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Three-Body Break-Up Processes at Higher Energies

Three-Body Break-Up Processes at Higher Energies. Hang Liu Charlotte Elster Walter Gl öckle. Supported by: U.S. DOE, NERSC. Full Faddeev. The Solution of Three-Body Amplitude T at Different Orders in Two-Body t -Matrix. 1 st order. 2 nd order. 3 rd order. 4 th order.

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Three-Body Break-Up Processes at Higher Energies

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  1. Three-Body Break-Up Processes at Higher Energies Hang Liu Charlotte Elster Walter Glöckle Supported by: U.S. DOE, NERSC

  2. Full Faddeev The Solution of Three-Body Amplitude T at Different Orders in Two-Body t -Matrix 1st order 2nd order 3rd order 4th order Do these expansions at certain orders well approximate the full Faddeev solution ? How do rescattering terms contribute to the total amplitude ?

  3. Break-Up Amplitudes and Cross sections Exclusive Cross Section (two particles measured) Inclusive Cross Section (one particle measured) Total Cross Section

  4. Inclusive Scattering Quasi Free: (QFS) one particle is at rest in lab Maximum amplitude of deuteron state and on-shell t-matrix Final state interaction: (FSI) two particles leave reaction region with zero relative momentum NN scattering length

  5. 1st order totally misses the FSI peak

  6. 1st order result accidentally close to the full Faddeev solution at certain energy region

  7. QFS + FSI interference

  8. The 3th order solution close to the full Faddeev result

  9. A specific break-up configuration and measurement: the neutron is ejected at extreme backward angles, and the two protons at extreme forward angles, only events with small PP relative energy are measured At 1.0 GeV scale: partial sum up to 3rd order is necessary Convergence improved by going higher orders at backward angle !

  10. Summary • Convergence Properties of Partial Summed Rescattering Contributions at QFS and FSI Region (observed from inclusive process) at higher energies • QFS: • rescattering effects behave regularly, no strong dependence on kinematics, results up to 3rd order is close to that from full Faddeev solution . • FSI: • small emission angle: complicated interference of rescattering effects, strong dependence on the kinematics,full Faddeev solution in general is necessary. • large emission angle: especially the exact backward angle, relatively simple and better convergence properties to validate lower order approximation, however, the 1st order is usually not sufficient.

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