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Title: Four-Body Calculation of Proton-{sup 3}He Scattering

Abstract

The four-body equations of Alt, Grassberger, and Sandhas are solved, for the first time, for proton-{sup 3}He scattering including the Coulomb interaction between the three protons using the method of screening and renormalization as was done recently for proton-deuteron scattering. Various realistic two-nucleon potentials are used. Large Coulomb effects are seen on all observables. Comparison with data at different energies shows large deviations in the proton analyzing power but quite reasonable agreement in other observables. The effect of the nucleon-nucleon magnetic moment interaction and correlations between p-d and p-{sup 3}He analyzing powers are studied.

Authors:
;  [1]
  1. Centro de Fisica Nuclear da Universidade de Lisboa, P-1649-003 Lisbon (Portugal)
Publication Date:
OSTI Identifier:
20951253
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 16; Other Information: DOI: 10.1103/PhysRevLett.98.162502; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CORRELATIONS; DEUTERONS; EQUATIONS; FOUR-BODY PROBLEM; HELIUM 3; MAGNETIC MOMENTS; NUCLEON-NUCLEON POTENTIAL; POLARIZATION-ASYMMETRY RATIO; PROTON BEAMS; PROTONS; RENORMALIZATION; SCATTERING

Citation Formats

Deltuva, A., and Fonseca, A. C. Four-Body Calculation of Proton-{sup 3}He Scattering. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.162502.
Deltuva, A., & Fonseca, A. C. Four-Body Calculation of Proton-{sup 3}He Scattering. United States. doi:10.1103/PHYSREVLETT.98.162502.
Deltuva, A., and Fonseca, A. C. Fri . "Four-Body Calculation of Proton-{sup 3}He Scattering". United States. doi:10.1103/PHYSREVLETT.98.162502.
@article{osti_20951253,
title = {Four-Body Calculation of Proton-{sup 3}He Scattering},
author = {Deltuva, A. and Fonseca, A. C.},
abstractNote = {The four-body equations of Alt, Grassberger, and Sandhas are solved, for the first time, for proton-{sup 3}He scattering including the Coulomb interaction between the three protons using the method of screening and renormalization as was done recently for proton-deuteron scattering. Various realistic two-nucleon potentials are used. Large Coulomb effects are seen on all observables. Comparison with data at different energies shows large deviations in the proton analyzing power but quite reasonable agreement in other observables. The effect of the nucleon-nucleon magnetic moment interaction and correlations between p-d and p-{sup 3}He analyzing powers are studied.},
doi = {10.1103/PHYSREVLETT.98.162502},
journal = {Physical Review Letters},
number = 16,
volume = 98,
place = {United States},
year = {Fri Apr 20 00:00:00 EDT 2007},
month = {Fri Apr 20 00:00:00 EDT 2007}
}
  • Four-body equations in momentum space are solved for neutron-{sup 3}He, proton-{sup 3}H, and deuteron-deuteron scattering; all three reactions are coupled. The Coulomb interaction between the protons is included using the screening and renormalization approach as was recently done for proton-deuteron and proton-{sup 3}He scattering. Realistic potentials are used between nucleon pairs. For the first time fully converged results for the observables pertaining to the six different elastic and transfer reactions are obtained and compared with experimental data.
  • The Alt, Grassberger, and Sandhas four-body theory has been used to calculate the differential cross sections for the kinematically complete breakup reaction /sup 3/He(p,pd)/sup 1/H at various proton energies and angles. The two-body input consists of Yamaguchi potentials without Coulomb corrections and the (3+1) and (2+2) amplitudes were expanded using the generalized unitary pole expansion. The resulting effective two-body equations have been solved in the first-order K-matrix approximation. Reasonable agreement with experiment was obtained.
  • {sup 4}He possesses a second 0{sup +} state; the transition form factor has been measured via inelastic electron scattering. The nature of the 0{sub 2}{sup +} state's spatial structure has been controversial. An accurate four-nucleon calculation utilizing a realistic NN force (Argonne V8{sup '}) plus phenomenological NNN three-body force has been performed for both the {sup 4}He ground state and second 0{sup +} state (E{sub x}=20.21 MeV) using the Gaussian expansion method. The calculated one-body densities and transition density show a significant difference between the states. The resulting impulse approximation transition form factor {sup 4}He(e,e{sup '}){sup 4}He(0{sub 2}{sup +}) agreesmore » with the available data. The overlap of the 0{sub 2}{sup +} wave function with the trinucleon ground state suggests that the structure is primarily a loosely bound 3N+N system and not a breathing mode. It is found that a major part of the energy-weighted E0 sum rule value is exhausted by nonresonant, low-energy continuum states other than the second 0{sup +} state, in contrast to heavier nuclei where a dominant fraction of the sum-rule limit is exhausted by the second 0{sup +} state because it corresponds to a collective, breathing mode.« less
  • The CE25 experiment at IUCF measured the quasielastic scattering asymmetries of the {sup 3}He({rvec p},2p) and the {sup 3}He({rvec p},pn) reactions. We report preliminary results. The measurements at 200 MeV incident beam energy show a strong momentum transfer dependence of the target asymmetry for the neutron. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
  • Experimental and theoretical cross sections are presented for the /sup 6/Li(/sup 3/He,/sup 3/He/sup 3/He)/sup 3/H and /sup 6/Li(/sup 3/He,t/sup 3/He)/sup 3/He reactions for the symmetric angle pairs 20/sup 0/-20/sup 0/, 28.3/sup 0/-28.3/sup 0/, and 35/sup 0/-35/sup 0/. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with /sup 6/Li being a /sup 3/He-/sup 3/H bound state. The trion-trion interaction is represented by S wave separable potentials with the breakup cross sections calculated with the tree-body Haftel-Ebenhoeh code. the Coulomb interaction is taken into account by fitting the separablemore » potential parameters to the trion-trion scattering data and is included approximately in the breakup code. The experimental cross sections are compared with both the plane-wave impulse approximation and the three-body model predictions. The plane-wave impulse approximation predicts both the shapes and magnitudes poorly (10 to 20 times experiment). Without Coulomb corrections the three-body model gives good agreement with experiment for the shapes of the spectra with the magnitudes generally being about 40% of experiment for /sup 6/Li(/sup 3/He,/sup 3/He/sup 3/He)/sup 3/H and about 80% for /sup 6/Li(/sup 3/He,t /sup 3/He)/sup 3/He. The Coulomb corrections improve the magnitudes predicted by the three-body model but not the shapes. It is observed that for these reactions S wave separable potentials describe the breakup data much better than they do the two-body trion-trion scattering data. This result should encourage further three-body treatment of these and similar reactions.« less