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from the observation, in which the primary Nöther current operator, being between the
physical (clothed) states |Ψ N 〉 = b † c |Ω〉, yields the usual on-mass-shell expression
〈Ψ p,n (p ′ )|J µ (0)|Ψ p,n (p)〉 = F µ p,n (p′ ,p)
in terms of the Dirac and Pauli nucleon form factors. By keeping only the one-body
contribution we arrive to certain off-energy-shell extrapolation of the so-called relativistic
impulse approximation (RIA) in the theory of e.m. interactions with nuclei (bound
systems).
Of course, the RIA results should be corrected including more complex mechanisms
of e-d scattering, that are contained in
∫
J µ two−body = dp ′ 1dp ′ 2dp 1 dp 2 F µ MEC (p′ 1,p ′ 2;p 1 ,p 2 )b † c(p ′ 1)b † c(p ′ 1)b c (p 1 )b c (p 2 ).
Analytic (approximate) expressions for the coefficients F µ MEC
stem from the R-commutators
(beginning with the third one) in the expansion (*), which, first, belong to the
class [2.2], as in operators K I and B I , and, second, depend on even numbers of mesons
involved. It requires a separate consideration aimed at finding a new family of meson
exchange currents to be useful, as we hope, not only for describing the e-d scattering.
At last, one should note that, as before (see, e.g. [4]), we prefer to handle the explicitly
gauge-independent (GI) representation of photonuclear reaction amplitudes with
one-proton absorption or emission [5]. This representation is an extension of the Siegert
theorem, in which, the amplitude of interest is expressed through the Fourier transforms
of electric (magnetic) field strengths and the generalized electric D(q) (magnetic M(q))
dipole moments of hadronic system. It allows us to retain the GI in the course of inevitably
approximate calculations. It has turned out that the Cartesian electric (magnetic)
moments of the distribution J 0 (x) (J(x)) can be deduced from the MacLaurin
series, respectively, of the longitudinal projection q ·D(q) and the function M(q) itself
in the vicinity of the point q = 0. In particular, we find the following formula
µ d = 1 [ ] z|
〈⃗0;M ′ = 1| ⃗B × J(0) ⃗ ⃗0;M = 1〉
2m d
for the magnetic moment of the deuteron. Of course, we could present details of our calculations
to compare them with the available ones and show the corresponding numerical
results.
References
[1] A. Shebeko, P. Frolov and I. Dubovyk, Proc. of the XX Intern. Baldin Seminar on
High Energy Physics Problems (Dubna, Russia, 2010) V. I pp. 75-81.
[2] A.V. Shebeko, Chapter 1 in: Advances in Quantum Field Theory, ed. S. Ketov, 2012
InTech, pp. 3-30.
[3] I. Dubovyk and A. Shebeko, Few Body Syst. 48 109 (2010).
[4] L. Levchuk, L. Canton and A. Shebeko, Eur. Phys. J. A 21 29 (2004).
[5] L. Levchuk and A. Shebeko, Phys. At. Nucl. 56 227 (1993).
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