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Non-negligible Oscillation Effects in the Crustal Geo-neutrino Calculations

An accurate prediction of the geo-neutrino signal from the crust serves as a necessary prerequisite in the determination of the geo-neutrino flux from the mantle. In this work we report the non-negligible effect associated to the exact three-flavor antineutrino survival probability in the calculation of the crustal geo-neutrino signal, which was usually approximated as a constant average in previous studies. A geo-neutrino signal underestimation of about 1-2 TNU is observed as a result of the oscillatory behaviour within the local crustal region extending for about 300 km from the experimental site. We also estimated that the Mikheyev-Smirnov-Wolfenstein matter oscillation is responsible for a $0.1\%$-$0.3\%$ increase of the local crustal signal, depending on the detector location. This work reminds that the exact oscillation possibility in matter should be considered for future prediction of the local crustal geo-neutrino signal.