Hypernuclear Production in proton- and pion- nucleus Collisions: A Fully Relativistic Description Radhey Shyam Saha Institute of Nuclear Physics, Kolkata,
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Hypernuclear Production in proton- and pion- nucleus Collisions: A Fully Relativistic Description Radhey Shyam Saha Institute of Nuclear Physics, Kolkata, India Z.Zt. Institut f. Theo. Physik, Uni Giessen, Germany 1.Introduction - Production of Hypernuclei 2.Kinematics and Elementary processes of the proton induced Hypernuclear production. 3. Brief sketch of the theoretical model 4. Results, cross sections, spectroscopy 5. Conclusions PLAN OF THE PRESENTATION
(K‾, ‾) reaction on Nuclei Production of Hypernuclei Low momentum transfer only substitutional states are populated. ( +, K + ) reaction on Nuclei Momentum transfer larger than the Fermi momentum (n-hole, -particle) configuration in a series of orbits (even deepest one) K - stopped + A Z A Z + - Streched states with maximum spin are preferentially excited.
p + A(N, Z) B(N-1, Z) + n + K +, With proton beams p + p p + + K + Elementary process p + A(N, Z) B(N, Z-1) + p + K +, p + A(N, Z) B(N, Z) + K +, (Exclusive Reaction, two-body FS)
pp p K + reaction: 1.582 GeV. Effective Lagrangian Model describes the pp p K + reaction well. Kinematics, elementary processes, theoretical formulation Thresholds for the A(p,K+) B reaction depends on the target mass. 0.739 GeV for 12 C and 0.602 GeV for 208 Pb. Excitation of N * (1650), N * (1710), N * (1720) baryonic resonances. R. Shyam, Phys. Rev. C 60 (1999) 055213, C73 (2006) 035211
Larger momentum transfer (1.0 GeV/c) as compared to (0.33 GeV/c) in ( , K + ) reaction Samples bound state wave functions in a region where they are very small. Unlikely with other reactions Some characteristics of the A(p,K + ) B reaction p CM = p i – p K
One-nucleon model Two-nucleon model TNM three active baryons to share the large momntum transfer Mechanism of the A(p,K+) B Reaction ONM one active nucleon to carry entire momentum transfer to the nucleus.
Target emission Projectile emission Effective Lagrangians. 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’. Distorted waves for initial and final states. A Covarient TNP model for A(p,K + ) B reaction Bound state nucleon and hyperon spinors R. Shyam, H. Lenske and U. Mosel, Nucl. Phys. 764 (2006) 313
Pure single particle configuration with core remaining inert Bound Hypernuclear wave function In the region of the momentum transfer of interest, the lower component of the spinor is not negligible.
PE: q 0 E p pion in-medium propagator D (q) = /[q 0 2 – q 2 - m 2 - (q)] Role of the parameter.g’Contributions of two TNM Diag. TE PE TE (q) is real and attractive PE (q) is complex TE: q 0 = B 1 - B 2 (q) is renormalized by including the short range repulsion effects through the Landau-Migdal parameter g’
Contributions of Various Meson Exchange Processes exchange dominates, and exchange more important at back angles due to large momentum transfers.
Relative Contribution of Various Resonances N * (1710) dominates But inteference effects are visible. Similar to what is found is the pp p K + reaction
Differetial cross sections on 12 C and 40 Ca targets B ( C) 0p 1/2 0.708 MeV 0p 3/2 0.860 MeV 0s 1/2 11.690 MeV B ( Ca) 41 13 0d 3/2 0.753 MeV 0d 5/2 1.544 MeV 0p 1/2 9.140 MeV 0s 1/2 17.882 MeV Maxima are not at 0 deg. effect of using Dirac spinors Strong binding energy selectivity, peak cross sections ~ 1 nb.
Results for 4 He target For momentum transfers of interest, the Dirac spinors are smoothly varying, and are devoid of structures.
Beam Energy Dependence of the Total Production Cross Section Threshold Energy 0.603 GeV Threshold opens at lower Beam energy Threshold Energy 0.739 GeV
Application to the ( +, K + ) reaction on Nuclei N * (1710) dominates in his case too. State with stretched angular momentum configuration has the largest cross section
SUMMARY AND OUTLOOK Hypernuclei can be produced by means of the A(p,K + ) B reaction, which is analternative way of studying such systems. A fully covariant description of this reaction is essential. Hypernuclear states with low binding energies are preferentially excited. Differences in the angular distributions of the reaction on very light and heavier targets. The covariant theory has also be used to describe the ( +, K + ) reaction. Work is in progress to include distortions in the entrance and outgoing Channels so also is the study of ( , K+) reaction on nuclei. Coll: H. Lenske, U. Mosel, S. Bender, Uni. Giessen Cross sections are maximum for the hypernuclear states with largest orbital angular momentum, typical of large momentum trasfer reaction.