Probing proton cross-shell excitations through the two-neutron removal from ${}^{38}\mathrm{Ca}$

Bound states of the neutron-deficient, near-dripline nucleus ${}^{36}\mathrm{Ca}$ were populated in two-neutron removal from the ground state of ${}^{38}\mathrm{Ca}$, a direct reaction sensitive to the single-particle configurations and couplings of the removed neutrons in the projectile wave function. Final-state exclusive cross sections for the formation of ${}^{36}\mathrm{Ca}$ and the corresponding longitudinal momentum distributions, both determined through the combination of particle and $\gamma$-ray spectroscopy, are compared to predictions combining eikonal reaction theory and shell-model two-nucleon amplitudes from the USDB, USDC, and ZBM2 effective interactions. The final-state cross-section ratio $\sigma \left(2_1^{+}\right)/\sigma \left(0^{+}\right)$ shows particular sensitivity and is approximately reproduced only with the two-nucleon amplitudes from the ZBM2 effective interaction that includes proton cross-shell excitations into the $pf$ shell. Characterizing the proton $pf$-shell occupancy locally and schematically, an increase of the $sd-pf$ shell gap by 250 keV yields an improved description of this cross-section ratio and simultaneously enables a reproduction of the $B(E2;0_1^{+}\to 2_1^{+})$ excitation strength of ${}^{36}\mathrm{Ca}$. This highlights an important aspect if a new shell-model effective interaction for the region was to be developed on the quest to model the neutron-deficient Ca isotopes and surrounding nuclei whose structure is impacted by proton cross-shell excitations.

Figure 1

Event-by-event particle identification plot of projectile-like residues produced in the ${}^9\mathrm{Be}({}^{38}\mathrm{Ca},X+\gamma )Y$ reaction. The figure displays the data used for determination of absolute inclusive cross sections and has a particle-$\gamma$ coincidence condition applied. Inelastically scattered ${}^{38}\mathrm{Ca}$ beam entering the focal plane and the ${}^{36}\mathrm{Ca}$ two-neutron removal residues are marked.

Figure 2

Doppler-corrected ($v/c=0.341$) $\gamma$-ray spectrum detected by GRETINA in coincidence with ${}^{36}\mathrm{Ca}$ residues registered in the focal plane of the S800 spectrograph. The solid red curve represents a background model comprising an exponential component (dashed red) and GRETINA's detector response (dotted red) obtained from simulations employing the geant4-based [30, 31] code UCGretina [32].

Figure 3

Parallel momentum distributions of ${}^{36}\mathrm{Ca}$ after two-neutron removal from ${}^{38}\mathrm{Ca}$. (a) shows the inclusive $p_{\parallel }$ distribution which is fully within the S800 acceptance. The uncertainties are purely statistical. (b) and (c) display the exclusive $p_{\parallel }$ distributions to the $0^{+}$ states and the $2_1^{+}$ state, respectively. They are compared to calculations using ZBM2 TNAs (red lines) which are horizontally shifted and vertically scaled for best agreement with the data. The calculation for (b) is the sum of the $0_1^{+}$ and $0_2^{+}$ contributions according to their predicted cross sections (Table 1). Due to the unknown proton decay branch, the $0_2^{+}$ contribution is an upper limits.

Figure 4

Comparison of calculated and measured cross sections. (a) Measured to theoretical inclusive cross-section ratios $R_s\left(2N\right)={\sigma }_{\text{inc}}^{\text{expt}}/{\sigma }_{\text{inc}}^{\text{th}\phantom{p}}$ [16] with (without) inclusion of the $0_2^{+}$ state in the calculation of the theoretical inclusive cross section are shown in black (grey), illustrating the small contribution of the $0_2^{+}$ state. The expected value of 0.5 [16, 34, 38] is indicated by the grey dashed line. (b) Ratio of the exclusive cross sections to the $2_1^{+}$ and $0^{+}$ final states of ${}^{36}\mathrm{Ca}$. The $1\sigma$ region around the experimental result is indicated in gray. For this comparison, the statistical and systematic uncertainties are added in quadrature.

Figure 5

Comparison of the partial experimental level scheme of ${}^{36}\mathrm{Ca}$ with shell-model calculations. The measured $0_2^{+}$ intruder state [10] is absent from the USD-type shell-model calculations and the second excited $0^{+}$ state in the USD computations is closer in structure to the $0_3^{+}$ state of ZBM2 and ZBM2gap. The experimental excitation energies of the $0_2^{+}$ and $2_2^{+}$ states as well as predictions from the SDPF-U-MIX interaction are taken from Ref. [10]. Energies are given in MeV.