1 / 27

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 .

leona
Download Presentation

Few-body systems as neutron targets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related