Low-lying resonant states in ${}^{16}\mathrm{F}$ using a ${}^{15}\mathrm{O}$ radioactive ion beam

A 120 MeV ${}^{15}\mathrm{O}$ radioactive ion beam with an intensity on target of $4.5\times {10}^4$ pps has been developed at the 88-Inch Cyclotron at the Lawrence Berkeley National Laboratory. This beam has been used to study the level structure of ${}^{16}\mathrm{F}$ at low energies via the $p$(${}^{15}\mathrm{O}$, $p$) reaction using the thick target inverse kinematics method on a polyethylene target. The experimental excitation function was analyzed using $R$-matrix calculations. Significantly improved values for the level widths of the four low-lying states in ${}^{16}\mathrm{F}$ are reported. Good agreement with the theoretical spectroscopic factors is also obtained.

Figure 1

An isobaric energy level diagram for the $A=16$, $T=1$ nuclear states [1].

Figure 2

The observed ${}^{15}\mathrm{O}$ beam profile at 0° in the laboratory without a Ni degrader and a target. A small tail consisting of ${}^{15}\mathrm{N}$ and other beam contaminants is observed. See text.

Figure 3

The experimental setup for the ${}^{15}\mathrm{O}$+$p$ resonance scattering reaction. See text.

Figure 4

A typical two-dimensional particle identification spectrum for $\Delta E$-$E1$ coincidences. Protons with energies below 2.7 MeV c.m. (around channel number 850 in $E1$) stopped in the $\Delta E$-$E1$ detector telescope. Protons above this energy punched through the $E1$ detector and were also recorded in coincidence in the $E$2 detector. Consequently, the deposited energy in both the $\Delta E$ and the $E1$ detectors starts decreasing after this point, as is shown. See text.

Figure 5

The measured ${}^{15}\mathrm{N}$+$p$ excitation function at 180° c.m. without background subtraction used for the energy calibration. ${}^{16}\mathrm{O}$ resonance states used in the energy calibration are indicated. Experimental results from previous studies at different c.m. angles are also shown.

Figure 6

The measured ${}^{15}\mathrm{O}$+$p$ excitation function at 180° c.m. up to 6.5 MeV c.m.

Figure 7

The $R$-matrix fit for the low-lying states in ${}^{16}\mathrm{F}$. The solid line represents the $R$-matrix calculation added to the background; the background function is shown as a dashed line. See text for details. The inset shows the best $R$-matrix fit, assuming a spin order of $0^{-}$, $2^{-}$, $1^{-}$, and $3^{-}$ for the low-lying states. It is clear that this spin order is unable to reproduce the measured data.

Figure 8

The variations in the chi-square value as a function of level width. A confidence level of 95% is represented by the dotted lines ($\Delta {\chi }^2=4$), and 68.3% by the solid lines ($\Delta {\chi }^2=1$). See text.