Structure Effects on the Giant Monopole Resonance and Determinations of the Nuclear Incompressibility

Giant resonances are archetypal forms of collective nuclear motion which provide a unique laboratory setting to probe the bulk properties of the nuclear force. One of the isoscalar compressional modes -- namely, the isoscalar giant monopole resonance (ISGMR) -- has been studied extensively with the goal of constraining the density dependence of the equation of state (EoS) for infinite nuclear matter. For example, the nuclear incompressibility is a fundamental quantity in the EoS and is directly correlated with the energies of the ISGMR in finite nuclei.

Previous work has shown that interactions with values of the incompressibility which reproduce the centroid energies of the ISGMR in 208Pb and 90Zr well, overestimate the ISGMR response of the tin and cadmium nuclei. To further elucidate this question as also to examine when this 'softness' appears in moving away from the doubly-closed nucleus 90Zr, and how this effect develops, the first portion of this thesis consists of measurements and analyses of the ISGMR within the molybdenum isotopes. The experiments were performed for 94Mo, 96Mo, 97Mo, 98Mo, and 100Mo, using inelastic scattering of 100 MeV/u alpha-particles at the Research Center for Nuclear Physics at Osaka University. The strength distributions for the giant resonances were extracted using multipole decomposition analyses within a Markov-Chain Monte Carlo framework to quantify the uncertainties in the strength distributions and the ISGMR energies. Comparison of the measured ISGMR strengths with Random Phase Approximation calculations demonstrates that the molybdenum nuclei have ISGMR energies which are overestimated to a similar degree as seen in the tin and cadmium nuclei, while the strength of 208Pb is precisely reproduced. This suggests clearly that the molybdenum nuclei exhibit the same open-shell softness which has been documented previously.

Studies of the ISGMR in isotopic chains encompassing a broad range of proton-neutron asymmetries allow for extraction of the dependence of the finite nuclear incompressibility on the isospin asymmetry, as quantified by the asymmetry term of the nuclear incompressibility. Recent data on the ISGMR in 40Ca, 44Ca, and 48Ca have contradicted prior results for the asymmetry term. To reconcile the otherwise highly concerning conclusion that its value is +582 MeV, the second portion of this thesis is focused upon independently studying this claim. A simultaneous measurement of the ISGMR in 40Ca, 42Ca, 44Ca, and 48Ca was completed and has resulted in a high-confidence exclusion of the possibility of a positive value for the asymmetry term, and indeed has found consistency with previous data, placing its value at -510 +/- 115 MeV.