Transcript The Strong Force: NN Interaction

The Strong Force:
NN Interaction
Febdian Rusydi
Student Seminar 2 Nov 05
KVI - RUG
Outline
• Yukawa theory of nuclear force
• NN Interaction
• Partial Wave Analysis: phase shift,
scattering length, and cross-section.
• Lippman-Schwinger equation: T-matrix
• Nijmegen analysis
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
http://www.pbs.org/wgbh/nova/elegant/
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Pohv et. al., Particles and Nuclei, Springer, 2002
Frauenfelder, Henley, Subatomic Physics, Prentice Hall, 1991
Krane, Introductory Nuclear Physics, John Wiley & Sons, 1988
http://fermi.la.asu.edu/PHY577/
Phy. Rev. C, 48 792, 1993
Fundamental Interactions
[1]
[2]
Yukawa theory of nuclear forces
• Early ’30: existence of a
very strong force known
in nuclei at distance ~ 2
[fm]
• ‘34: Yukawa suggested a
new sort of quantum, a
meson, with 100 [MeV/c2]
mass.
• ‘38: found a new particle
suspected to be the
meson.  the muon ()
• ’78: The real meson
found, the pion or meson.
[3]
Yukawa Potential [4]
Classical electrodynamics
Yukawa Interaction
Hamiltonian:
Substitution:
Hfree
Hint
Add. term
Poisson Eq.:
Solution:
x’  0
Maxwell Eq.:
What is k?
Poisson Eq.:
Solution:
k  inverse of Compton wavelength
Strength
(dimensionless)
NN Interactions
What we do know:
• 2 nuclei interact 
meson exchange,
with minimum energy
~ mc2.
• Distance ~ 1.4 [fm]
• Hold nucleus together
• At some senses
analogue to EM
interaction.
How do we know:
• Scattering method
• Wave mechanics
• m  reduced mass
• E  kinetic energy = binding energy
NN Interactions
Many experiments have
been done to study NN
interaction.
- Deuteron system
- pp scattering
– np scattering
What we do not know:
• Interaction potential
Some methods to
analyze the potential:
– Phase shift method
– Lippman – Schwinger
equation
Phase shift method
Partial wave analysis
NN Scattering at low energy:
• Incident particle with speed
~v
• Angular momentum ~
• If:
• Corresponding kinetic
energy:
[5]
•
•
•
•
Features:
Incident wave is plane wave
 I(r-2), A(r-1)
Scattered wave is diffracted
 I(, )
Detector records both
incident and scattered
waves.
Partial wave analysis
Radial part of Schrödinger equation:
Solution, assume the potential well and l = 0:
Boundary condition at r = R:
inside
outside
[5]
Phase shift & scattering length
outgoing
[5]
phase
shift
incoming
Scattering
length
Phase shift
Amplitude
Cross section
Scattering gives information on the interaction
between incoming and target particles, such as:
- Reaction rates,
Cross-section
- Energy spectrum
- Angular distribution
Current of particles per unit area:
Cross section
Scattering
length
pp/np scattering (E  20 MeV)
pp scattering:
• Isovector
• Charge  easy to
detect
[5]
np/pn scattering:
• Isovector and
isoscalar
• Neutral  difficult to
detect
• V V(r), determined by measuring E-dependent
of NN parameters (such as phase shift)
• Spin-dependent  only 1S0
• Charge symmetry  pp & nn interactions are
identical, nearly charge-independent
Lippman – Schwinger
[6]
Schrödinger eq.
No interaction
Interaction
Lippman-Schwinger eq.
T-matrix
Cross section
E density of
outgoing particle
Scattering
length
Nijmegen Analysis
[7]
• Fact: pp scattering analysis (multi-energy, m.e.) is easier
than np scattering.
• pp scattering analysis is established.
• np scattering analysis:
– parameterize isoscalar lower partial wave.
– substitute isovector lower partial wave from pp scattering result
• General method:
– Long-range part of NN interaction is well known: EM & Yukawa
interaction  higher J are understood.
– Short-range is sufficiently short for higher partial wave to be
screened by central barrier  small number of lower partial
waves need to be parameterized.
Long-range interaction
[7]
The long-range potential consists of an EM part VEM and a nuclear part VN
EM part
Nuclear part
Coupling constants:
OPE = One Pion Exchange
HBE = Heavier Boson Exchange
Short-range interaction [7]
Boundary-condition parameterization at r = R
Quantum
number (l, s, J)
E-dependent of pp 3P0 phase shift
Radial wave
function
no param.
1 param.
Treatment isovector and isoscalar np
phase parameter
- Parameterize isoscalar lower partial waves.
- Calculate pp phase shift by solving Schrödinger
eq. (VN & VC)
- OPE (pp) replaced by OPE (np)
Nijmegen.
solution
What to be fitted?
an, according to the data
Neutral-to-charged m difference
What we have so far…
1. Strong force in nuclei is studied by scattering
and partial-wave analysis.
2. Potential of NN interaction is not well
understood; there are many approaches
(scattering length, T-matrix).
3. Nijmegen potential: OPE and HBE
4. Nijmegen analysis: long- and short-range.
5. Not covered yet: Bonn and Argonne Potentials.