Experimental study of the isomeric state in ${}^{16}\mathrm{N}$ using the ${}^{16}\mathrm{N}^{g,m}(d,{}^3\mathrm{He})$ reaction

The isomeric state of ${}^{16}\mathrm{N}$ was studied using the ${}^{16}\mathrm{N}{}^{g,m}(d,{}^3\mathrm{He})$ proton-removal reactions at 11.8 MeV/u in inverse kinematics. The ${}^{16}\mathrm{N}$ beam, of which 24% was in the isomeric state, was produced using the Argonne Tandem-Linac Accelerator System (ATLAS) in-flight system and delivered to the Helical Orbit Spectrometer (HELIOS), which was used to analyze the ${}^3\mathrm{He}$ ions from the $(d,{}^3\mathrm{He})$ reactions. The simultaneous measurement of reactions on both the ground state and the isomeric states, reduced the systematic uncertainties from the experiment and in the analysis. A direct and reliable extraction of the relative spectroscopic factors was made based on a distorted-wave Born approximation approach. The experimental results suggest that the isomeric state of ${}^{16}\mathrm{N}$ is an excited neutron-halo state. The results can be understood through calculations using a Woods-Saxon potential model, which captures the effects of weak binding.

Figure 1

The energy levels of ${}^{16}\mathrm{N}$ and ${}^{15}\mathrm{C}$. The two arrows indicate the transition for the $0p_{1/2}$ proton removal.

Figure 2

(a) Illustration of the experimental setup. See the main text for additional details. (b) The center-of-mass angle ${\theta }_{\mathrm{c}.\mathrm{m}.}$ vs $Z$ position. The green bands indicate the detector positions of the Si array. The blue (gray) square box indicates the common ${\theta }_{\mathrm{c}.\mathrm{m}.}$ region for the $(d,{}^3\mathrm{He})$ reactions.

Figure 3

The ${}^{16}\mathrm{N}^{g,m}$(d,${}^3\mathrm{He}$) experimental $Q$-value spectrum and angular distributions with gating on the coincident time for ${}^3\mathrm{He}$ and ${}^{15}\mathrm{C}$, which was identified by the recoil detector. The peaks and differential cross sections have not been normalized by the relative isomer- to ground-state content of the beam. (a) The $Q$ value of the ${}^{16}\mathrm{N}$($\mathrm{iso}){\to }^{15}$C(0.00) reaction is $-$5.985 MeV, and that of the ${}^{16}\mathrm{N}$(g.s.)${\to }^{15}$C(0.74) reaction is $-$5.125 MeV [21, 24]. The peaks are fitted with Gaussian distributions and the full width at half maximum (FWHM) is $\approx$500 keV. The reduced ${\chi }^2$ of the fitting was 1.54. (b) and (c) The angular distributions for the two final states were fitted with an $\ell =1p$-wave angular distribution calculated from the DWBA approach (see text).

Figure 4

Effective neutron single-particle energies for the $0d_{5/2}$ and $1s_{1/2}$ orbitals taken from Table 1.

Figure 5

The orbital rms radii of carbon and nitrogen isotopes from the WS calculation with the parameter set given in the main text. The outermost neutron orbital for ${}^{12-14}$C is the $p$ orbital. The configuration of 54% $s^2$ $+$ 46% $d^2$ is used for the outermost orbital in ${}^{16}\mathrm{C}$ [46].

Figure 6

The density distributions of ${}^{12}\mathrm{C}$, ${}^{14}\mathrm{C}$, ${}^{15}\mathrm{C}$, ${}^{16}\mathrm{N}$, and ${}^{16}\mathrm{N}{}^m$ from the Woods-Saxon calculation (Table 1). The tails of the density functions of ${}^{12,14}$C are from the $p$ orbital, and those of ${}^{15}\mathrm{C}$ and ${}^{16}\mathrm{N}$(iso) are from the $s$ orbital, and that of ${}^{16}\mathrm{N}$ is from the $d$ orbital. The energy level of $1s_{1/2}$ ${}^{16}\mathrm{N}{}^m$ is lower then that of ${}^{15}\mathrm{C}$, so that the density is not as extended as ${}^{15}\mathrm{C}$. The $d$ state in ${}^{16}\mathrm{N}$ is much less bound than the $p$ state in ${}^{12,14}$C, by $\approx$12 MeV (Table 1), which makes it slightly more extended.

Figure 7

The reaction cross section of ${}^A$C $+$ ${}^{12}\mathrm{C}$ at 83 MeV/u. A zero-range Coulomb-corrected Glauber model [50] was used to calculate cross sections from the density distributions from Fig. 6. The experimental cross sections were extracted from Ref. [10]. The configuration of $54\%s^2+46\%d^2$ was used in the case of ${}^{16}\mathrm{C}$.