Nuclear shell structure has profound impact in shaping the elemental abundance in the Universe. Nuclei with filled proton and/or neutron shells, i.e., magic numbers, play a significant role. Doubly magic nuclei are key benchmarks for constraining the nuclear force and nuclear models. Oxygen isotopes have closed proton shell (Z ¼ 8). The doubly magic nature of 16 O leads to its copious abundance hence enabling sustaining life in the Universe. The rare isotopes are unveiling new nuclear shells and exotic neutron skin and halo structures. At the edge of neutron binding, the neutron drip line, a new magic number has surfaced at N ¼ 16 making the heaviest oxygen isotope 24 O an unexpected doubly magic nucleus. A subshell closure at N ¼ 14 also emerges in 22 O. Do these neutron shell closures impact the proton distribution? Does the doubly magic nature of 22;24 O hinder neutron skin formation?

This Letter addresses the questions above through experimental determination of the root mean square radii of the point proton density distributions, henceforth referred to as point proton radii, in 16;18-24 O.

The signature of shell closures N ¼ 50 and 82 is seen from a local dip in the proton radius for isotopes [1]. In neutron-rich light nuclei a new subshell gap at N ¼ 6 shows prominent minimum in the proton radii for He to B isotopes [1]. The proton radii of nitrogen isotopes hinted a dip at N ¼ 14 [2]. If the possible origin of this subshell closure is due to the attractive isospin ðTÞ ¼ 0 pn tensor interaction it would be reflected also in the proton radii of neutron-rich oxygen isotopes.

The new shell closure at N ¼ 16 is seen in the high excitation energy of the first excited state [3] of 24 O and from the large 2s 1=2 orbital [4] occupancy of the valence neutrons, reflected in the neutron removal momentum distribution. Proton inelastic scattering of 24 O shows a small quadrupole deformation of 0.15(4), confirming a spherical shell closure at N ¼ 16 [5].

A subshell closure at N ¼ 14 for 22 O is discussed from high energy of its 2 þ first excited state [6] and a small quadrupole deformation parameter 0.26(4) [7] compared to 20 O. Quasifree ðp; pnÞ neutron knockout [8] and neutron removal with carbon target [9] from 22 O result in a wider momentum distribution reflecting knockout of 1d 5=2 neutrons, consistent with the N ¼ 14 subshell gap. A narrower momentum distribution for 21 N suggests reduction of N ¼ 14 shell gap in nitrogen. The quenching is derived from unbound states in 22 N [10]. It is predicted that a 2s 1=2 -1d 5=2 level inversion may occur in 20 C. Proton knockout via ðp; 2pÞ reactions show a larger cross section for 22;23 O than 21 N [8] interpreted as being due to more protons in the 1p 1=2 orbital in oxygen isotopes. The wider proton removal momentum distribution for 22 O is qualitatively suggested to be due to its compact nature from a filled valence shell for protons. However, that for 23 O is indicated to be narrow, which remains to be understood.

The large matter radii for 23 O [11] and 24 O [12,13] from interaction cross section (σ I ) measurements signal the possibility of a thick neutron surface. The large σ I of

O is explained by the 22 O core þ neutron in the 2s 1=2 orbital [11]. This is consistent with its narrow one-neutron removal longitudinal momentum distribution [9,14] and its large Coulomb dissociation cross section [15]. The neutron removal momentum distribution of 24 O shows predominant valence neutron occupancy in the 2s 1=2 orbital [4]. The matter radii derived from low-energy proton elastic scattering [16] is systematically higher than from the σ I measurements. At energies below 100A MeV medium modification effects of the nuclear interaction can lead to large uncertainty in the extraction of the radii.

Ab initio calculations with chiral interactions as introduced in Ref. [16] predicted the radii of oxygen isotopes. In-medium similarity renormalization group (IMSRG) and Gorkov self-consistent Green's function theory (GGF) with the Entem-Machleidt (EM) chiral interaction resulting in smaller radii than with the NNLO sat interaction [16]. An increase of charge radius ∼0.03-0.05 fm is predicted between 16 O and 24 O using the SRG evolved chiral interaction [17] and the Δ-full interaction at N 2 LO [18]. The NN þ 3NðlnlÞ chiral Hamiltonian and the NNLO sat interactions in the Gorkov self-consistent Green's function theory [19] predicts a continuous increase of the charge radii with increasing mass number. In the relativistic mean field framework an ansatz simulating the pairing effect [20] predicts charge radii with odd-even staggering.

For neutron-rich isotopes they predict 20;22 O having a larger charge radius. There is no experimental information on the proton distribution radii beyond 18 O.

In this Letter, we present the first determination of root mean square point proton radii for 19-24 O and those for the stable isotopes 16;18 O derived from measurements of charge changing cross sections (σ CC ). The experiment was performed using the fragment separator FRS [21] at GSI. The 16-24 O isotopes were produced by fragmentation of 40 Ar accelerated to 1A GeV which interacted with a Be target of thickness 6.3 g=cm 2 . The fragments produced were separated and identified using the FRS by employing the eventby-event determination of mass to charge ratio (A=Q) and atomic number Z information derived from the magnetic rigidity (Bρ), time of flight (TOF), and energy loss (ΔE). The isotopes were fully stripped hence Q ¼ Z. A schematic of the detector placement is shown in Fig. 1(a) and the particle identification is shown in Fig. 1(b). The energy loss of the fragments in a multisampling ionization chamber (MUSIC) [22] provided the Z information. The time of flight was measured between the dispersive midfocal plane F2 and the achromatic final focal plane F4 using the fast plastic scintillators. Position sensitive time projection chamber (TPC) detectors placed at these focal planes were used for beam tracking. The position information and the magnetic field provided the Bρ determination of the incoming beam.

The σ CC was measured with a 4.010 g=cm 2 thick C target placed at F4. The measurement was done using the transmission technique, where the ratio of the number of particles transmitted through the target without any loss of protons to the number of incoming particles gives the desired cross section for determining the root mean square radius of the point proton distribution, hereafter referred to as the proton radius. For this measurement the number (N in ) of the incident nuclei A Z in before the reaction target is identified and counted event by event. Behind the reaction target, the nuclei with charge Z out ≥ Z in are identified and counted on an event-by-event basis (N Z≥Z in ). The charge changing cross section is given by σ

Here R T in and R T out are the ratios of N Z≥Z in =N in with and without the reaction target, respectively, and t is the target thickness. Data without the reaction target were collected in order to account for losses due to interaction with the nontarget materials. There is no uncertainty in N in due to freedom of any incident beam event selection in the eventby-event counting.

In order to eliminate beam particle losses due to the restricted acceptance of the target and/or detectors the incident beam events were chosen with a restricted phase space. This reduces the systematic uncertainty in the transmission ratio. A veto scintillator with a central aperture was placed in front of the target to reject beam events incident on the edges of the target scattered by matter upstream and multihit events that can cause erroneous reaction information in the MUSIC detector placed after the target. In the incident beam identification the estimated contamination from Z ¼ 7 and 9 are 6 × 10 -5 and 2 × 10 -5 , respectively.

In order to count the A O beam events that did not undergo proton removal reactions in the target, the spectrum of the MUSIC detector placed after the target was used with the condition of the selected incoming A O beam events for the Z out ≥ 8 identification [Fig. 1(c)]. The limits are chosen to be the 3.5σ ends of the Z ¼ 8 and 9 peaks. The Z ¼ 9 peak is included in the unreacted event counting because proton pickup or ðp; nÞ reactions leading to higher Z do not involve interaction with protons in the projectile. Hence, for determining the proton radius these are unreacted proton events. The energy loss in the TPC and plastic scintillator detectors placed further downstream of the target provided additional information to confirm the Z identification as well as determine the detection efficiency of the MUSIC detector. The MUSIC detector resolution for Z was ∼0.1 (σ). The estimated Z out ¼ 7 contamination in the selection region of unreacted Z out is ∼5 × 10 -5 , which leads to an average uncertainty of AE0.07 mb in the σ CC .

The measured cross sections and their one standard deviation total uncertainties are given in Table I. This includes the target thickness uncertainty of ∼0.1%. The systematic uncertainty from contaminants vary for the different isotopes ranging from 0.05-1 mb. The cross section for 16 O aligns with the value 813(8) mb reported in Ref. [23] at a slightly higher energy of 903A MeV. The cross sections reported in Ref. [24] at 930 AE 44A MeV are systematically higher as found also for other isotopic chains and have larger uncertainties making them unsuitable to accurately derive the proton radii.

To extract the root mean square radii the measured σ CC are compared to cross sections calculated (σ cal CC ) using the Glauber model framework [25]. The formalism uses harmonic oscillator density profiles for the protons and neutrons in the projectile nucleus and the carbon target. The variation of the harmonic oscillator width yields projectile proton densities with different root mean square proton radii (R p ) which give different σ cal CC . The consistency of the measured σ CC and σ cal CC determines the range of R ex p that agrees with the data. The derived R ex p are listed in Table I. A good agreement of R ex p and the root mean square point proton radii derived from electron scattering (R ðe -Þ p ) is seen for 16;18 O. This supports the successful determination of R ex p from the measured σ CC . The gradual filling of neutrons in the 1d 5=2 orbital is found to decrease the R ex p progressively for 20-22;24 O (Table I and Fig. 2). This is consistent with lower B(E2) values [26]. A local minimum seen at N ¼ 14 is reflecting this new subshell closure. The consistent decrease in the proton radius for both 21 N [2] and 22 O shows the N ¼ 14 subshell gap arises from the attractive T ¼ 0 monopole tensor interaction between the protons in the 1p 1=2 orbital and neutrons in the 1d 5=2 orbital.

The proton radius of 23 O increases due to its extended neutron density distribution where the valence neutron is occupying predominantly the 2s 1=2 orbital. The proton radius of 24 O is found to be smaller than 23 O but similar to that of 22 O. This suggest the center of mass of the two valence neutrons in 24 O is not greatly separated spatially from that of the core. The filling of the 2s 1=2 orbital also leads to stronger neutron binding of the two-valence neutrons in 24 O due to pairing.

Using the R ex p determined in this Letter we find the point matter radius by analyzing the interaction cross sections (σ I ) reported in Refs. [11,12]. At the high energies inelastic scattering cross section to bound excited states is negligible. Therefore, σ I ¼ σ R , the reaction cross section. The nucleontarget profile function in the Glauber model (NTG) [27] with the profile function given in Ref. [28] is used for calculating σ cal R , for which harmonic oscillator densities of protons and neutrons for A O are adopted. The densities that result in σ cal R agreeing with the measured σ I yield the point matter radii (R ex m ) that are listed in Table I. The R ex m of 19-22 O shows a small gradual increase, a trend that is broken at 23 O which shows a larger increase in R ex m . We note that the later measurement of interaction cross section of 22;23 O [11] yields matter radii that agree with the description of 23 O in a 22 O core plus a neutron model with large spectroscopic factor for the neutron in the 2s 1=2 orbital. This is consistent with the observations from knockout reactions [14] and Coulomb dissociation [15].

Ab initio coupled-cluster and valence-space (VS) IMSRG computations are performed employing the chiral NN þ 3N interaction NNLO sat [29], which generally reproduces absolute and relative trends in radii across isotopic chains in both the sd [30] and pf shells [31,32]. For the coupled-cluster calculations we employ the singles-anddoubles (CCSD) approximation [33], and start from an axially deformed Hartree-Fock reference state (assuming a prolate shape) following Refs. [34,35]. In the VS-IMSRG, an approximate unitary transformation is constructed to decouple a core and effective valence-space Hamiltonian [36][37][38] diagonalized with the KSHELL code [39]. Applying the same transformation to the point proton radius operator we further construct an effective valencespace operator consistent with the Hamiltonian. Other details of the ab initio radii calculations can be found in Ref. [32]. Combining the effects from neglected manybody correlations, model-space truncations, and symmetry breaking we estimate an uncertainty of AE3% on the coupled-cluster computations, which is correlated for the point nucleon radii, hence negligible for relative quantities.

The R ex p are compared [Fig. 2(a)] with the CCSD predictions (red curves). The NNLO sat interaction reproduces binding energies of oxygen isotopes [29,40]. It reproduces also the trends of R ex p reasonably well for neutron-rich isotopes predicting a radius dip at N ¼ 14 consistent with the data. The IMSRG (star symbols) results with the NNLO sat interaction from Ref. [16], are within the uncertainty band of the CCSD results and also show a local minimum at N ¼ 14. In contrast, Ref. [20] predicts an increase in the charge radius of 22 O. The NN þ 3NðlnlÞ chiral interaction predictions [19] are smaller than the data showing an improved description of the nuclear interaction by NNLO sat . Within the data uncertainties the R ex p of the doubly closed shell nuclei 16 O and 24 O are similar, with an indication, from the central values, of a possible reduction in 24 O due to its stronger proton binding.

Shell model calculations with the YSOX Hamiltonian [41] are shown in Figs. 2 and3 (filled squares). Occupation numbers for the orbits obtained with the YSOX are used to evaluate the proton and matter radii as well as the neutron skin thickness. The proton orbits are obtained in a Woods-Saxon potential with the standard parameters [42], the resulting proton radii [Fig. 2(a) filled pink squares] are in fair agreement with the data. Using these proton radii, the matter radii are computed using harmonic oscillator functions for neutron orbits with ℏω ¼ 45=A 1=3 -25=A 2=3 except for the 2s 1=2 orbital in 23;24 O, which are obtained by the three-body model with an inert 22 O core plus 2s 1=2 valence neutron description [43]. Use is made of a lowenergy limit of the valence neutron-neutron interaction, which can reproduce the known NN scattering length and effective range [43].

Mean-field Hartree-Fock calculations with Sk3, SLy4, and SKM forces (Fig. 2 green bars and dashed lines) show proton radii of 22 O and 24 O larger than that of 16 O, independent of the Skyrme forces. This is contrary to the I) σ I from Ref. [12] (open circles), Ref. [11] (solid circles). The curves show predictions with coupled cluster theory for NNLO sat interaction (red curves). The dotted curves represent the AE3% uncertainty of the theory. The predictions with NNLO sat interaction and the IMSRG model are shown by the star symbols. The pink squares show shell model predictions. The green bars and dashed lines show mean field results. data trend. Inclusion of the coupling to the monopole resonances and improvements of proton-neutron interaction need to be considered in the future for the study of neutron-rich nuclei in the mean-field approximation.

The point matter radii are compared to the model predictions in Fig. 2 In summary, the point proton radii of 16;18-24 O derived from measurements of charge changing cross sections show an extended radius for 23 O and local minimum for 22 O that relates to the N ¼ 14 subshell closure due to the tensor force. The doubly magic nature of 22;24 O does not hinder neutron skin development, which rapidly increases for 22-24 O. Shell model predictions reproduce the observed neutron skin. Ab initio predictions with the NNLO sat chiral interaction agree within theoretical uncertainty with R ex p showing a dip for 22 O as observed in the data. The predictions for neutron skin thickness of 22-24 O underestimate the data. The data therefore open new avenues for refining the chiral interaction.