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Hypernuclear Production with Hadronic and Electromagnetic Probes

Hypernuclear Production with Hadronic and Electromagnetic Probes. Radhey Shyam. Introduction. A brief review and comparison of production reactions. 2. Brief sketch of the theoretical model. 3. Results, cross sections, spectroscopy. 4. Conclusions.

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Hypernuclear Production with Hadronic and Electromagnetic Probes

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  1. Hypernuclear Production with Hadronic and Electromagnetic Probes Radhey Shyam • Introduction A brief review and comparison of production reactions 2. Brief sketch of the theoretical model 3. Results, cross sections, spectroscopy 4. Conclusions Coll. H. Lenske, and U. Mosel

  2. Hypernuclei are systems where one nucleon is replaced by a hyperon  Hypernuclei A Z is a bound state of Z protons (A-Z-1) neutrons and a  hyperon Λ Number of Baryons (N+Z+Y) Element = Total charge   B YX  Number of hyperons Double Hypernuclei, Be,  Hypernuclei 10

  3. Why are Hypernuclei interesting! New type of nuclear matter, new symmetries, New selection rules. First kind of flavored nuclei. Hyperons are free from Pauli principle restrictions Can occupy quantum states already filled up with nucleons 89 Y Good probe for deeply bound single particle states.

  4. Production of  Hypernuclei MESONIC PROBES Prog. Part. Nucl. Phys. 57, 564 (2006) (K-, - ) reaction Strangeness exchange (+, K+) reaction Associated strangeness production

  5. Electromagnetic and baryonic Probes + p  + K+ (,K+) reaction H. Yamazaki et al., Phys. Rev. C 52, R1157 (1995) * + p   + K+ (e,e’ K+) reaction Jlab, L. Yuan et al. Phys. Rev. C 73, 044607 (2006) p + p  p +  + K+ (p,K+) reaction COSY p + p  p +  + K+ Heavy Ion reactions GSI

  6. KINEMATICS (p,K+) reaction 12C Large Momentum transfers (+,K+) and (,K+) reactions Momentum transfer > pF (K-,-) reaction Low momentum transfer (,K+) and (e,e’K+) reactions can also excite unnatural parity stretched states

  7. Excitation Energy Spectra Ex: (p3/2-1,p3/2Λ) 11+,21+,3+ GS: (p3/2-1,s1/2Λ) 1–,2– (p3/2-1,p1/2Λ) 12+,22+ (K–,–) substitutional 0+ state dominates (+,K+) nonsubstitutional 1– and 2+ states dominate (,K+) unnatural parity states dominate Int.J. Mod. Phys. 21, 4021 (1990)

  8. Production processes for various reactions Target emission A (p,K+)B Projectile emission + A (+,K+)B* A (,K+)B′ N * (1650), N*(1710), N*(1720) baryonic resonances.

  9. A Covarient Description of A(h,K+)B reaction Effective Lagrangians at various vertices Coupling constants, form-factors Bound state nucleon and hyperon spinors Initial and final state interactions (distorted waves). Medium modification of N* (also of intermediate mesons in proton induced reactions) self energies. All calculations in momentum space, so nonlocalities are included.

  10. A(p,K+)B reaction Kinematics: Thresholds depends on the target mass. pp  pK+ reaction 1.582 GeV RS, H. Lenske and U. Mosel, Nucl. Phys. 764 (2006) 313

  11. Bound state spinors A mean field approach Momentum space Dirac Eq.

  12. Bound Hypernuclear wave spinors In the region of the momentum transfer of interest, the lower component of the spinor is not negligible.

  13. A(p,K+)B Relative Contribution of Various resonances Role of pion self energy RS, H. Lenske and U. Mosel, Phys. Rev.C 69 (2004) 065205

  14. Contributions of Various Meson Exchange Processes       • exchange dominates,  and  exchange more important at back angles due to large momentum transfers.

  15. Binding energy selectivity 0d3/2 0.753 0d5/2 1.544 0p1/2 9.140 0s1/2 17.882 0p1/2 0.708 MeV 0p3/2 0.860 0s1/2 11.690 13 41 B (C) B ( Ca)

  16. Results for 4He target For momentum transfers of interest, Dirac spinors smoothly varying, and are devoid of structures.

  17. Beam Energy Dependence of the Total Production Cross Section Threshold Energy 0.603 GeV Threshold Energy 0.739 GeV Peak same energy above the threshold as is the peak in the elementary cross sections from its threshold

  18. (+, K+) reaction on Nuclei N*(1710) dominates in this case too. S. Bender

  19. (,K+) reaction on Nuclei • K+ is weakly absorbing so reaction • occurs deep in the nuclear interior. • A proton is converted into a Λ, • produces neutron rich hypernuclei. • Unnatural parity states strongly • excited • p→ΛK+ reaction well understood • within an effective Lagrangian picture Excitations of N*(1650), N*(1710), N*(1720) resonances. V. Shklyar, H. Lenske, and U. Mosel, Phys. Rev. C 58, 015210 (2005)

  20. 16O (,K+) 16N Reaction Λ Hole states B (p3/2) – B (p1/2) = 6.3 MeV [ p1/2 -1,sΛ], [ p3/2 -1,sΛ], [ p1/2 -1,pΛ], [ p3/2 -1,pΛ] 16N spectrum Λ Bound Hypernuclear spinors It is only for q << 1.5 fm-1 |g(q)| << |f(q)|

  21. Relative Contribution of Various resonances Different J excitation N*(1720) weaker by 3-4 orders of magnitude Largest J state is dominant Peak ≈ 900 MeV

  22. Excitation spectrum of 4 groups of (p-1,Λ) states In each group highest J is most strong. Unnatural Parity states dominate.

  23. Distorted waves for the scattering states pf (pK) =  (pK0 – EK) ℓ m(-) ℓ Yℓm (pf ) Y*ℓm (pK ) Fℓ (pK ) Fℓ (pK) =  jℓ (pK r) ƒℓ (pf ,r) r2 dr Kaon optical potential 800 MeV/c 2EVK(r) = -Ab0k2 (r)+Ab1. b0 and b1 are parameters of the potential This provides ƒℓ (pf ,r)

  24. Fℓ (pK) = 0 jℓ (pK r) ƒℓ (pf ,r) r2 dr

  25. ƒℓ (pf ,r)  = 15 Fℓ (pK)

  26. SUMMARY AND OUTLOOK A(h,K+)B reactions provide mutually complimentary information about the hypernuclear spectrum. A fully covariant description of these reactions is essential. Hypernuclear states with largest angular momentum are dominant, typical of large momentum trasfer reactions. (,K+) strongly excites also the unnatural parity states. Tighter constraints on the models of Λ-N interaction In-medium Chiral Dynamics, orxiv:0709.2298 (Weise)

  27. Scattering wave function in momentum space  Fℓ (pK) = 0 jℓ (pK r) ƒℓ (pf ,r) r2 dr Rmax  = 0jℓ (pK r) ƒℓ (pf ,r) r2 dr + Rmaxjℓ (pK r) ƒℓ (pf ,r) r2 dr 1 2 - + h (pKr) + h (pKr) H (pf r) - S H (pf r) I2 = exp [ ±i(pK pf )r ] Z = x + iy y= Im (r) Z=x+iy C0  Z=x-iy Z = x - iy

  28. A(p,K+)B Thresholds for the reaction depends on the target mass. 0.739 GeV for 12C and 0.602 GeV for 208Pb. pp  pK+ reaction: 1.582 GeV. R. Shyam, H. Lenske and U. Mosel, Nucl. Phys. 764 (2006) 313 R. Shyam, Phys. Rev. C 60 (1999) 055213, C73 (2006) 035211 Excitation of N * (1650), N*(1710), N*(1720) baryonic resonances.

  29. A Covarient TNP model for A(p,K+)B reaction Effective Lagrangians Target emission In medium meson propagators MESON SELF ENERGIES: For pion, p-h and -h excitations produced by the propagating pion. Short range repulsion by Landau-Migdal parameter g′. . Bound state nucleon and hyperon spinors Distorted waves for initial and final states. R. Shyam, H. Lenske and U. Mosel, Nucl. Phys. 764 (2006) 313 Projectile emission

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