1,721,007 research outputs found
Distribution properties of the channel interactions in N-body scattering and applications
No full textWe derive several classes of distribution properties for the channel internal and external interactions, as well as for generalized residual interactions, in the framework of the N-body scattering theory An essential feature of our distribution properties is that all coefficients are unity (natural distributions). We give several examples of the great advantages coming from the employment of the natural distributions in practical applications. Several classes of cluster expansions are derived for the channel resolvent operators and the Hepp-Narodetskiî-Yakubovskiî expansion is proved in a simple algebraic way. We present compact procedures leading to both the Sloan-Bencze-Redish equations and the Faddeev-Yakubovskiî equations with artificial indexes in the unknowns. We consider also many types of decompositions for the full N-body scattering wave functions and, finally, we present general reversion properties for linked-cluster strings of resolvents
and interactions
On a generalized distorted-wave approximation for nuclear rearrangement reactions
No full textStarting from an exact three-body theory for the nuclear rearrangement reaction a+(b+c)→b+(a+c), we study a generalized distorted-wave approximation in the momentum-space representation. Using suitable kinematic transformations we recast this representation in a form coinciding with the one obtained by means of the Feynman diagram summation method. The generalized potential responsible for the transition will be written in a compact form involving the resolvent operator for the a-b subsystem
Uniqueness of the N-body Lippmann-Schwinger-Glöckle-Tobocman equations
No full textIt is proved that the 2N-1-1 Lippmann-Schwinger-Glöckle-Tobocman equations provide a unique solution to the N-body scattering problem and that they represent the minimum number of Lippman-Schwinger-type equations necessary and sufficient to ensure uniqueness
Quantum oscillations and entanglement in Aharonov–Bohm rings with two magnetic impurities and asymmetric electron injection
No full textWe study spin-polarized transport through an Aharonov-Bohm ring threaded by magnetic flux, which is serially or laterally coupled to an external waveguide. The ring contains two magnetic impurities, whose spins are coupled to the electron spin through contact spin-spin interactions. In the framework of a quantum waveguide approach, asymmetry effects in the coupling of the ring to the environment are taken into account through a suitable, unitary parametrization of the vertex scattering operator, containing an asymmetry parameter lambda and a coupling parameter epsilon For lambda = 1, epsilon = 4/9 this parametrization gives the same results as the employment of Griffith's boundary conditions. We find that asymmetry may considerably influence the transmission of maximally entangled states through the ring. To this end, we analyze both the Aharonov-Bohm oscillations of the transmission coefficients, and the entanglement between the impurities spins by means of concurrencies. We show that asymmetry is less influential in the side-coupled configuration, with respect to the serial case
New developments in N-body scattering theory III
No full textIn the framework of the new approach to the N-body problem developed in the first two papers of this series we carry out exact effective few-cluster reductions of N-body Faddeev-Yakubovskiî-type equations. In particular we derive a single effective one-vector variable Lippmann-Schwinger equation in correspondence to a dominant two-cluster partition, and effective two-vector variable three-body Karlsson-Zeiger equations in correspondence to a dominant three-cluster partition. The effective interactions appearing in these few-cluster models can be evaluated through a perturbative solution of Faddeev-Yakubovskiî-type auxiliary equations. In our chain-of-partition-labelled approach we introduce several kinds of elementary transition operators which can be simply related to the physical transition amplitudes. Among them a privileged role is played by proper left asymmetric elementary transition operators: they lead to few-cluster approximation schemes having exactly the same structure as the usual phenomenological models
Truncated N-body formalisms and coupled-channel methods
No full textThe coupled-channel method is discussed in the light of connected-kernel
formulations of scattering theor
A systematic treatment of cluster models in multiparticle dynamics
No full textGeneralizing the leading ideas and the standard methods of modern approaches to the N-body problem, we devise direct procedures for describing the dynamics of clustered N-body systems. We show that these procedures, leading to m-cluster integral equations, can be developed starting from any type of multiparticle coupling scheme. Cluster models are formulated in the framework of the Faddeev-Yakubovskii coupling scheme (both in the original sophisticated language and, more simply, in terms of variables with artificial indexes) as well as in the context of any approach with highly-connected-kernel equations. Our general formulation reproduces all the existing N-particle equations in the limit case m =N
A generalized Gell-Mann-Goldberger transformation for many-body scattering
No full textThe celebrated Gell-Mann-Goldberger transformation is discussed in the
framework of N-body scattering theory
Coupled-channel equations and off-shell transformations in many-body scattering
No full textThe general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. We clarify the connection between different formulations and discuss the role played by some off-shell transformations for manybody transition operators. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. We also present several sets of linear relations between transition operators and use them in a three-body context to derive uncoupled integral equations with connected kernel
On the off-shell continuation of the physical transition operators
No full textA generalized Gell-Mann-Goldberger formula for many-body symmetric transition operators is derived for arbitrary splittings of the channel external interactions. This exact formula is compared with previous results obtained for asymmetric transition operators. From our Gell-Mann-Goldberger formula we derive uncoupled integral equations with connected kernel for three-body symmetric transition operators. We compare these equations with similar equations obtained for transition operators having a different off-shell behavior
- …
