Ultrafast interatomic electronic decay in multiply excited clusters

An ultrafast mechanism belonging to the family of interatomic Coulombic decay (ICD) phenomena is proposed. When two excited species are present, an ultrafast energy transfer can take place bringing one of them to its ground state and ionizing the other one. It is shown that if large homoatomic clusters are exposed to an ultrashort and intense laser pulse whose photon energy is in resonance with an excitation transition of the cluster constituents, the large majority of ions will be produced by this ICD mechanism rather than by two-photon ionization. A related collective-ICD process that is operative in heteroatomic systems is also discussed.Comment: 4 pages, 3 figure

Environment assisted electron capture

Electron capture by {\it isolated} atoms and ions proceeds by photorecombination. In this process a species captures a free electron by emitting a photon which carries away the excess energy. It is shown here that in the presence of an {\it environment} a competing non-radiative electron capture process can take place due to long range electron correlation. In this interatomic (intermolecular) process the excess energy is transferred to neighboring species. The asymptotic expression for the cross section of this process is derived. We demonstrate by explicit examples that under realizable conditions the cross section of this interatomic process can clearly dominate that of photorecombination

Attosecond spectroscopy reveals alignment dependent core-hole dynamics in the ICl molecule.

The removal of electrons located in the core shells of molecules creates transient states that live between a few femtoseconds to attoseconds. Owing to these short lifetimes, time-resolved studies of these states are challenging and complex molecular dynamics driven solely by electronic correlation are difficult to observe. Here, we obtain few-femtosecond core-excited state lifetimes of iodine monochloride by using attosecond transient absorption on iodine 4d-16p transitions around 55 eV. Core-level ligand field splitting allows direct access of excited states aligned along and perpendicular to the ICl molecular axis. Lifetimes of 3.5 ± 0.4 fs and 4.3 ± 0.4 fs are obtained for core-hole states parallel to the bond and 6.5 ± 0.6 fs and 6.9 ± 0.6 fs for perpendicular states, while nuclear motion is essentially frozen on this timescale. Theory shows that the dramatic decrease of lifetime for core-vacancies parallel to the covalent bond is a manifestation of non-local interactions with the neighboring Cl atom of ICl

Discrete singular integrals in a half-space

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf Z}^m_{+}$) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.Comment: 9 pages, 1 figur

Resonances of the cusp family

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius--Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.

Intracluster Coulombic decay following intense NIR ionization of clusters

We report on the observation of a novel intracluster Coulombic decay process following Rydberg atom formation in clusters ionized by intense near-infrared fields. A new decay channel emerges, in which a Rydberg atom relaxes to the ground state by transferring its excess energy to a weakly bound electron in the environment that is emitted from the cluster. We find evidence for this process in the electron spectra, where a peak close to the corresponding atomic ionization potential is observed. For Ar clusters, a decay time of 87 ps is measured, which is significantly longer than in previous time-resolved studies of interatomic Coulombic decay

Operator interpretation of resonances generated by some operator matrices

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.Comment: LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, August 18-22, 199

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page