The Size and Shape of the Deuteron

The deuteron is not a spherical nucleus. In the standard proton-neutron picture of this simplest nucleus, its shape is largely determined by the exchange of a pion, which leads to strong noncentral (namely "tensor") interactions. While this description works very well at large distances, many expected it to break down as the proton and neutron quark wavefunctions began to overlap one another. Surprising to some, the nucleons seem to retain their identity even at these very short distances.

LPSC-Grenoble, CEA-Saclay, IPN-Orsay, IN2P3-LNS Saturne, FRANCEUniv. of Maryland, Jefferson Lab, MIT, Indiana Univ., Rutgers Univ., USA

Florida International Univ., North Carolina A+T, Hampton Univ., Old Dominion Univ. USA Univ. Basel, SWITZERLAND

Yerevan Institute of Physics, ARMENIAVrije Universiteit Amsterdam, NETHERLANDS

The unpolarized scattering cross section determines the structure functions A(Q2) and B(Q2) which describe the spatial extent of the deuteron. At our kinematics the cross section is dominated by A(Q2).

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A and B contain the details of the charge, magnetization, quadrupole structure of the deuteron.

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If GC, GQ, and GM are each known separately, deuteron’s shape can be reconstructed. To separate them, a third quantity, such as the deuteron’s tensor polarization, is required. The tensor moment t20 is most sensitive to the deuteron’s charge distribution, while the other two moments provide important symmetry checks and information about the deuteron’s magnetization. The quantities and are kinematic factors.

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POLDER uses spin-dependent scattering of deuterons from protons hydrogen to determine the deuteron’s polarization. The deuteron, after interaction with the target, becomes a pair of protons which angular distribution is sensitive to the different possible polarization states.

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The analyzing powers Tij were measured prior to the JLab experiment using a polarized deuteron beam at SATURNE in suburban Paris, France.

The t20 experiment was carried out in Hall C at Jefferson Lab in 1997,

and collected data for approximately six months. It involved the first major installation of new equipment beyond the complement of spectrometers and targets that make up the main Hall C apparatus. Electrons were scattered from a 12 cm liquid deuterium target and detected in the HMS. Beam currents of up to 110 A were used. The recoiling target deuterons were collected and focused onto the POLDER polarimeter by a series of magnets, including one built specifically for this experiment by CEA-Saclay in France. POLDER was constructed by a collaboration between LPSC-Grenoble and CEA-Saclay.

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Relevant publications:S. Kox, et al., Nucl. Inst. Meth. A346, 527 (1994).D. Abbott, et al., Phys. Rev. Lett 82, 1379 (1999).D. Abbott, et al., Phys. Rev. Lett 84, 5053 (2000).D. Abbott, et al., Euro. Phys. Jour. A7, 421 (2000).

Ph.D. theses:L. Eyraud, Univ. Joseph Fourier, Grenoble, 1998K. Hafidi, Univ. Paris-Sud, Orsay, 1999A. Honegger, Univ. Basel, 1999W. Zhao, Mass. Inst. of Tech., 1999D. Pitz, Universite Caen/Basse-Normandie, 2000K. Gustafsson, Univ. Maryland, 2000

R. Wiringa, V.G. Stoks, and R. Schiavilla, Phys. Rev. C51, 38 (1995).

Elastic electron scattering at high momentum transfer probes the details of this short distance structure of the interior of the deuteron by looking at its distribution of charge and magnetism. Because the deuteron is not spherical, its charge distribution cannot be cleanly determined simply using unpolarized scattering. The “t20” experiment provided polarization

information that allows one to cleanly separate the deuteron’s shape into its spherical and deformed components.

While the quadrupole distribution (not shown) reveals the details of the “long distance” tensor interaction modeled by pion exchange, the zero crossing of GC gives a measure of the overall size of the deuteron and is related to the short distance behavior of the NN force. The zero crossing of GM, for which there is a hint in B(Q2) and which is also seen in t21, puts constraints on the contributions from relativistic effects.

From the t20 data one sees that even at distance scales that are small compared to the size of a single nucleon (at and above Q21), the conventional meson exchange picture works well (red curve). These data have helped constrain modern calculations that include relativistic effects as well (green curves). Extrapolations based on the underlying theory of QCD which uses quark-gluon degrees of freedom (blue curves) cannot yet describe these data.

POLDER

1H(d, 2p) nEd = 160-520 MeV

POLDER