J. M. Namysłowski

4-Nucleon scattering processes with unitary pole approximation

Abstract Generalized separable potential model of Alt, Grassberger and Sandhas is applied to 4-N system with the use of Bateman method and unitary pole approximation (UPA). Our principal aim is the evaluation of cross sections for processes like p 3He → p 3He and dd → pt. Bound states for 2-, 3-, and 4-body systems turned out to be very close to the experimental data either by input or by accident. However, the good fit at the negative energy, combined with the UPA method gave us a very good agreement for scattering processes at laboratory energies 9.75, 13.8, 25.3 and 51.5 MeV.

Breakdown of simple cancellation in the operator multiple-scattering series

SummaryWe consider the Watson multiple-scattering series for a three-body problem in the eikonal approximation. The sum of the series,i.e. the off-shell three-body transition amplitude, is expressed in closed form entirely in terms of off-shell two-body transition amplitudes. The result shows that the simple cancellation that occurs in the eikonal multiple-scattering series for the on-shell amplitude breaks down for the off-shell amplitude.RiassuntoSi studia la serie di Watson per lo scattering multiplo per un problema di tre corpi nell’approssimazione eiconale. Si esprime la somma della serie, cioè l’ampiezza della transizione di tre corpi fuori strato, in forma chiusa interamente in termini delle ampiezze delle transizioni di due corpi fuori strato. Il risultato mostra che la semplice cancellazione che ha luogo nella serie eiconale dello scattering multiplo per l’ampiezza sullo strato fallisce per l’ampiezza fuori strato.

Slow and fast quarks in nucleons

Abstract Using light-front dynamics, and the notion of the running effective quark mass, we propose a model of the three-quark nucleon wave function, which accounts simultaneously both for the low and the high energy experimental data. Our wave function is a product of a spinor part, inferred from the QCD sum rules, and a gaussian scalar factor, taken for simplicity. Including all three Ioffe currents we get from one wave function both the negative neutron charge radius 〈 r 2 〉 neutron =-0.108 fm 2 and the decreasing d/u ratio in the proton for x Bj increasing from 0.5 to 1.

SU(6) symmetry and the quark forces

Abstract The short distance forces between 3 valence quarks in the proton are investigated in perturbative QCD formulated on the light cone. These forces are the driving terms in the Brodsky-Lepage type evolution equation for the partially decomposed distribution amplitudes. The one-gluon exchange force, which is the lowest order force in the running coupling constant α s retains the SU(6) symmetry, while the α s 2 -order force, corresponding to one Coulomb gluon and one transverse gluon, breaks the SU(6) symmetry. The latter force contributes to the deviation from 1 2 of the d/u ratio for the proton, observed experimentally. In the kinematical domain of one fast quark, the α s 2 -order force gives the leading (1− x ) 3 behaviour of the deep inelastic structure function F 2 ( x ), in contrast to the α s -order force, which gives (1− x ) 5 , for x ≈1.

Recoil form factor for the deuteron

SummaryMaking an eikonal approximation in two relative momenta in a 3-body system, keeping trace of all recoil terms, and assuming that the ranges of forces responsible for πp and πn elastic scattering are small, we find the following form factor for the double-scattering term in πd → πd:

Stringy confinement of light quarks

\left[ {1 + \left( {\frac{{\Delta \mu }}{{4kM}}} \right)^2 } \right]^{\frac{3}{2}} \left\langle {\frac{1}{{\varrho ^2 }}\exp \left[ {i\varrho \left[ {\frac{{\Delta ^2 }}{{8k}}\left( {1 + \frac{\mu }{{2M}}} \right) - \frac{{\mu B}}{k}} \right]} \right]\cos \left( {\varrho \frac{{\Delta ^2 \mu }}{{8kM}}} \right)} \right\rangle _d ,

Scaling and impact parameter structure in pp scattering

, whereϱ≡r[1+(Δμ/4kM)2]−1/2,B is the binding energy of the deuteron,μ, M are pion and nucleon masses, respectively,Δ is the momentum transfer in the πd → πd process. The above form factor should be compared with the ordinary one of Glauber