Background:The R matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled channel systems. The theory provides solutions to bound states, scattering states, and resonances for microscopic models in one formalism. Purpose: The first purpose is to extend this formalism to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The second purpose is to employ this formalism in a relativistic continuum shell model. Methods: Expressions for the collision matrix and the scattering amplitude, from which observables may be calculated, are derived. The formalism is applied to the 1p-1h relativistic continuum shell model with an interaction extracted from relativistic mean field theory. Results:The simplest of the σ + ω + ρ exchange interactions produces a reasonable description of proton scattering from 15 N, and, therefore, provides a simple, relatively self-consist, physically justifiable model for use in knockout reactions. 24.10.Eq, 24.10.Jv, 25.40.Cm

We discuss issues related to pairing dynamics in nuclear large amplitude collective motion. The examples of effects which are not properly described within BCS theory are presented. In the second part we review properties of time-dependent density functional theory (TDDFT) and in particular we discuss the time-dependent superfluid local density approximation (TDSLDA) starting from the stationary action principle.

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We investigate properties of the method based on time dependent superfluid local density approximation (TDSLDA) within an application to induced fission of 240 Pu and surrounding nuclei. Various issues related to accuracy of time evolution and the determination of the fission fragment properties are discussed.

A procedure is suggested for calculating electro-excitation multipoles to order 1/M 2 N with only the operators required in the calculations to order 1/MN . It is also shown that calculations to order 1/M 2 N cannot account for the contributions of a fully relativistic calculation of the transverse response.PACS numbers: 24.10. Jv, 25.30.Bf The role of relativity in (e, e ′ p) has been investigated by many authors [1][2][3][4][5]. In most of these works, a Dirac equation with vector and scalar potentials is written for the outgoing proton, and then various elements of the Dirac equation are investigated as one proceeds to make a non-relativistic reduction. For example in Ref.[2], a Darwin factor, containing the potentials, was shown to reduce the upper component of the outgoing proton wave function in the interior, and hence, produce lower (e, e ′ p) cross sections than the equivalent non-relativistic calculation. In a similar fashion this potential containing term was included in the nuclear current in Ref. [1]. This Brief Report is concerned with including relativistic effects in non-relativistic calculations for (e, e ′ ) processes where the vector and scalar potentials are unavailable.The standard procedure for describing electron-nucleus scattering is to assume a current-current interaction. In a Born approximation for the electron, the electron current takes the simple form of a free Dirac particle. The nuclear current would ideally come from a relativistic manybody calculation. However, sophisticated structure calculations for light systems are basically non-relativistic. The purpose of this brief report is two-fold. The first is to provide a suggestion for including relativistic effects to order 1/M 2 N and second, to demonstrate that this procedure, and related procedures, can be inaccurate when describing transverse responses.Two approaches have been employed to derive the second order corrections to the nuclear current. In Ref.[6] the authors begin with a single particle Dirac equation for a spin-1/2 particle in a given electromagnetic field [7],where A Foldy-Wouthuysen transformation decouples Eq. (1) * Present address: Physique Nucléaire Théorique et Physique Mathématique, C.P. 229, Université Libre de Bruxelles (ULB), B 1050 Brussels, Belgium into one which is non-relativistic from which the secondorder corrections are obtained and one that describes the negative-energy states. The advantage of this procedure is that it can also give higher order corrections. The zeroth and first order multipoles from this procedure are