The $^{22}$Ne(p,$gamma$)$^{23}$Na reaction is included in the neon-sodium cycle of hydrogen burning. A number of narrow resonances in the Gamow window dominates the thermonuclear reaction rate. Several resonance strengths are only poorly known. As a result, the $^{22}$Ne(p,$gamma$)$^{23}$Na thermonuclear reaction rate is the most uncertain rate of the cycle. Here, a new experimental study of the strengths of the resonances at 436, 479, 639, 661, and 1279 keV proton beam energy is reported. The data have been obtained using a tantalum target implanted with $^{22}$Ne. The strengths $omegagamma$ of the resonances at 436, 639, and 661 keV have been determined with a relative approach, using the 479 and 1279 keV resonances for normalization. Subsequently, the ratio of resonance strengths of the 479 and 1279 keV resonances was determined, improving the precision of these two standards. The new data are consistent with, but more precise than, the literature with the exception of the resonance at 661 keV, which is found to be less intense by one order of magnitude. In addition, improved branching ratios have been determined for the gamma decay of the resonances at 436, 479, and 639 keV.
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