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L. Canton

Publications and source records attributed to L. Canton.

64 records · Page 4Linked to original sources
arXiv2000

Why is the three-nucleon force so odd?

By considering a class of diagrams which has been overlooked also in the most recent literature on three-body forces, we extract a new contribution to the three-nucleon interaction which specifically acts on the triplet odd states of the two nucleon subsystem. In the static approximation, this 3N-force contribution is fixed by the underlying 2N interaction, so in principle there are no free parameters to adjust. The 2N amplitude however enters in the 3NF diagram in a form which cannot be directly accessed or constrained by NN phase-shift analysis. We conclude that this new 3N-force contribution provides a mechanism which implies that the presence of the third nucleon modifies the p-wave (and possibly the f-wave) components of the 2N subsystem in the triplet-isotriplet channels.

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arXiv2000

Spin observables for pion production from pd collisions

We have calculated the proton analyzing power A_{y0} of the pion-production reaction from pd collisions for one energy close to threshold and for another in the region of the $Δ$-resonance. A fair reproduction of the experimental data could be obtained in both cases with a model which includes isoscalar and isovector $πN$ rescatterings in s waves, as well as the p-wave rescattering mechanisms mediated by the $πNN$ and $πN Δ$ vertices. For the analyzing power at threshold we found that the initial-state interaction (ISI) is also quite important.

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arXiv2000

Practical approximation scheme for the pion dynamics in the three-nucleon system

We discuss a working approximation scheme to a recently developed formulation of the coupled piNNN-NNN problem. The approximation scheme is based on the physical assumption that, at low energies, the 2N-subsystem dynamics in the elastic channel is conveniently described by the usual 2N-potential approach, while the explicit pion dynamics describes small, correction-type effects. Using the standard separable-expansion method, we obtain a dynamical equation of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because the computational techniques used for solving the normal AGS equation can also be used to describe the pion dynamics in the 3N system once the matrix dimension is increased by one component. We have also shown that this approximation scheme treats the conventional 3N problem once the pion degrees of freedom are projected out. Then the 3N system is described with an extended AGS-type equation where the spin-off of the pion dynamics (beyond the 2N potential) is taken into account in additional contributions to the driving term. These new terms are shown to reproduce the diagrams leading to modern 3N-force models. We also recover two sets of irreducible diagrams that are commonly neglected in 3N-force discussions, and conclude that these sets should be further investigated, because a claimed cancellation is questionable.

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arXiv1998

The pion-three-nucleon problem with two-cluster connected-kernel equations

It is found that the coupled piNNN-NNN system breaks into fragments in a nontrivial way. Assuming the particles as distinguishable, there are indeed four modes of fragmentation into two clusters, while in the standard three-body problem there are three possible two-cluster partitions and conversely the four-body problem has seven different possibilities. It is shown how to formulate the pion-three-nucleon collision problem through the integral-equation approach by taking into account the proper fragmentation of the system. The final result does not depend on the assumption of separability of the two-body t-matrices. Then, the quasiparticle method a' la Grassberger-Sandhas is applied and effective two-cluster connected-kernel equations are obtained. The corresponding bound-state problem is also formulated, and the resulting homogeneous equation provides a new approach which generalizes the commonly used techniques to describe the three-nucleon bound-state problem, where the meson degrees of freedom are usually suppressed.

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arXiv1998

Spin observables for the pd <-> pi+ t process around the Delta resonance

The proton analyzing power Ay0 and the deuteron tensor analyzing power T20 are evaluated for the pd <-> pi+ t process, in the energy region around and above the Delta resonance. These calculations extend a previous analysis of the excitation function and differential cross-section, based on a model embodying one-- and two-body p-wave absorption mechanisms and isobar excitation. The three-nucleon bound state and the pd scattering state are evaluated through Faddeev techniques for both the Bonn and Paris potentials. The spin variables exhibit a greater sensitivity to the number of included three-nucleon partial waves than the cross-sections, while the role played by the initial-- or final-state interactions appears to be small. The results for the tensor analyzing power at backward angles show a non-negligible dependence on the potentials employed, consistently with what has been previously found for the cross-sections. The calculation of spin observables gives a clear indication that other reaction mechanisms (presumably s-wave two-body absorption) have to be included in the model, in order to reproduce the experimental data below the Delta-resonance, in analogy with the simpler pp <-> pi+ d process.

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arXiv1998

pp <-> pi+ d process at low energy: Interplay between s-- and p-wave mechanisms

The large variety of experimental data around the pion-production threshold are compared with a meson-exchange isobar model which includes the pion-nucleon interaction in s-- and p-waves. Theoretical results obtained with two different NN potentials (Bonn and Paris) indicate that the behavior of the excitation function at threshold is sensitive to the details of the NN correlations. The complete model presented, while developed originally to reproduce the reaction around the Delta resonance, is shown to describe well the integral (Coulomb-corrected) cross-section at threshold along with its angular distribution. At low energies the angular dependence of the analyzing power Ay0 is well reproduced also. Finally, the energy dependence of the analyzing power for theta=90 from threshold up to the Delta resonance is considered and discussed.

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arXiv1994

N-Body Theory Revisited and its Extension to the pinnn-NNN Problem^*

In order to approach the pion--multinucleon problem, we have found it convenient to reformulate the general N--body theory starting from the fully unclusterized (i.e., N <- N) amplitude. If we rewrite such an amplitude in terms of new unknowns which can be later identified as the amplitudes for all the (N-1) <- (N-1) cluster processes, and repeat recursively the procedure up to the treatment of the 2 <- 2 cluster processes, we obtain very naturally the hierarchy of equations which ranges from the N--body fully--disconnected Lippmann--Schwinger equation to the N--body connected--kernel Yakubovskii--Grassberger--Sandhas one. This revisitation turns out to be very useful when considering the modifications required in case one of the bodies is a pion and the remaining are nucleons, with the pion being allowed to disappear and reappear through the action of a pion--nucleon vertex. In fact, we obtain a new set of coupled pion-- multinucleon equations which allow a consistent and simultaneous treatment of pion scattering and absorption. For the piNNN system, the kernel of these coupled equations is shown to be connected after three iterations.

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arXiv1993

Complex Conjugate Pairs in Stationary Sturmians

Sturmian eigenstates specified by stationary scattering boundary conditions are particularly useful in contexts such as forming simple separable two nucleon t matrices, and are determined via solution of generalised eigenvalue equation using real and symmetric matrices. In general, the spectrum of such an equation may contain complex eigenvalues. But to each complex eigenvalue there is a corresponding conjugate partner. In studies using realistic nucleon--nucleon potentials, and in certain positive energy intervals, these complex conjugated pairs indeed appear in the Sturmian spectrum. However, as we demonstrate herein, it is possible to recombine the complex conjugate pairs and corresponding states into a new, sign--definite pair of real quantities with which to effect separable expansions of the (real) nucleon--nucleon reactance matrices.

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arXiv1993

Theory of Coupled Pion--Trinucleon Systems

We derive the dynamical equations which consistently couple the four--body ($π$NNN) system to the underlying three--nucleon system. Our treatment can be considered the proper generalization of the Afnan--Blankleider equations for the coupled NN--$π$NN system. The resulting connected--kernel equation resembles in structure the Yakubovskii--Grassberger--Sandhas equation for the standard four--body problem, but involves 24 chain--labelled components (rather than the usual 18 ones) and allows for a consistent evaluation of reaction amplitudes involving $π$ absorption/production.

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