A beam containing a substantial component of both the $J^{pi}=5^+$, $T_{1/2}=162$ ns isomeric state of $^{18}$F and its $1^+$, 109.77-min ground state has been utilized to study members of the ground-state rotational band in $^{19}$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.
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