  The $^{22}$Ne(p,$\gamma$)$^{23}$Na reaction takes part in the neon-sodium
cycle of hydrogen burning. This cycle affects the synthesis of the elements
between $^{20}$Ne and $^{27}$Al in asymptotic giant branch stars and novae. The
$^{22}$Ne(p,$\gamma$)$^{23}$Na reaction rate is very uncertain because of a
large number of unobserved resonances lying in the Gamow window. At proton
energies below 400\,keV, only upper limits exist in the literature for the
resonance strengths. Previous reaction rate evaluations differ by large
factors. In the present work, the first direct observations of the
$^{22}$Ne(p,$\gamma$)$^{23}$Na resonances at 156.2, 189.5, and 259.7\,keV are
reported. Their resonance strengths have been derived with 2-7\% uncertainty.
In addition, upper limits for three other resonances have been greatly reduced.
Data were taken using a windowless $^{22}$Ne gas target and high-purity
germanium detectors at the Laboratory for Underground Nuclear Astrophysics in
the Gran Sasso laboratory of the National Institute for Nuclear Physics, Italy,
taking advantage of the ultra-low background observed deep underground. The new
reaction rate is a factor of 5 higher than the recent evaluation at
temperatures relevant to novae and asymptotic giant branch stars
nucleosynthesis.
