Where we stand on structure dependence of ISGMR in the Zr-Mo region: Implications on K_\infty

Abstract: Isoscalar giant resonances, being the archetypal forms of collective nuclear behavior, have been studied extensively for decades with the goal of constraining bulk nuclear properties of the equation of state, as well as for modeling dynamical behaviors within stellar environments. An important such mode is the isoscalar electric giant monopole resonance (ISGMR) that can be understood as a radially symmetric density vibration within the saturated nuclear volume. The field has a few key open questions, which have been proposed and remain unresolved. One of the more provocative questions is the extra high-energy strength in the $A\approx 90$ region, which manifested in large percentages of the $E0$ sum rule in $^{92}$Zr and $^{92}$Mo above the main ISGMR peak. The purpose of this article is to introduce these questions within the context of experimental investigations into the phenomena in the zirconium and molybdenum isotopic chains, and to address, via a discussion of previously published and preliminary results, the implications of recent experimental efforts on extraction of the nuclear incompressibility from this data.