Nuclear spin transitions in the kHz range in Rydberg matter clusters give precise values of the internal magnetic field from orbiting Rydberg electrons

Clusters of the electronically excited condensed matter Rydberg matter (RM) are planar and sixfold symmetric with specific magic numbers N as shown by rotational spectroscopy of potassium KN clusters [L. Holmlid, Mol. Phys. 105 (2007) 933; L. Holmlid, J. Mol. Struct. 885 (2008) 122]. In radio frequency emission spectra from such clusters, features are observed that are due to the hyperfine interaction between the atomic nucleus 39K and two Rydberg electrons. These electrons exist in a doubly excited K atom at n″ = 5 or 6 in a “sleeping-top” type rotating cluster. Such low excited electrons were observed recently in optical intra-cavity experiments in K(RM), where the electrons in the conduction band are involved in the angular momentum conservation in the stimulated emission. Here we show that the agreement with the theoretical description of circular Rydberg states is excellent within ±0.2% in the magnetic field, invoking angular momentum conservation by electrons in the condensed phase. Sleeping-top clusters may form stacks of clusters, and it is likely that such stacks are the emitting entities involved in the two nuclear spin series observed.