). The 2PR-EOM result for 52 Ar is consistent with the DCE-EOM result, but does not reproduce the steep increase of the E(2 + 1 ) state from 50 Ar to 52 Ar. We note that 2PR-EOM gives a E(2 + 1 ) energy at 3.0 MeV consistent with the N = 28 shell closure, although almost twice the experimental value.
Being rooted in the same chiral effective interaction, i.e., 1.8/2.0 (EM), the VS-IMSRG and coupled-cluster approaches predict different E(2 + 1 ) in 52 Ar. However, for closed (sub-)shell Ca isotopes, VS-IMSRG predicts similar E(2 + 1 ) as coupled-cluster calculations with singles and doubles excitations (EOM-CCSD), despite they both overestimate the E(2 + 1 ) in 48,52 Ca. Compared to EOM-CCSD and VS-IMSRG, EOM-CCSDT-3 gives overall lower E(2 + 1 ). It reproduces the measured E(2 + 1 ) in 48,52 Ca, but underestimates the E(2 + 1 ) in 54 Ca by 300 keV. The differences in the calculated E(2 + 1 ) states in calcium and argon isotopes using the employed many-body methods, indicate that the total theoretical uncertainties might be larger than the estimated error bars shown in Fig. 3. Thus, the measured E(2 + 1 ) state of 52 Ar in the current work serves as an important benchmark to understand these uncertainties.
It is worth noting that the modified SDPF-MU shell model calculations and the VS-IMSRG approach using the 1.8/2.0 (EM) interaction have both been used along the N = 34 isotonic chain to investigate the evolution of the shell closure. Both calculations suggest that the N = 34 shell gap persists from 54 Ca towards more exotic N = 34 isotones, which is consistent with the measured high-lying 2 + 1 state in 52 Ar presented here. However, the shell gap is not an observable, so calculations predicting similar E(2 + 1 ) might give different sizes of shell gaps. Indeed, the modified SDPF-MU calculations indicate that the magnitude of the N = 34 shell gap in 52 Ar is ∼3.1 MeV, which exceeds the value in 54 Ca (∼2.6 MeV) [16]. Conversely, using the method of Ref. [64] to extract the effective single-particle energies, VS-IMSRG predicts the N = 34 shell gap in 52 Ar to be ∼2.6 MeV, smaller than that in 54 Ca (∼3.2 MeV). In addition, the VS-IMSRG approach also provides the orbital occupancies of the 0 + 1 and 2 + 1 states in 52 Ar and 54 Ca. It reveals that only ∼0.5 neutrons are excited from p 1/2 to f 5/2 in the 2 + 1 excitation of 52 Ar, whereas in the case of 54 Ca, ∼0.9 neutrons are excited across the N = 34 shell gap. This is consistent with the observed decrease in E(2 + 1 ) between 54 Ca and 52 Ar. Nevertheless, both calculations predict 48 Si as a new doubly magic nucleus. The E(2 + 1 ) of 48 Si in SDPF-MU [30] and VS-IMSRG [65] calculations lies at 2.85 and 3.13 MeV, respectively. However, it is not yet known whether 48 Si is stable against neutron emission. Mass models that reproduce well the observed limits of existence in the pf-shell region [66] tend to predict 48 Si as a drip line nucleus.
To summarize, the low-lying structure of the N = 34 nucleus 52 Ar was investigated using the 53 K(p,2p) 52 Ar one-proton removal reaction at ∼210 MeV/u mid-target energy. The 2 + 1 state was measured to be 1656(18) keV, the highest among the Ar isotopes with N > 20. The measured (p,2p) cross sections to different final states of 52 Ar are in line with calculations and support the proposed spin-parity assignment. Shell-model calculations with phenomenological and the chiral interaction 1.8/2.0 (EM) both reproduce the measured 2 + 1 systematics of the neutron-rich Ar isotopes, and suggest a N = 34 subshell closure in 52 Ar. However, the coupled-cluster calculations based on the same chiral interaction underestimate the 2 + 1 excitations in 52 Ar. The measured E(2 + 1 ) of 52 Ar serves as an important benchmark to understand the uncertainties of the employed many-body methods and chiral effective-field-theory interactions. Our results offer the first experimental signature of the persistence of the N = 34 subshell closure below Z = 20, and agree with shell-model calculations predicting 48 Si as a new doubly magic nucleus far from stability.
We thank the RIBF accelerator staff for their work in the primary beam delivery and the BigRIPS team for preparing the secondary beams. We acknowledge Y. Utsuno for providing us the SDPF-MU calculated