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In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found, we explore numerous open problems and obstructions to finding other infinite configurations in every set of natural numbers with positive density.
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Abstract The$$^{90}$$ Zr(p,$$\gamma $$ )$$^{91}$$ Nb reaction is one of the important reactions in the$$A\approx 90$$ mass region and part of the nucleosynthesis path responsible for production of$$^{92}$$ Mo during the$$\gamma $$ -process. Discrepant data in the literature provide a cross section that varies up to 30% within the Gamow window for the$$^{90}$$ Zr(p,$$\gamma $$ )$$^{91}$$ Nb reaction. Thus, the cross section measurements of$$^{90}$$ Zr(p,$$\gamma $$ )$$^{91}$$ Nb reaction were revisited using the$$\gamma $$ -summing technique. The results are consistent with the lower-value cross sections found in the literature. Based on the new data an updated reaction rate for$$^{90}$$ Zr(p,$$\gamma $$ )$$^{91}$$ Nb is provided that is up to 20% higher than that obtained from thenon-smokercode.more » « less
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