Probing the Single-Particle Character of Rotational States in ${}^{19}\mathrm{F}$ Using a Short-Lived Isomeric Beam

A beam containing a substantial component of both the $J^{\pi }=5^{+}$, $T_{1/2}=162\mathrm{ns}$ isomeric state of ${}^{18}\mathrm{F}$ and its $1^{+}$, 109.77-min ground state is utilized to study members of the ground-state rotational band in ${}^{19}\mathrm{F}$ through the neutron transfer reaction ($d$,$p$) in inverse kinematics. The resulting spectroscopic strengths confirm the single-particle nature of the $13/2^{+}$ band-terminating state. The agreement between shell-model calculations using an interaction constructed within the $sd$ shell, and our experimental results reinforces the idea of a single-particle–collective duality in the descriptions of the structure of atomic nuclei.

Figure 1

Apparent excitation energy in ${}^{19}\mathrm{F}$ extracted from protons in coincidence with ${}^{19}\mathrm{F}$ recoils following ${}^{18g,m}\mathrm{F}$($d$,$p$) reactions (black points with statistical uncertainties). A multi-Gaussian fit of the known levels in ${}^{19}\mathrm{F}$ including a small linear background and fixed widths is shown in gray. States populated from ($d$,$p$) reactions on ${}^{18g}\mathrm{F}$ are in blue, while those from ${}^{18m}\mathrm{F}$ are in red. Weak levels, which, if removed from the fit would have little effect on the ${\chi }^2$ value, are represented by dashed lines. Black labels identify states belonging to the ground-state rotational band.

Figure 2

Angular distributions for states in ${}^{19}\mathrm{F}$ obtained from ${}^{18g}\mathrm{F}$($d$,$p$) reactions, (a) $1/2_1^{+}$ and $5/2_1^{+}$ doublet, (b) $3/2_1^{+}$, (c) $7/2_1^{+}$, and from ${}^{18m}\mathrm{F}$($d$,$p$) reactions, (d) $13/2_1^{+}$. The $13/2_1^{+}$ data include the 0.11(2) normalization factor to account for the ${}^{18m}\mathrm{F}/{}^{18g}\mathrm{F}$ secondary beam ratio. The DWBA calculations are represented by the lines.

Figure 3

The information on relative strengths of states in ${}^{19}\mathrm{F}$ is plotted as a function of their spin separately for the ${}^{18g}\mathrm{F}$($d$,$p$) (a) and ${}^{18m}\mathrm{F}$($d$,$p$) reaction (b). The limit on the $9/2^{+}$ state is obtained assuming $\ell =2$. Shell-model calculations using the USDB interaction are represented by bars for $\ell =0$ (striped), 2 (open), or 0 and 2 (hatched) strengths.