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Register a new userThe electro-disintegration of few body systems revisited
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J.-M. Laget
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Recent studies of the electro-disintegration of the few body systems at JLab have revived the field. Not only recoil momentum distributions have been determined in a single shot. But also they confirm that the diagrammatic approach, which I developed 25 years ago, is relevant to analyze them, provided that the Nucleon-Nucleon scattering amplitude, determined in the same energy range, is used. They provide us with a solid starting point to address the issue of the propagation of exotic components of hadrons in nuclear matter
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Twenty years after P. Sauer released the state of the art Faddeev solution of the bound state three nucleon systems, I revisit photo and electrodisengration of few body systems with a special emphasis on the prospects opened at Jefferson Laboratory.
Hadronic composite states are introduced as few-body systems in hadron physics. The $Lambda(1405)$ resonance is a good example of the hadronic few-body systems. It has turned out that $Lambda(1405)$ can be described by hadronic dynamics in a modern technology which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic $bar KN$ composite state of $Lambda(1405)$ is extended to kaonic few-body states. It is concluded that, due to the fact that $K$ and $N$ have similar interaction nature in s-wave $bar K$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like $bar KNN$, $bar KKN$ and $bar KKK$, as well as $Lambda(1405)$ as a $bar KN$ quasibound state and $f_{0}(980)$ and $a_{0}(980)$ as $bar KK$.
Realistic solutions of the spinor-spinor Bethe-Salpeter equation for the deuteron with realistic interaction kernel including the exchange of pi, sigma, omega, rho, eta and delta mesons, are used to systematically investigate relativistic effects in inclusive quasi-elastic electron-deuteron scattering within the relativistic impulse approximation. Relativistic y-scaling is considered by generalising the non relativistic scaling function to the relativistic case, and it is shown that y-scaling does occur in the usual relativistic scaling variable resulting from the energy conservation in the instant form of dynamics. The present approach of y-scaling is fully covariant, with the deuteron being described by eight components, viz. the 3S_1^{++}, 3S_1^{--}, 3D_1^{++}, 3D_1^{--}, 3P_1^{+-}, 3P_1^{-+}, 1P_1^{+-}, 1P_1^{-+} waves. It is demonstrated that if the negative relative energy states 1P_1, 3P_1 are disregarded, the concept of covariant momentum distributions N(p_0,p), with p_0=M_D/2-sqrt{p^2+m^2}, can be introduced, and that calculations of lectro-disintegration cross section in terms of these distributions agree within few percents with the exact calculations which include the 1P_1, 3P_1 states, provided the nucleon three momentum |p|<= 1 GeV/c; in this momentum range, the asymptotic relativistic scaling function is shown to coincide with the longitudinal covariant momentum distribution.
Differential cross sections for the electro-disintegration process $e + {^4He} longrightarrow {^3H}+ p + e$ are calculated, using a model in which the final state interaction is included by means of a nucleon-nucleus (3+1) potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach (IDEA). In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p{^3H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our Plane-Wave Impulse Approximation results exhibit, similarly to other calculations, a dip in the five-fold differential cross-section around a missing momentum of $sim 450 MeV/c$, it is argued that this is an artifact of the omission of re-scattering four-nucleon processes.
A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed.
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