Structure and photoluminescence of helium-intercalated fullerite C₆₀

Intercalation of C₆₀ single crystals with helium was studied by powder x-ray diffractometry. It was established that the intercalation is a two-stage process, octahedral cavities are filled first and then tetrahedral ones, the chemical pressure being negative during both stages. For the first time low-temperature (5 K) photoluminescence spectra of helium-intercalated fullerite C₆₀ were studied. The presence of helium in lattice voids was shown to reduce that part of the luminescent intensity which is due to the emission of covalently bound pairs of C₆₀ molecules, the socalled "deep traps" with the 0-0 transition energy close to 1.69 eV. The mechanism of the effect of the intercalation with helium on the pair formation in fullerite C₆₀ is discussed

On spectral minimal partitions: the case of the sphere

We consider spectral minimal partitions. Continuing work of the the present authors about problems for planar domains, [23], we focus on the sphere and obtain a sharp result for 3-partitions which is related to questions from harmonic analysis, in particular to a conjecture of Bishop