Church-Rosser groups and growing context-sensitive groups

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are Church-Rosser groups. As the free abelian group of rank 2 is a non-context-free Church-Rosser group, this inclusion is proper. On the other hand, we show that there are co-context-free groups that are not growing context-sensitive. Also some closure and non-closure properties are established for the classes of Church-Rosser and growing context-sensitive groups. More generally, we also establish some new characterizations and closure properties for the classes of Church-Rosser and growing context-sensitive languages.

Delocalization of a hole in van der Waals clusters: Ionization potential of rare-gas and small Hg_n clusters

The size dependence of the ionization potential I_p(n) of van der Waals (vdW) bound clusters has been calculated by using a model Hamiltonian, which includes electron hopping, vdW interactions, and charge-dipole interactions. The charge-density and dipole-density distributions for both neutral and ionized n-atom clusters are determined self-consistently. The competition between the polarization energy of the neutral atoms surrounding a partially localized hole and the tendency toward hole delocalization in the ionized clusters is found to dominate the size dependence of I_p(n). To test our theory, we culculate I_p(Xe_n) and I_p(Kr_n) for n \le 300. Good quantitative agreement with experiment is obtained. The theory is also applied to calculate I_p(Hg_n). Comparison with experiments suggests that in Hg_n^+ clusters with n \le 20 the positive charge is mainly distributed within a trimer which is situated at the center of the cluster and which polarizes the n - 3 surrounding neutral atoms.

Slave-boson approach to the size-dependent transition from van der Waals to covalent bonding in Hg_n clusters

We use a microscopic theory to describe the dynamics of the valence electrons in divalent-metal clusters. The theory is based on a many-body model Harniltonian H which takes into account, on the same electronic level, the van der Waals and the covalent bonding. In order to study the ground-state properties of H we have developed an extended slave-boson method. We have studied the bonding character and the degree of electronic delocalization in Hg_n clusters as a function of cluster size. Results show that, for increasing cluster size, an abrupt change occurs in the bond character from van der Waals to covalent bonding at a critical cluster size n_c ~ 10-20. This change also involves a transition from localized to delocalized valence electrons, as a consequence of the competition between both bonding mechanisms.