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The relation between level crossings, entanglement, and Berry phases isinvestigated for the Breit-Rabi Hamiltonian of hydrogen and sodium atoms,describing a hyperfine interaction of electron and nuclear spins in a magneticfield. It is shown that the entanglement between nuclear and electron spins ismaximum at avoided crossings. An entangled state encircling avoided crossingsacquires a marginal Berry phase of a subsystem like an instantaneous eigenstatemoving around real crossings accumulates a Berry phase. Especially, the nodalpoints of a marginal Berry phase correspond to the avoided crossing points.

Entanglement, Berry Phases, and Level Crossings for the Atomic Breit-Rabi Hamiltonian