This appendix is intended for the reader who wants further background on the properties of RM. Just a few points will be described, of direct interest in this context. A more complete coverage can be found on the web .
The bonding in RM is a metallic type of bonding, with the valence electrons delocalized in a conduction band. However, the state of the electrons is not l = 0 as in an ordinary metal, with the separate electrons characterized by different k wave number vectors. Instead, the electrons in each RM cluster have a special l number (or n B for simplicity) >0, for K N clusters being l = 4, 5, … since lower values are not possible due to overlap with inner electrons. This means that the valence electrons form closed circular standing waves , giving a mathematical description of the material very similar to the standing waves used to describe electrons in an ordinary metal. The bonding between such circular Rydberg-like atoms is due to exchange–correlation as in other cases of chemical bonding. In the classical limit, this can be modeled as a strong correlation between the electrons, which can only exist if all electrons in a cluster have the same l value. This classical model with strong electron correlation was studied in  and shown to give results similar to the quantum mechanical description due to Manykin et al. [6, 7]. The form of the RM clusters as concluded from theory is definitely a one-atom thick planar layer.
The bond energy in an RM cluster has been calculated both classically and by quantum mechanics. At the low values of l (or n B for simplicity) studied here, the calculations are probably not very accurate, but they indicate a substantial bond energy of 0.9–1.5 eV at n B = 4 . This means that condensation is expected at room temperature and even at the temperature of the RM emitter used in the experiments.
Trying to form RM clusters from an ensemble of Rydberg atoms in the gas phase is of course meaningless. Many problems with such an approach are detailed in . Instead, a process based on an energy-absorbing surface (heat bath) which does not remove the electrons from the atoms (non-metal or low work function surface) has been shown to work very efficiently. On such a surface, Rydberg species of the adsorbed atoms are formed thermally and exist at a useful concentration in the surface boundary layer. The energy of forming a low Rydberg state of an alkali atom is not much higher than the desorption energy for the atom. In the case of K, the lowest Rydberg-like state at n = 4 has an excitation energy of 3.5 eV, while the desorption energy from an iron oxide surface similar to the emitter used here varies between 2.5 and 3.7 eV depending on the detailed surface composition . Similar values are found for other metal oxides. Further, the Rydberg atom–surface bond is weakened considerably when it becomes attached to other atoms in any form, like in an RM cluster. Thus, desorption of RM clusters K N is kinetically promoted relative to desorption of K atoms from many catalytically active surfaces. This is also found experimentally from the narrow angular distributions of desorption of K(RM) clusters [41, 42], which do not show the cosine distribution expected for desorption in thermal equilibrium with the surface. The results agree with a model in which several atoms combine in the surface boundary layer to a cluster which desorbs on-the-flight. Molecular beam experiments have also been done with addition of K atoms in the ground state to such desorbing K N (RM) clusters . This process presumably includes excitation energy transfer from a K Rydberg state in the surface boundary layer. It may also include redistribution of the excitation energy within the cluster, which is still coupled to the surface and can exchange energy with it. This study shows that the collision of K atoms with a K N (RM) cluster gives cluster growth, not fragmentation or deexcitation.
The form of the RM cloud created by desorption of small RM clusters is quite chaotic. The size of the cloud can be determined from the angular variation of the TOF signals and from variation of the emitter position relative to the laser beam, and is usually of the order of 2 cm in radius . It is probably a loose structure, mainly composed of preformed stable clusters characterized by magic numbers N = 7, 19, 37, 61 and 91. The clusters are loosely and transiently interconnected. They may even form stacks  at low enough temperatures. Their rotational motion has been studied by emission spectroscopy in the radiofrequency range [8, 12], as well as by nuclear spin-flips in the field from the orbiting electrons . The vibrational (phonon type) and electronic excitations in the K(RM) clusters were recently studied by Raman scattering in the IR . Amplified spontaneous emission (ASE) can be observed from the RM clusters both in the IR and the NIR  and in the radiofrequency range [8, 12], which means that selective emission processes exist. The ASE process is the basis for the stimulated emission in the widely tunable RM laser . The temperature of the RM, both in cluster translation and vibrational motion decreases due to these selective emission effects. This is observed as a smaller peak broadening in the TOF experiments since the initial kinetic energy (prior to the CE process) of any cluster or fragment released is smaller. Experiments regularly show temperatures of the K(RM) clusters down to 10 K and below , as also found in the present study.