Analysis of the contribution of resonance poles of $^{16}$O based on the Mittag-Leffler theorem within the Jost-RPA framework

Abstract: This study investigates resonance states in $<sup>{16}$O, specifically the $E$1 giant resonance and isoscalar/isovector quadrupole resonances, using the Jost-RPA method. By applying the Mittag-Leffler theorem, we decompose the RPA response function to analyze the individual contributions from poles corresponding to collective excitation modes. This decomposition clarifies the role of each pole in shaping the strength function, providing insights into the nature and classification of resonance states essential for understanding collective nuclear excitations. Our analysis identifies the dominant pole contributions to the observed resonance structures, offering a novel approach for exploring collective excitation phenomena in nuclei with complex many-body correlations.