Spectroscopy of ${}^{10}\mathrm{N}$ with the invariant-mass method

Proton decays of ${}^{10}\mathrm{N}$ states have been investigated with the invariant-mass technique using data from two reactions. In the first experiment, ${}^{10}\mathrm{N}$ states were created via multinucleon knockout from a fast ${}^{13}\mathrm{O}$ beam. The second experiment involved proton pickup from a ${}^9\mathrm{Be}$ target to a fast ${}^9\mathrm{C}$ beam. Both data sets produce similar distributions with a peak centered at a decay energy of 2.8 MeV and a width of $\approx 2.5$ MeV. This result is consistent with a previous study using a multinucleon transfer reaction which was originally fit with an $\ell =0$ resonance but later interpreted as an $\ell =1$ resonance. This later interpretation is affirmed as the proton pickup reaction should favor $\ell =1$. This strength is located near the predicted energies of two $\ell =1$ resonances in calculations using complex scaling and the Gamow shell model. The multinucleon knockout data also show excess strength below the main peak which is interpreted as contributions from one or more $\ell =0$ resonances.

Figure 1

(a) Raw experimental $p+{}^9\mathrm{C}$ invariant-mass distribution (black) and the estimated contamination from $p+{}^{10}\mathrm{C}$ and $p+{}^{11}\mathrm{C}$ events where the carbon fragment was misidentified as ${}^9\mathrm{C}$. The contamination from ${}^{11}\mathrm{O}\to 2p+{}^9\mathrm{C}$ events where only one of the two protons is detected is also shown. (b), (c) Contamination-subtracted spectrum (data points) with two-level fits (solid-red curve). The fits were obtained using the $\ell =0$ line shapes constrained by Hooker et al. in their analysis of the resonance elastic scattering excitation function. Two fits are shown corresponding to the two fits by Hooker et al. with different energy ordering of the $1^{-}$ and $2^{-}\ell =0$ resonances. The fitted individual level contributions are indicated by the dotted curves and the blue-dashed curves show contributions from an additional linear background which was allowed in the fits. The latter contribution is very small.

Figure 2

Decay-energy distributions obtained from $p+{}^9\mathrm{C}$ coincidences in the two experiments. (a) is the background-subtracted distribution produced in the knockout reaction while (b) is from the proton-pickup experiment. The solid red curve in (a) shows a fit assuming an $\ell =0$ ground state and $\ell =1$ excited states using $R$-matrix line shapes. The individual contributions are shown as the dotted curves. The fit also allowed for an additional linear background, which is indicated by the blue-dashed curve and is only significant in the high-energy tail of the distribution. The same line shapes were used to fit the distribution in (b) where only their magnitudes were varied.