Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ρ 2 (E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for : single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also give attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ρ 2 (E0) and isotopic shifts.

The systematics of the even light P o isotopes (N126) are studied in the framework of the Particle-Core Model. The strong perturbation of the systematics in the very light isotopes is interpreted as arising from the interaction between regular and intruder structures. Results of Potential Energy Surface (PES) calculations and predictions of the Pairing Vibration Model support this interpretation. The mixing between the regular and intruder structures is studied within the IBM-2 and in a simple two-state mixing picture. Matrix elements of the interaction and their spin-dependence are extracted. The 'reconstructed systematics' show the coexistence of a spherical structure, which v aries little with the neutron number, with an intruder band, strongly lowered in energy as the neutron numberapproaches midshell. The crossing of the two congurations takes place over a few isotopes; the intruder band becomes the ground-state conguration in 192 Po.

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