Calculation and Preliminary High-order Correction of Geo-neutrino Energy Spectrum

Geo-neutrino is one of the best messengers for experimentally measuring radiogenic power and exploring the Earth’s interior. Energy spectrum is the prerequisite for predicting the geo-neutrino flux and analyzing backgrounds. By calculating and summing up the normalized β decay spectra of 113 transitions in ²³⁸U chain and 83 transitions in ²³²Th chain, the energy spectra for these two isotopes were obtained. The spectra were calculated with more beta transitions compared with the commonly used spectra at present. To improve the accuracy, four high-order corrections including the finite size correction, radioactive correction, and weak magnetism correction were considered. The biggest correction size reaches 8.5%. The corrected spectra can be used for accurate prediction and analysis of geo-neutrinos.