Non-spherical proton shape and hydrogen hyperfine splittingThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

Abstract

We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.

Improved empirical parametrizations of theγ*N→Δ(1232)andγ*N<

“…This correction is the result of the expansion of the quadrupole operators in powers of Q 2 with the proper normalization [51,59]. A direct consequence of Eq.…”

“…In addition, the electric and Coulomb quadrupole moments would both vanish [G E (0) = G C (0) = 0]. Non-zero results for G En , G E (0) and G C (0) are then a consequence of the SU (6) symmetry breaking [32,[51][52][53].…”

“…Combining the low Q 2 expansion of the electric form factor, G En (Q 2 ) = −r 2 n Q 2 /6, where r 2 n is the neutron squared radius, one can show in the context of a constituent quark model with two-body exchange currents, that G E (0), G C (0) ∝ r 2 n [47, 51,52]. It then becomes clear that, the mechanisms responsible for the symmetry breaking, which induce r 2 n = 0, are also the mechanisms responsible for the non-zero quadrupole moments [32,[51][52][53]. The relation (5.8) is still valid when the three-body exchange currents are included for both observables, as can be shown using the expansion in 1/N c [48,54].…”

“…In particular a is determined by the second momentum r 2 n (neutron squared radius) through a = 2M 2 3µn r 2 n . As for d, it is determined by r 2 n and the fourth momentum r 4 n [51,52]. The MAID2007 parametrization for G C is inspired by the Galster form (5.10) [15].…”

“…A direct consequence of Eq. (5.11) is that in the case of the large N c parametrizations we can write the Coulomb quadrupole squared radius as r 2 C = 7 10 r 4 n r 2 n [51]. Since the parametrizations MAID2007, MAID-SG1 and MAID-SG2 are analytic, both radius can be calculated using the coefficients of the parametrizations.…”