On induced double-nucleon emission, III. 12C (π−, NN) and short-range correlations

ANNALS

OF PHYSICS:

77, 602-603 (1973)

Abstracts

of Papers

to Appear

in Future

Issues

Expansion. STEPHEN J. WALLACE. Department of Physics, University of Washington, Seattle, Washington and Department of Physics and Astronomy, University of Florida, Gainesville, Florida. An eikonal expansion of the potential scattering T matrix is evaluated, without approximation, through third order in the inverse momentum. Based on the results, their correspondence with the WKB approximation and a new statement of the unitarity constraint, we propose a sequence of four approximations to the exact impact parameter (Fourier-Bessel) representation of the scattering matrix. The sequence consists of the Glauber approximation and three systematic corrections to the Glauber approximation. The corrections are analytic functions of the impact parameter for Yukawa and Gaussian potentials; they vanish for a Coulomb potential. The sequence of eikonal amplitudes is convergent at high energy and is clearly established for small momentum transfer. Validity for all momentum transfer is conjectured based on systematic cancellation, explicitly verified through third order in the expansion, of momentum transfer dependence in the eikonal impact parameter representation. Such cancellation is shown to occur in the explicit construction of the eikonal expansion of the second Born amplitude for a Yukawa potential. Numerical tests of the sequence of eikonal amplitudes show systematic increase of the angular range of validity by comparison with partial wave results for continuous potentials; the theory is not convergent for discontinuous potentials. The WKB phase shift formula is shown to produce a systematic connection with eikonal expansion results. From this we deduce a generating function for the eikonal phase corrections of arbitrary order and also conjecture a sum of the eikonal expansion valid in the limit of high energy and arbitrary potential strength. Eikonal

Helicity Amplitude Approach to Low Energy Theorems. NORMAN DOMBEY. University of Sussex, School of Mathematical and Physical Sciences, Brighton BNl 9QH, Sussex, England AND N. C. MCKENZIE, Research Institute for Fundamental Physics, Kyoto University, Kyoto, Japan. It is shown that Low Energy Theorems for charged vector and axial vector currents have a natural derivation in terms of helicity amplitudes. This is done by reconsidering the kinematic constraints as a function of the virtual photon mass, X. The crucial point is that in general a certain limit of the longitudinal amplitudes is required as an input to the theorem. Two new Y* sum rules are also obtained. The

On Induced MORRIS,

Double-Nucleon JR. AND

H.

J.

Emission,

III.

WEBER. Department

12C (w-,

NN)

and

Short-Range

J. W. Charlottesville,

Correlations.

of Physics, University of Virginia,

Virginia. The reaction channel (r-, NN) for the absorption of bound negative pions by nuclei is used as a means to study nuclear short range correlations. A three-body partial-wave analysis has been carried out for the final-state scattering which includes a Reid soft-core nucleon-nucleon interaction and an optical potential. This coupled-channel formalism rapidly converges as we eliminate the asymptotic single-nucleon and deuteron interactions. It is found that for r2C reasonable agreement with experiment cannot be obtained in this model without modification of the high relative-momentum components of bound shell model pair wave functions.

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0 1973 by Academic Press, Inc. of reproduction in any form reserved.