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Anomalous Behavior of Giant Monopole Resonance Energy with Nuclear Matter Incompressibility in the framework of Relativistic Mean Field Formalism and Coherent Density Fluctuation Model

The finite nucleus incompressibility $K^A$ is evaluated using the coherent density fluctuation model with the extended relativistic mean field density. The relativistic energy density functional for nuclear matter is replaced by the local density approximation for finite nuclei. The equation is used to calculate the finite nuclear incompressibility, which is further utilized to evaluate the isoscalar giant monopole excitation (ISGMR) energy $E_M$. This excitation energy is compared with other theoretical calculations and experimental data, wherever available. The results are comparable to the data. In contrast to the general understanding, the $E_M$ of finite nucleus is found to be maximum for the lowest nuclear matter incompressibility $K_{\infty}$, whereas it is minimum for the maximum $K_{\infty}$. These reverse results may be due to the self- and cross-interactions of the vector mesons in the nuclear potential.