Model Study Of Three-Body Forces in the Three-Body Bound State

1
Model Study Of Three-Body Forces in the
Three-Body Bound State

• Hang Liu Charlotte Elster Walter Glöckle

2
Research Objectives

• Develop reliable computational procedure to
  calculate the three-nucleon (3N) bound state
  with two-body and three-body forces .
• Novel aspect calculations are carried out
  without traditionally employed angular momentum
  decomposition.
• 3D calculations algebraically and
  computationally easier.
• Goal Explore the dynamics of 3N forces in 3N
  System.

3
Faddeev Equation for 3N bound state
Faddeev component
Two-body transition operator
Total wave function
Three-body force
Permutation operator
Faddeev Equation for 2NF only
The eigenvalue problem Lanczos type method
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3N force in Jacobi Variables
Jacobi variables
ijk123, 231, 312
3N force
3
1
2
Two consecutive meson exchange
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3N Force Matrix Element
Transform from type2 to type 1 system
Second integration in type 2 system
Transform from type 3 to type 2 system
First integration in type 3 system
3N force integration gt Two integrations of 2N
force like
Two coordinate transformations.
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The 3N bound state with MT3-II force
MT2-II
MT3-II
MT2-II MT3-II
Measured value 8.482 MeV
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Momentum Distribution and Correlation Function
The probability to find single nucleon with
momentum q
The probability to find two nucleons with
distance r
Results based on MT2-II MT3-I
MT3-I
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Triangular Shape in Coordinate Space

• Three identical nucleons interact
• Each one feels the same interaction
• Equilateral triangle

Results based on MT2-II MT3-I
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The 3N Bound State by 3N Force Only
MT2-I Only attractive 2N force MT2-II
2N force with repulsive core MMT3-I Only
attractive 3N force MMT3-II 3N force with
repulsive core
MMT3-II
MMT3-I
MT2-II
MT2-I
7.582
7.554
7.698
7.580
1.170
0.864
2.521
1.783
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MT2-I
MMT3-I
MT2-II
MMT3-II
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2NF .vs. 3NF
MT2-I
MMT3-B same functional form as MMT3-I but
different parameters
MMT3-B
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Summary

• The Faddeev equations for 3N bound state with
  both 2N and 3N forces are solved in 3D momentum
  space.
• 3N force integration can be carried out
  accurately and efficiently in 3D manner.
• 3N forces influence mostly
• high momentum components
• size of the 3N system
• The influences of 3N forces on 3N bound state are
  very sensitive to strength and meson mass of 3N
  force.

nucl-th/0204027, nucl-th/0207062