Prague Summer School

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The Production of Strange Nuclear
Systems-Strangeness Happens

• Ed V. Hungerford
• University of Houston
• Hunger_at_uh.edu

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Acknowledgements
I am indebted to many of my colleagues who have
both taught me the physics and contributed to
this field their research. I acknowledge their
contributions. Although the paper containing
these lectures will have appropriate
referencing, contributions by others will not be
so apparent in these slides. However, I credit
everyone of my mentors where this lecture
succeeds, and to my shortcomings where it does
not.
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Whats so New in Nu-clear Physics ?
According to Pogo
Nuclear Physics is not so new, and not so
clear either.
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In the Beginning
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In the Beginning
Actually I will talk a little about the
beginning, but let me now start 75 years ago.
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75 years ago Nuclear Physics was New And maybe
not so clear

• The Proton and Neutron were considered elementary
  particles
• The neutron had just been discovered
• The nuclear force was not understood
• Nuclear models were primitive and based on
  classical
• liquids

Nuclear Physics is the Study of the effects
of Many-body Hadronic System Interacting via QCD
(or QHD)
Today Nuclear Physics in some sense is Mature

• Nucleons are not elementary but are composed of
  other
• particles called quarks
• The nuclear force is understood as an exchange of
  field quanta
• (gluons)
• The nucleus is a VERY complicated interaction of
  many hadrons
• whose interaction is described by QCD

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A Brief Summary

• Nuclear Science has tremendous breadth and
  complexity
• After 75 years we have found some to the right
  questions to ask but
• others remain
• I have purposely avoided discussion of the more
  traditional nuclear studies
• There are impressive new results and insights
  into nuclear matter. But these
• require detailed exposition and are difficult
  to develop to grasp without some
• prior knowledge.
• As a mature, advanced science, there are
  significant applications in
• Including the fields of Medicine, Computing,
  Industrial Products, Energy,
• Finance, etc.
• More than 50 of the Phd graduates in Nuclear
  Physics are employed
• in industry, medicine, and national defense.

Nuclear Physics is a vibrant, exciting Field That
impacts many others
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Each of the 4 interactions is has its own impact
on the existence of our Universe
The Strong (nuclear) force is responsible for the
creation and stability nuclear matter
Phase Diagram of Matter
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Outline of the Lectures
1st Lecture
Background, Structure, Production Formulism,
Beams and Detectors
2nd Lecture
Quasi-Free Production, Specific Reactions (K, p
), (p ,K), ( g, K)
3rd Lecture
Exotic reactions, S -2 Production
4th Lecture
Multi-Strangeness, Strange Astrophysical Objects
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(us)
Mesons and baryons are composed of quarks
Flavor SU(3)f Symmetry Allows Placement of
lowest Mesons And Baryons in Symmetry Octets
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The Elementary ?N Amplitude
Hyperons live for only a fraction of a ns (eg t?
0.26 ns)
Low energy YN scattering is difficult. Only 600
data points exist
Use NN data and apply broken SU(6) Symmetry
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A Phase shift fit is not possible
The data cannot define the scattering lengths
and effective ranges
as
at
rt
rs
at and as scattering length rt and rs effective
range
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Comparison of models of the ?N interaction
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Hypernuclear Binding Energies
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Hypernuclear Binding Energy/A
BL/A shows Saturation
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As in Nuclear Physics, Baryons in the
Hypernucleus be treated as Fundamental Objects
7?He
The Structure is discussed in the particle-hole
formulism
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Charge Symmetry Breaking and ? Separation
energies
pairs (isospin symmetry)
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Charge Symmetry Breaking
A4 hypernuclei are the main source for CSB
?B(0) 0.35 MeV
?B(1) 0.24 MeV
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Charge Symmetry Breaking
If the radius is the same (8)
The Couloumb self energy
?Ec (6/5)(Ze2/R)(1 e)
? e (ex energy) -0.613z1/3 0.60
(-1)z0.3e2/R
If CSB is known then R could be determined
A 4
?Bc ?Ec
As a consequence CSB is 3x that of ordinary
nucleus (A4)
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An elementary potential form inserted into The
hadronic many-body problem yields a one-body
effective potential
V( r ) V0 VsSn SY VtS12 Vls(L x S)
Vals(L x S-) S12 is the usual spin-tensor
operator S- ½(Sn -SY) are the symmetric and
anti-symmetric spin operators
The assumption is that the Lambda can be
represented by a superposition of a set of single
particle states
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The 7Li Hypernucleus
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Production can occur by
Exchange
Replace a u or d quark with an s quark
Example(K-,?-)in-flight
Associated Production
Produce an S anti-S Pair Example (p,K)
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Quark Flow Diagrams
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Production Kinematics
High Momentum Transfer
Recoilless Production
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Comparison of Two Different Lambda Production
Reactions
(K-,?-)in-flight

• Can have Low Momentum Transfer
• Substitutional Reaction
• Natural Parity Excitations
• Neutron hole-Lambda particle

(?,K)in-flight

• High Momentum Transfer
• Excitation of Stretched Spin States
• Natural Parity Excitations
• Neutron hole-Lambda particle

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The (K-,?-) Reaction Producing Lambda or Sigma
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The Interaction Averaged over The Fermi Momentum
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Thus a Natural form to Express Production of a
Hypernucleus is DWIA
T(a,?,ms)2
Elementary Amplitude
Effective Number of Nucleons
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DWIA for 12C(K-,?-)12LC
Comparison of calculation with and without
Fermi motion averaging
Distortions can change the size The cross
section by 10-1 Off shell effects are small
for low momentum transfers.
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The Elementary ?n K ? Cross Section
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The Elementary gamma pK? Cross Section
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The ?p reaction is a composite of many amplitudes
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?p Data is fantastically detailed
Cross section vs cos(?)
Energies 1.05 - 2.6 GeV in steps of 0.025 GeV
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To produce strange baryons requires Intense beams
of pions, kaons, or gammas
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The Production of Secondary Beams by Protons
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Data and beamline design
Flux maximized at forward angles
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A Schematic Separated Kaon Line
Higher Order Optic Elements
Dispersed or Combined Focus
Vertical Separation using E x B
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?/K separation is required
Beam focused in x parallel in y
Crossed E and B fields Vertical separation
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Typical Parameters for a Modern Separated Low
Energy Kaon Line
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A Reaction leads To the excitation Of Various
Hypernuclear Levels
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(K-,?-) Spectrum
7Li(K,?)7?Li
Bound, Un_bound, Breakup
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Mean Free Path in Nuclear Matter
Positive Kaons and Pions are Penetrating
Remember that Kaons have a lifetime of ct 3.7 m
so low momentum beamlines must be short
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Effects of high momentum transfer Production of
56?Fe
Fe Target
(K-,p-)in-flight
Q F
High Penetration
Q F
(p,K)
(K-,p-)stop
Q F
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Next up
Production of Hypernuclei in Specific Reactions