Impulse approximation in nuclear pion production reactions: Absence of a one-body operator

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.83.064003· OSTI ID:21502758

Bolton, Daniel R; Miller, Gerald A ^[1]

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1. Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)

The impulse approximation of pion production reactions is studied by developing a relativistic formalism, consistent with that used to define the nucleon-nucleon potential. For plane wave initial states we find that the usual one-body (1B) expression O{sub 1B} is replaced by O{sub 2B}=-iK(m{sub {pi}}/2)O{sub 1B}/m{sub {pi}}, where K(m{sub {pi}}/2) is the sum of all irreducible contributions to nucleon-nucleon scattering with energy transfer of m{sub {pi}}/2. We show that O{sub 2B}{approx_equal}O{sub 1B} for plane wave initial states. For distorted waves, we find that the usual operator is replaced with a sum of two-body operators that are well approximated by the operator O{sub 2B}. Our new formalism solves the (previously ignored) problem of energy transfer forbidding a one-body impulse operator. Using a purely one pion exchange deuteron, the net result is that the impulse amplitude for np{yields}d{pi}{sup 0} at threshold is enhanced by a factor of approximately two. This amplitude is added to the larger ''rescattering'' amplitude and, although experimental data remain in disagreement, the theoretical prediction of the threshold cross section is brought closer to (and in agreement with) the data.

• OSTI ID: 21502758
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevC.83.064003; (c) 2011 American Institute of Physics; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
CROSS SECTIONS
DEUTERONS
DISTORTED WAVE THEORY
ENERGY TRANSFER
FORECASTING
IMPULSE APPROXIMATION
NUCLEON-NUCLEON INTERACTIONS
NUCLEON-NUCLEON POTENTIAL
PARTICLE PRODUCTION
PIONS
RELATIVISTIC RANGE
RESCATTERING
TWO-BODY PROBLEM
WAVE PROPAGATION
APPROXIMATIONS
BARYON-BARYON INTERACTIONS
BOSONS
CALCULATION METHODS
CHARGED PARTICLES
ELEMENTARY PARTICLES
ENERGY RANGE
HADRON-HADRON INTERACTIONS
HADRONS
INTERACTIONS
MANY-BODY PROBLEM
MESONS
PARTICLE INTERACTIONS
POTENTIALS
PSEUDOSCALAR MESONS
SCATTERING