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Few-body systems as neutron targets

Few-body systems as neutron targets. A. Fix (Tomsk polytechnic university). Photoproduction of π, η, and η´ on few-body nuclei. a . Deuteron parameters:. a. Deuteron is particularly suited as a neutron target. n. p. Schr ö dinger equation for the deuteron w.f. Asymptotic Region .

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Few-body systems as neutron targets

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  1. Few-body systems as neutron targets A. Fix (Tomsk polytechnic university)

  2. Photoproduction of π, η, andη´on few-body nuclei a Deuteron parameters: a Deuteron is particularly suited as a neutron target n p

  3. Schrödinger equation for the deuteron w.f. • Asymptotic Region • Deuteron size parameter a n p r0 Nucleons are on average outside the interaction range a Rd > r0

  4. Simplest approximation toσ(γd→mX) a (diffuse structure) • Amplitude: a (weak binding) • Cross section: a (weak interference) • Spectator model: γ m a n p

  5. Results for π– photoproduction (total cross section) σn (MAID2003) Total cross section σn(free)≈σn(bound) a • Reason:Transparency of the target Fulltheory

  6. Validity of the spectator model ∆(1232)region: Tπ ≈ mπ a • 1st condition: weakbinding easily satisfied for not very slow mesons • 2nd condition: short “collision” time (impulse character of reaction) Violated because of resonance time delay ∆t= 2/Γ∆ ~ 10–23 s a∆R= ∆tβΔ~ 1fm • ∆R /Rd~1 • spectator model is • somewhat marginal in • the resonance region • 3rd condition: dominance of incoherent mechanisms Violated for for π0σcoh≈ 1/3 σincoh

  7. Important corrections • Fermi motion • NN interaction • Pauli blocking • Meson rescattering • Other two-nucleon mechanisms (MEC, pion absorption on nucleon pairs, etc.)

  8. Fermi motion γN frame γd frame Momentum distribution • Doppler shift of the photon energy • Effect: smearing of the resonance structure • Preserves energy integrated σ σn

  9. Influence on Σasymmetry 1.05 GeV 1.00 GeV 1.10 GeV 1.20 GeV Data: GRAAL, 2008 S11(1535) Effect of FM depends on specific behaviour of elementary cross section a

  10. GDH on neutron • Spins of nucleons are aligned along the • deuteron spin free γ γ Δσ bound free Δσ/Eγ Δσ • However IGDH bound n n (due to Fermi motion) p p • Solution:Exclusion of FM through • transition to γN frame

  11. NN Final state interaction Bound pp πspectrum in NN FSI Virtual pp SM Pπ (MeV/c) a Effect: peak near high energy limit of πspectrum caused by strong NN attraction in 1S0 state

  12. NN FSI in near-threshold region • Leads to strong enhancement of SM cross section γd→ηnp FSI neglected: NN FSI effect (threshold) SM Initial nucleon momentum p > 200 MeV/c strongly exceeds typical momentum in the deuteron α=√MEd≈ 45 MeV/c • strong suppression of the SM cross section

  13. NN FSI in near-threshold region FSI included: • Large initial • nucleon momentum • not required γd→ηX • Enhancement effect • is larger for η´ 7 η η´ 5 3body 3 NN FSI η • Very difficult • to extract σn 1 0 20 40 SM

  14. Orthogonality γd→ηnp SM SM SM FSI FSI FSI • ηnp,π–pp: FSI is insignificant • π0np: FSI is important • Reason: Orthogonality of ψd(r) and ψnp(r)inγd→ π0np equal quantum numbers ‹ d (2S+1LJ =3S1) | → | np (3S1) › dominates at θπ→ 0 initial state final state

  15. Orthogonality and are eigenstates Orthogonality relation: a of the same Hamiltonian γd→π0np Amplitude: SM FSI a dσ/dΩsuppressedat θπ→0 In spectator model: is a plane wave a Orthogonality is ignored

  16. Absorption of pions πoPhotoproduction Energy integrated σ x102 σp+ σn (MAID 2003) 6 4 σ [μb] σd(B.Krusche et al, 1999) 2 0 200 400 600 800 apions are absorbed Photon energy [MeV]

  17. Absorption of pions • Large exchanged momentum • short-range nature of the absorption mechanism a p1 p π } ra n p2 • Estimate of absorption effects: a pion is necessarily absorbed if r ≤ra with Hulthen w.f. and ra = 0.5 fm Pabs= ≈0.1

  18. 2nd resonance region theory ≈ 1.5 • Disagreement at Eγ≈ 0.7 ± 0.2 GeV : data • Assumptions: 1. Strong absorption (unlikely) σp+ σn 2. ? Measurement of Full model Then C.Bacciet al (1969): R ≈ 1 Data: R≈ 1/3 Data: B.Kruscheet al, 1999

  19. Spectator model for ηandη´ photoproduction • Works well, especially if Fermi motion is excluded (through • transition to γN) γn* →η´n free neutron • Corrections to SM are insignificant (except low energies) Correction Why small NNFSI large momentum transfer to NN Orthogonality small coherent component Absorption large meson mass and weak ηNN (η´ NN) coupling

  20. Conclusion Corrections to the spectator model • Generally important for πphotoproduction in the resonance region, especially for π0where coherence effects are strong • Insignificant for ηandη´ (except trivial Fermi motion and NN FSI in the near- threshold region) • Rather well understood a study of reactions on neutrons is not problematic • ? 2nd resonance region in γd →π0np reason of discrepancy is unclear σp+ σn Full model NN FSI ? absorption shadowing F e r m i m o t i o n

  21. Simple method to estimate FSI effect is used • If closure sm A FSI A ≈ B πd B

  22. Absorption of η and η´ • Two-nucleon absorption requires large momentum exchange • not effective a • Main abs. mechanism – transition to pionsηd→πNN, ηd→ππNN, ... • Time delay in the resonance region ΔQ ~ 2/ΓR • strong influence of inelastic channels a Example: ηdelasticscattering in theS11(1535)region Argand diagram for L=0 Inelasticity parameter Complex nuclei: σ(γA → ηX) ~ A2/3 (surface production) S11(1535) Three-body calculation

  23. Meson rescattering at low energies a πrescattering isinsignificant • Small πN scattering length • S11(1535) near ηNthreshold a strong ηNattraction a rescattering concept is inadequate 3-body η + … N N rescattering • Few-body models are • the only proper base • for ηNN, ηNNN … 3-body • Very difficult • to extract σn rescattering

  24. π– Photoproduction at higher energies γd→π–p p NKS02 947 MeV NKS02 1097 MeV 10 10 SCH74 957 MeV SCH74 1100 MeV dσ/dΩ [μb/sr] dσ/dΩ [μb/sr] 5 5 0 0 50 100 150 50 100 150 θ [deg] θ [deg] theory • At θ ≈ 0 ≈ 2 data

  25. Rescattering corrections a shadowing effects p n γ π n p Shadowing of incident photon Shadowing of produced pion a

  26. Why is orthogonality important only for π0 ? • 1st condition: fraction of 3S1in final NN is large • 2nd condition: momentum transfer qto NN is small γd→π0np: 3S1 large, q small a effect is important γd→ηnp: 3S1small, q large a effect is insignificant Isovector (Tγ=1)a Id = 0 → Inp= 1 (3S1forbidden) γd→ηnp SM SM FSI FSI

  27. Pauli exclusion • Important at forward meson angles • (small relative momentum of recoil • nucleons) • Effect: Decreases cross section Allowed Excluded

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