Exploiting dissipative reactions to perform in-beam $\gamma$-ray spectroscopy of the neutron-deficient isotopes ${}^{38,39}\mathrm{Ca}$

The neutron-deficient Ca isotopes continue to attract attention due to their importance for testing isospin symmetry and their relevance in capture reactions of interest for nova nucleosynthesis and the shape of light curves in Type I x-ray bursts. To date, spectroscopic information on ${}^{38,39}\mathrm{Ca}$ is largely limited to data on lower-spin excited states. Here, we report in-beam $\gamma$-ray spectroscopy of complementary higher-spin, complex-structure states in ${}^{39}\mathrm{Ca}$ populated in fast-beam-induced, momentum-dissipative processes leading to neutron pickup onto excited configurations of the projectile, ${}^9\mathrm{Be}({}^{38}\mathrm{Ca}^{*},{}^{39}\mathrm{Ca}+\gamma )X$. Such a dissipative reaction was recently characterized for the case of inelastic scattering of ${}^{38}\mathrm{Ca}$ off ${}^9\mathrm{Be}, {}^9\mathrm{Be}({}^{38}\mathrm{Ca}, {}^{38}\mathrm{Ca}+\gamma )X$. Additional data and discussion on the nuclear structure of ${}^{38}\mathrm{Ca}$ is also presented. An explanation for the more-complex-structure states, populated with small cross sections in one-nucleon knockout reactions, and observed in the tails of their longitudinal momentum distributions, is also offered.

Figure 1

Part of the nuclear chart showing the projectile beam ${}^{38}\mathrm{Ca}$ and the one-neutron pickup residue ${}^{39}\mathrm{Ca}$ in the proximity of the proton dripline.

Figure 2

Particle identification showing the same data as in Fig. 2 of Ref. [26] with ${}^{38,39}\mathrm{Ca}$ highlighted.

Figure 3

Measured tails of the parallel momentum distributions, versus $\mathrm{\Delta }p=p-p_0$ (with $p_0=11.222$ GeV/$c$) for the ${}^{39}\mathrm{Ca}$ one-neutron pickup residues (purple curve) and, as an inset, for the ${}^{38}\mathrm{Ca}$ nuclei that have undergone a momentum loss of order of 700 MeV/$c$ (black curve). The latter is shown on a logarithmic scale, revealing its exponential character. The momentum distribution versus $\mathrm{\Delta }p=p-p_0$ (with $p_0=11.932$ GeV/$c$) of the unreacted ${}^{38}\mathrm{Ca}$ after passage through the target is also shown (blue curve). These central momentum values, $p_0$, for each isotope, correspond to the respective magnetic rigidity setting of the S800 spectrograph. The low-momentum tail distributions of the ${}^{39}\mathrm{Ca}$ reaction residues and of the reacted ${}^{38}\mathrm{Ca}$ entered the focal plane in the same setting and thus $p_0$ value, while the unreacted ${}^{38}\mathrm{Ca}$ is from a different magnetic setting with a different $p_0$ value.

Figure 4

Doppler-reconstructed addback $\gamma$-ray spectrum as detected in coincidence with the ${}^{39}\mathrm{Ca}$ one-neutron pickup residues identified in the S800 focal plane. All $\gamma$-ray transitions are labeled by their energy. The two insets magnify low-statistics regions of the spectrum. All transitions are known—nine of the ten reported energies agree with the literature values within uncertainties and the discrepancy for the 2797-keV transition [25] is attributed to lifetime effects as discussed in the text.

Figure 5

Level scheme of ${}^{39}\mathrm{Ca}$ as populated in this work. The line width of the arrows corresponds to the intensities of the transitions quoted in Table 1. We note that the ${}^{39}\mathrm{Ca}$ proton separation energy is $S_p=5.7709\left(6\right)$ MeV [45], placing the $J=15/2$ states above this value. For the purpose of this level scheme, we use the energies quoted in Ref. [25], which, except for the 2797-keV transition due to lifetime effects as discussed in the text, agree within uncertainties with the present work.

Figure 6

Comparison of the energies of the low-lying states of ${}^{39}\mathrm{Ca}$, with the states observed here labeled, with shell-model calculations using the FSU $spsdfp$ interaction and the mirror nucleus ${}^{39}\mathrm{K}$ [43]. In these plots, the length of the levels indicates the $J$ value and the color positive parity (red), negative parity (blue), and $sd$-shell origin (green). For the panels showing experimental data, the black dots indicate levels with unknown spin-parity assignment.

Figure 7

Doppler-reconstructed addback $\gamma$-ray spectrum as detected in coincidence with the scattered ${}^{38}\mathrm{Ca}$ nuclei that underwent a large momentum loss. All $\gamma$-ray transitions are labeled by their energy. Panels (a) and (b) show the low-energy and high-energy region of the spectrum, respectively.

Figure 8

Left: Coincidence relationships in the lower-energy part of the spectrum, with a clear level scheme emerging from these (see Fig. 9 and [6]). Right: Doppler-corrected projection of the $\gamma \gamma$ matrix in the higher-energy region of the spectrum and coincidence spectra in this energy range obtained from cuts on the labeled transitions. Background was subtracted via a cut of equal width at slightly higher energy. Evidence for coincidence relationships is present also in the higher-energy region of the spectra. The inset shows that there may be unresolved weak high-energy transitions that feed the 3684-keV state.

Figure 9

Proposed level scheme for ${}^{38}\mathrm{Ca}$, extended version based on Ref. [6]. The width of the arrows is proportional to the $\gamma$-ray intensity of the corresponding transition. The proton separation energy of $S_p=4.54727\left(22\right)$ MeV [45] places the four highest-excited states in this level scheme above the proton separation energy. Spin-parity assignments in parenthesis are tentative.

Figure 10

Coincidence spectrum gated on the 489-keV feeder to the ($3_1^{-}$) level at 3702 keV. No evidence for the $\left(3_1^{-}\right)\to 0_1^{+}$ transition at 3702 keV is observed.