By S. M. Bilenky (Auth.)
Ebook by way of Bilenky, S. M
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1. For the matrix element of the process we obtain the following expression: = ie*Nk,Nkü''(k') γΛ*(® ^ X(p', s' | / . 68) (k and k' are the momenta of the initial and final electrons, p and p' are the momenta of the initial and final nucléons, q = k—k'). The matrix element of the hadron electromagnetic current operator has the form (see Chapter 2, Section 1) ', • | / . 69) where Fi(q2) and F2(q2) are the Dirac and Pauli nucléon form factors. (p). 70) Here Γα(ρ', P) = y«GM(q*)+inaF(q*).
System. We have ^W^-^T*· (2 82) · 2. ) Further, in the case of elastic scattering under consideration the variables q2 and v occur in the δ-function and are not, consequently, independent. This means that integration over one of the variables must be performed. 83) l+(2£/M)sin 2 0/2 Finally, the nucléon polarization vector in the lab. system has the form I = (P, iO). 85), contribution to the cross-section is made only by the component of the nucléon polarization vector lying in the scattering plane (the plane of k, k').
175) it is possible to determine the polarization structure functions G\ and G2. Generally, G\ and G2 can depend on the variables pq and q2 or - - q2 —2pq - q2 2Mv and i». In conformity with the scaling hypothesis the dimensionless functions M2vGi = gi and Mv2G2 = gi depend only on x as q2 -»- °° and v -*■ ~ and at x fixed. 1* In this approximation exact scaling holds for the structure functions gi and g2. To conclude, we may point out that the asymmetry A^ was measured in experiments with the beam of longitudinally polarized electrons, obtained at the Stanford Linear Accelerator.