High-Energy Approach for Heavy-Ion Scattering with Excitations of Nuclear Collective States

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach analytical expressions for elastic and inelastic scattering amplitudes are obtained where all the orders in the deformation parameters are included. The multistep effect of the 2$^+$ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the $^{17}$O ions scattered on different nuclei at about hundred Mev/nucleon are compared with experimental data, and important role of the Coulomb excitation is established.Comment: 9 pages; 3 figures. Submitted to the Physics of Atomic Nucle

Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory

Relation between the vacuum eigenvalues of CFT Q-operators and spectral determinants of one-dimensional Schroedinger operator with homogeneous potential, recently conjectured by Dorey and Tateo for special value of Virasoro vacuum parameter p, is proven to hold, with suitable modification of the Schroedinger operator, for all values of p.Comment: 9 pages, harvmac.tex, typos correcte

Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections of the punctured Riemann sphere, similarly to Hitchin's self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed.Comment: 63 pages, 8 figures; v2:typos correcte