Energy levels of ${}^{18}\mathrm{F}$ from the ${}^{14}\text{N}+\alpha$ resonant reaction

Measurements were made of the differential cross section of the resonant reactions ${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha )$ and, ${}^4\mathrm{He}({}^{14}\mathrm{N},d){}^{16}\mathrm{O}$ with the intention of investigating the compound nucleus ${}^{18}\mathrm{F}$. These measurements were performed in inverse kinematics at a center-of-mass scattering angle of ${\theta }_{\mathrm{c}.\mathrm{m}.}={180}^{\circ }$ by using a thick ${}^4\mathrm{He}$ gas target and a ${}^{14}\mathrm{N}$ beam. Data were recorded which covered ${}^{18}\mathrm{F}$ excitation energies from 5.5–16 MeV. An $R$-matrix analysis was performed on the data up to 9 MeV, and the energies, spins, parities, and partial widths were extracted. Nine new states have been identified in ${}^{18}\mathrm{F}$ based on this analysis between 8.326 and 8.915 MeV.

Figure 1

Schematic drawing of the reaction chamber.

Figure 2

Raw Spectrum, prior to efficiency correction: Measurement 1 ${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha )$ data. The region marked is guaranteed kinematically to be free of inelastic contaminants in the $\alpha$ channel.

Figure 3

A Monte Carlo simulation of the distribution of measured angles as a function of ${}^{18}\mathrm{F}$ excitation energy, for measurement-one $\alpha$ particles.

Figure 4

Particle-identification plot from measurement one. Windows A and C selected the ${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha )$ reaction and window D selected the ${}^4\mathrm{He}({}^{14}\mathrm{N},d){}^{16}\mathrm{O}$ reaction. Window B was discarded.

Figure 5

${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha )$ cross section from the present work, plotted with the $R$-matrix fit convolved with the experimental resolution. Inset shows an enlarged view of the $R$-matrix fit; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.6$ (where “d.o.f.” means “degrees of freedom”).

Figure 6

${}^4\mathrm{He}({}^{14}\mathrm{N},d){}^{16}\mathrm{O}$ cross section from the present work, plotted with the $R$-matrix fit convolved with the experimental resolution. Inset shows an enlarged view of the $R$-matrix fit; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=1.8$.

Figure 7

${}^{16}\mathrm{O}(d,\alpha ){}^{14}\mathrm{N}$ cross section at ${\theta }_{\mathrm{c}.\mathrm{m}.}={166}^{\circ }$ from the work by Seiler et al. [15], with the present $R$-matrix fit. ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.9$. Inset shows ${}^{16}\mathrm{O}(d,d){}^{16}\mathrm{O}$ from the same work, at ${\theta }_{\mathrm{c}.\mathrm{m}.}=166.5^{\circ }$, compared with pure Rutherford scattering. Data rescaled by a factor of 1.1, as explained in the text.

Figure 8

${}^{14}\mathrm{N}(\alpha ,\alpha ){}^{14}\mathrm{N}$ cross section from the work by Terwagne et al. [11], with the present $R$-matrix fit; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.2$.

Figure 9

${}^{14}\mathrm{N}(\alpha ,p){}^{17}\mathrm{O}$ cross sections from the work by Terwagne et al. [11], with the present $R$-matrix fits; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=1.6$.

Figure 10

Comparison between the $R$-matrix fit from the present work (red dashed line) and the fit using the spins from Gurbich et al. [17] (blue line). Top row shows ${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha ){}^{14}\mathrm{N}$ data from the present work and Ref. [11]. Bottom row shows ${}^{14}\mathrm{N}(\alpha ,p_0){}^{17}\mathrm{O}$ data from Ref. [11]. (a) Fit only constrained by data in the $\alpha$ channel; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=4.3$. (b) Fit constrained by all data sets; ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.\sim 100$.

Figure 11

Potential $\alpha$-clustered states from the present work compared with those from the semimicroscopic-cluster model [4] and the experimental assignments by Middleton et al. [5]. States from the present work are identified as being $\alpha$ clustered if ${\theta }_{\alpha 0}^2>0.2$.

Figure 12

${}^4\mathrm{He}({}^{14}\mathrm{N},\alpha )$ cross section, compared with a theoretical calculation of the cross section generated from just one $\alpha$-clustered state at the Wigner limit, predicted in Ref. [4], and the moving average of the data taken over a range of $\pm 0.5$ MeV