Hypernuclear Production with Hadronic and

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
?
Number of Baryons (NZY)
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 gt pF
(K-,?-) reaction
Low momentum transfer
(?,K) and (e,eK) reactions can also excite
unnatural parity stretched states
7
Excitation Energy Spectra
Ex (p3/2-1,p3/2? ) 11,21,3
GS (p3/2-1,s1/2? ) 1,2
(p3/2-1,p1/2? ) 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
Projectile emission
A (p,K)?B

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
41
13
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 ?,
• produces neutron rich hypernuclei.

• Unnatural parity states strongly
• excited

• ?p??K 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
?
Hole states B (p3/2) B (p1/2) 6.3 MeV
p1/2 -1,s? , p3/2 -1,s? , p1/2 -1,p? ,
p3/2 -1,p? 16N spectrum
?
Bound Hypernuclear spinors
It is only for q ltlt 1.5 fm-1 g(q) ltlt 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,?) 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 ) Ylm
(pK ) Fl (pK )
Fl (pK) ? jl (pK r) l (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
l (pf ,r)
24
?
Fl (pK) ?0 jl (pK r) l (pf ,r) r2 dr
25
l (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 ?-N
interaction
In-medium Chiral Dynamics, orxiv0709.2298
(Weise)
27
Scattering wave function in momentum space
?
Fl (pK) ?0 jl (pK r) l (pf ,r) r2 dr
Rmax
?
?0 jl (pK r) l (pf ,r) r2 dr ?Rmax jl
(pK r) l (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)
Zxiy
?
C0
Zx-iy
Z x - iy
28
(No Transcript)
29
A(p,K)?B
Thresholds for the reaction depends on the
target mass.
pp ? p?K reaction 1.582 GeV.
0.739 GeV for 12C and 0.602 GeV for 208Pb.
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.
30
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