Hypernuclear Production in proton- and pion- nucleus Collisions: A Fully Relativistic Description

Radhey Shyam

Saha Institute of Nuclear Physics, Kolkata, IndiaZ.Zt. Institut f. Theo. Physik, Uni Giessen, Germany

1. Introduction - Production of Hypernuclei2. Kinematics and Elementary processes of the proton

induced Hypernuclear production.3. Brief sketch of the theoretical model4. Results, cross sections, spectroscopy5. 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 theFermi momentum (n-hole, -particle) configuration in aseries of orbits (even deepest one)

K- stopped + AZ 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 pK+ reaction: 1.582 GeV.

Effective Lagrangian Model describes the pp pK+ reaction well.

Kinematics, elementary processes, theoretical formulation

Thresholds for the A(p,K+)B reaction depends on the target mass.

0.739 GeV for 12C and 0.602 GeV for 208Pb.

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

pCM = pi – pK

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: q0 Ep

pion in-medium propagator D(q) = /[q0

2 – q2 - m2 - (q)]

Role of the parameter.g’Contributions of two TNM Diag.

TE

PE

TE (q) is real and attractivePE (q) is complex

TE: q0 = B1 - B2(q) is renormalized by including theshort range repulsion effects through the Landau-Migdal parameter g’

Contributions of Various Meson Exchange Processes

exchange dominates, and exchange more important atback angles due to large momentum transfers.

Relative Contribution of Various Resonances

N*(1710) dominates

But inteference effectsare visible.

Similar to what is found is the pp pK+ reaction

Differetial cross sections on 12C and 40Ca targets

B (C)

0p1/2 0.708 MeV 0p3/2 0.860 MeV0s1/2 11.690 MeV

B (Ca)41

13

0d3/2 0.753 MeV0d5/2 1.544 MeV0p1/2 9.140 MeV0s1/2 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 4He 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 momentumconfiguration 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.