Nucleon deformation and atomic spectroscopy

Abstract

Recent ineleastic electron-proton scattering experiments have led to rather accurate values for the N → ∆ transition quadrupole moment Q N →∆ . The experimental results imply a prolate (cigar-shaped) intrinsic deformation of the nucleon. The nonsphericity of the proton's charge distribution might be seen in the spectrum of atomic hydrogen. The possibilities and limitations for determining the geometric shape of the nucleon in an atomic physics experiment are discussed.

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.

“…(15) as discussed in Ref. [10]. At low Q 2 the nucleons's prolate deformation is reflected in a proton charge radius increase by an amount −r 2 n , or more directly by a newly introduced size parameter r 2 def = r 2 C2 = (7/10)(r 4 n /r 2 n ) that can be experimentally determined.…”

“…The concept of an intrinsic quadrupole moment of the nucleon can be generalized to an intrinsic quadrupole charge distribution and a corresponding form factor [10]. To show this, we first decompose the proton and neutron charge form factors in two terms G sym and G def , coming from the spherically symmetric and the intrinsic quadrupole part of the physical charge density repectively…”

“…Employing polarized electron beams and hydrogen targets, it has recently become possible to experimentally determine the p → ∆ + (1232) charge quadrupole transition form factor [8]. It has been proposed that the quadrupole excitation of the nucleon N (939) to the ∆(1232) resonance is closely related to a quadrupole deformation of the nucleon's ground state charge distribution as reflected by a positive intrinsic quadrupole moment [9] and an intrinsic charge quadrupole form factor [10]. This interpretation is based on relations between nucleon ground state and N → ∆ transition form factors that follow from broken strong interaction symmetries.…”

“…As a spin 1/2 particle the proton does not have a spectroscopic quadrupole moment and its non-spherical charge distribution does not result in a quadrupole interaction term in the hfs energy shift formula [10]. Nevertheless, deviations from a spherically symmetric proton charge distribution are detectable in hydrogen hfs via the quadrupole excitation of the nucleon to the ∆ + (1232) resonance by the atomic electron (polarization shift) and via their effect on the electromagnetic size of the proton (Zemach radius).…”

“…The constants A, B, and C contained in the one-, twoand three-quark charge density operators parametrize the orbital and color matrix elements so that ρ is only an operator in spin-flavor space. The factors 2 and -1 in front of the spin scalar and spin tensor terms are dictated by group theory and reflect the fact that both terms arise from a common SU(6) spin-flavor tensor [10]. In terms of fundamental processes (see Fig.…”