One-neutron pickup into ${}^{49}\mathrm{Ca}$: Bound neutron $g_{9/2}$ spectroscopic strength at $N=29$

The highly selective, intermediate-energy heavy-ion-induced neutron-pickup reaction, in combination with $\gamma$-ray spectroscopy using the $\gamma$-ray energy-tracking in-beam nuclear array (GRETINA), is shown to provide reliable relative spectroscopic strengths for high-$\ell$ orbitals in nuclei more neutron rich than the projectile. The reaction mechanism gives a significant final-state-spin alignment that is validated through $\gamma$-ray angular-distribution measurements enabled by the position sensitivity of GRETINA. This is the first time that $\gamma$-ray angular distributions could be extracted from a high-luminosity, fast-beam reaction other than inelastic scattering. This holds great promise for the restriction and assignment of $J^{\pi }$ quantum numbers in exotic nuclei. We advance this approach to study the crucial $N=28$ shell closure and extract the ratio $g_{9/2}:f_{5/2}$ of bound neutron single-particle strengths in ${}^{49}\mathrm{Ca}$, a benchmark for emerging multi-shell ab initio and configuration-interaction theories that are applicable along the Ca isotopic chain.

Figure 1

Doppler-reconstructed $\gamma$-ray spectra in coincidence with ${}^{49}\mathrm{Ca}$ reaction residues. The inset magnifies the low-statistics transitions from very weakly populated states. The statistics corresponds to about 4.5 hours of data taken at $3\times {10}^5{}^{48}\mathrm{Ca}$/s.

Figure 2

Neutron-pickup single-particle cross sections (with $C^{2}S=1$) for transitions to states in the low-energy spectrum of ${}^{49}\mathrm{Ca}$, showing the large-$\ell$ selectivity of the reaction mechanism. The solid points use the ground-state to ground-state $Q$ value, with $S_n$ from ${}^{49}\mathrm{Ca}$ of 5.15 MeV [21]. The open points represent transitions to bound excited ${}^{49}\mathrm{Ca}$ states near 4 MeV, for which $S_n=1$ MeV, showing the effects of the higher $Q$ value and greater mismatch in this case.

Figure 3

Measured $\gamma$-ray angular distributions for the $9/2^{+}\to 7/2^{-}\to 3/2^{-}$ ($E1$: 660 keV to $E2$: 3385 keV) cascade. The $9/2^{+}$ state is dominantly fed directly in the reaction and the $7/2^{-}$ state is populated essentially exclusively via the 660 keV transition from the $9/2^{+}$ state. The calculated angular distributions assuming the specified spins and pure multipolarities are shown. The input $M$-substate distribution, $P_J\left(M\right)$, of the $9/2^{+}$ state was taken from the reaction calculations while $P_J\left(M\right)$ for the $7/2^{-}$ state was calculated from the angular-momentum coupling and $P_J\left(M\right)$ of the feeding state.

Figure 4

Measured cross sections compared to calculations that use the reaction theory outlined above and spectroscopic factors from Ref. [6]. While the $f_{5/2}$ and high-lying $g_{9/2}$ strengths are consistent, we deduce a higher $g_{9/2}$ spectroscopic strength of $C^{2}S=0.27{\left(1\right)}_{\mathrm{stat}}$ at 4 MeV.