1. APS April Meeting 2002 The Dynamics of Three Body Forces in Three Nucleon Bound State Hang Liu Charlotte Elster Walter Glöckle

2. APS April Meeting 2002 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 Total wave function Permutation operator Two-body transition operator Three-body force Faddeev component Faddeev Equation for 2NF only The eigenvalue problem: Lanczo’s type method

4. 3N force in Jacobi Variables Two consecutive meson exchange Jacobi variables: ijk=123, 231, 312 3N force: 312

5. 3N Force Matrix Element First integration in type 3 system Transform from type 3 to type 2 system Second integration in type 2 system Transform from type2 to type 1 system 3N force integration => Two integrations of 2N force like + Two coordinate transformations.

6. The 3N bound state with 3N force  (p,q,x) at x=cos(  )=1 with the unit of fm 3 2N force only: 1500612.4809.4081500330.210-3.577 2N force + 3N force: -1.7291000305.8595.000 Measured value = 8.482 MeV

7. Momentum Distribution The probability to find two nucleons with relative momentum p : The probability to find the single nucleon And pair with momentum q :

9. Correlation Function The probability to find two nucleons with distance r : The probability to find the single nucleon and the pair with distance R : Wave Function in coordinate space:

11. Triangular Shape in Coordinate Space Three identical nucleons interact  Each one feels the same interaction  Equilateral triangle a2a4a 2.382.231.88 2.101.961.65 0.88 m (MeV) 300250150 2.382.261.77 2.101.981.56 0.88

12. The 3N Bound State by 3N Force Only MFT2NF-II: 2N force with repulsive core MFT3NF-II : 3N force with repulsive core 7.587.69 1.172.52 MFT3NF-IIMFT2NF-II

13. APS April Meeting 2002 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.  Attractive 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.