Strong Evidence for ${}^9\mathrm{N}$ and the Limits of Existence of Atomic Nuclei

The boundaries of the chart of nuclides contain exotic isotopes that possess extreme proton-to-neutron asymmetries. Here we report on strong evidence of ${}^9\mathrm{N}$, one of the most exotic proton-rich isotopes where more than one half of its constitute nucleons are unbound. With seven protons and two neutrons, this extremely proton-rich system would represent the first-known example of a ground-state five-proton emitter. The invariant-mass spectrum of its decay products can be fit with two peaks whose energies are consistent with the theoretical predictions of an open-quantum-system approach; however, we cannot rule out the possibility that only a single resonancelike peak is present in the spectrum.

Figure 1

Classification of resonant states based on the location of the scattering-matrix poles in the complex-$k$ plane. The same arbitrary units (a.u.) are used on both axes. Bound, antibound, decaying, and capturing resonant states are marked, as well as narrow resonances (nr), broad resonant states (br), and subthreshold resonant states (sr). The distribution of poles is symmetric with respect to the imaginary $k$ axis because of time reversal symmetry; thus, capturing states are presented as the time-reversed decaying states. The dashed $-45°$ line separates decaying resonant states from subthreshold poles. The inset shows the polar angle $\theta$ of the resonant pole in the complex momentum plane.

Figure 2

Invariant-mass spectra for ${}^9\mathrm{N}$ and ${}^8\mathrm{C}$. (a) Histogram shows the distribution of the decay energy $Q_{5p}$ obtained from $5p+\alpha$ events with the invariant-mass method. The data points show the distribution where an ${}^8\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ intermediate state was identified. (b) The data points show the distribution of ${}^8\mathrm{C}$ decay energy ($Q_{4p}$) from the five $4p+\alpha$ subevents in each $5p+\alpha$ event. The solid red curve shows a fit to this distribution using the experimental ${}^8\mathrm{C}$ line shape obtained from detected $4p+\alpha$ events (dotted green curve) plus a smooth background (dashed blue curve). The gate used to select $p+{}^8\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ events is indicated.

Figure 3

Level diagrams of ${}^8\mathrm{C}$ and ${}^9\mathrm{N}$ obtained experimentally and calculated with the GSM. Energies are given relative to the ${}^4\mathrm{He}$ threshold. The level diagram of ${}^9\mathrm{He}$, the mirror partner of ${}^9\mathrm{N}$, is shown in the inset. The $1/2^{+}$ antibound state in ${}^9\mathrm{He}$ is shown with a wavy line to indicate its status more as a scattering feature rather than a real state. The proposed $1/2^{+}$ state in ${}^9\mathrm{N}$ is shown with both straight and wavy lines to indicate the uncertainty as to its nature (a resonance or scattering feature) while the GSM interprets it as a broad resonant state.

Figure 4

Fits (solid red curves) to the selected $p+{}^8\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ distribution. (a) Fit with a single peak parametrized by an $\ell =1$ $R$-matrix line shape. (b),(c) Two peak fits where the contributions from both levels are given by the dotted green curves. The fit in (b) was using a $p+{}^8\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ $R$-matrix line shape where energy and width of the upper peak are set to the GSM predictions for the $J^{\pi }=1/2^{-}$ state of ${}^9\mathrm{N}$. The dependence of the detection efficiency as a function of $Q_{5p}$ as determined in our Monte Carlo simulations (see Supplemental Material [31]) is shown by the dashed magenta curve. The fit in (c) was obtained where the fixed width of the $1/2^{-}$ was halved from its value in (b) and the $1/2^{+}$ strength is described by a subthreshold resonant state using GCC line shape. In all panels, the $p+{}^8\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ threshold is indicated by an arrow and the fitted background from nonresonant protons is shown by the dashed blue curves.