Exclusive Reactions in Few-body Systems

1. Exclusive Reactions in Few-body Systems Nir Nevo Dinur,W. Leidemann,and N. Barnea Hebrew University, Jerusalem, Israel 10.10.2013 Inelastic Reactions in LightNuclei IIAS-ISF Conference Jerusalem

2. Outline • Introduction • Motivation • Methods • Results • Summary Exclusive reactions in few-body systems

3. Introduction:Nuclear Ab initio Calculations • Ab initio - treat the dynamics of all D.o.F • Nuclear physics: • A – number of nucleons • D.o.F – spatial, spin, isospin • State-of-the-art nuclear force models • limited to a small number of particles Exclusive reactions in few-body systems

4. Introduction:Nuclear Force Models • Simple MT(I-III) – MalflietTjon (+ Coulomb) <ISC> • Phenomenological AV18 (+ EM int.) + UIX (/TM/IL2,7) <ISB> → Simplified: AV8` + UIX` <ISC> • EFT-χPT N3LO (NNF) + N2LO (3NF) <ISB> Exclusive reactions in few-body systems

5. Motivation:Why Exclusive Reactions? • A laboratoryfor testing the nuclear force models • Calculate observables needed for: Astrophysics; Supernovae; Unstable isotopes; Fusion reactions; etc. • Why (EM) reactions? Exclusive reactions in few-body systems

6. EM reactions:4He photodisintegration • EM probe the nuclear system • structure • dynamics • QED • 4He • Test NN+3NF in 4-body system • Mimics heavy nuclei (nuclear matter) • Jπ= 0+ • 4He photodisintegration (and electron scattering) Exclusive reactions in few-body systems

7. Exclusive Two-body4He photodisintegration p + 3H n + 3He W. Tornow et al., Phys. Rev. C 85, 061001(R) (2012) R. Raut et al., PRL 108, 042502 (2012) S. Quaglioni et al., Phys. Rev. C 69, 044002 (2004) Experimental status: • A lot of data, many discrepancies • 2012: ‘Active target’ @ TUNL with monoenergetic photons from HIγS Exclusive reactions in few-body systems

8. Exclusive Two-body4He photodisintegration MT I-III MT I-III Theoretical status: • 2004: (MT I-III + Coulomb) [LIT] • 2012: (AV8’ + 3NF) [MRM & CSM] does not coincide with the state-of-the-art inclusive CS S. Quaglioni et al., Phys. Rev. C 69, 044002 (2004) W. Horiuchi et al., Phys. Rev. C 85, 054002 (2012) inclusive CS Exclusive reactions in few-body systems

9. Hints from inclusive4He photodisintegration • (χEFT) [NCSM] agree with (AV18+UIX) [EIHH] • Theory vs. experiments: agreement ? PRL 96, 112301 PLB 652, 370 Exclusive reactions in few-body systems

10. Hints from inclusive4He photodisintegration • MT overestimates the peak 10 − 15% and strongly underestimates tail • 3NF leads to a 5-6% peak damping and 35% tail enhancement Exclusive reactions in few-body systems

11. R(p/n) – The ratio of mirror channels p + 3H n + 3He Summary: • Experiments – GDR, R~1, not accurate enough. Tornow: R~<1 (n too high?) • Theory – (MT/ AV8’+3NF) + Coulomb: R~1 [reproduce B. Wachter, et al., PRC38, 1139 (1988)] • ISB forces: ? • Need accurate exptl. data (ISB sensitive) to constrain ISB terms in the force model W. Horiuchi et al., Phys. Rev. C 85, 054002 (2012) Exclusive reactions in few-body systems

12. Methods Exclusive reactions in few-body systems

13. Few-Body Method • Hyperspherical Harmonics N = (A-1) Jacobi vectors Hyper-radius + (3N-1) angles • The Hamiltonian: • Bound state problems: Laguerre (PL); Jacobi (PJ) M. Fabre de la Ripelle, Ann. Phys. (N.Y.) 147, 281 (1983) Exclusive reactions in few-body systems

14. Few-Body Method • Problems: • Permutational symmetry • Slow convergence (huge basis needed) • Solutions: • HH ON SA: KN LNλΓA • Effective Interaction (EIHH): Lee-Suzuki similarity transformation Improved convergence N. Barnea and A. Novoselsky, Ann. Phys. 256, 192 (1997) N. Barnea et al., Phys. Rev. C 61, 054001 (2000) Exclusive reactions in few-body systems

15. Exclusive reactions in few-body systems

16. Calculating Reactions – Problem 1 Continuum wave function – conflicting asymptotics: 4He • A=3 – Faddeev 3 coupled equations • A=4 – FY (/AGS/KVP) 18 coupled equations • A>4 – No ab initio calculation above 3-body threshold (except with the LIT method) 3H+p 3He+n 2H+2H 2H+p+n p+n+p+n Two-body CS More-body CS Exclusive reactions in few-body systems

17. Calculating Reactions – Problem 2 Asymptotic few-body wave function: • Two fragments: Relative motion is a plane-wave or Coulomb-function • Three fragments: • no analytic solution • numerical - very complicated! Exclusive reactions in few-body systems

18. Calculating Reactions – Solution The LIT method (inclusive case): • No solution for the homogeneous equation • Local boundary condition V. Efros, W. Leidemann, and G .Orlandini, PLB 238, 130 (1994) V. Efros, W. Leidemann, G .Orlandini and N. Barnea, JPG 34, R459(2007) Exclusive reactions in few-body systems

19. The Inclusive LIT Equation • Solve the equation • Invert the LIT – solve an integral equation: Exclusive reactions in few-body systems

20. Exclusive Reactions – Born & FSI Antisymmetrized asymptotic wave function Final State Interaction Exclusive reactions in few-body systems

21. Exclusive Reactions – Born & FSI …... Born ___ Born+FSI S. Quaglioni et al., Phys. Rev. C 69, 044002 (2004) Exclusive reactions in few-body systems

22. Exclusive LIT Equations (FSI) Exclusive reactions in few-body systems

23. The Exclusive LIT Equations • Inclusive: • Exclusive: • Hadron scattering: The challenge: Calculate FSI on the asymptotic w.f. Other possible LIT applications: • Semi inclusive (spectral func. approx.) • Fast projectile (the Glauber approx.) V. D. Efros, Phys. At. Nucl. 62, 1833 (1999) V. D. Efroset al., PRC58, 582 (1998) <your name here> (2014) Exclusive reactions in few-body systems

24. Calculating the FSI • Construct an antisymmetric w.f. with spatial, spin and isospin D.o.F. coupled to have A-particle quantum numbers • Calculate explicitly: • Use a trick: Exclusive reactions in few-body systems

25. Calculating the FSI p vs. n: • Treat Coulomb correctly: • Add and subtract Coulomb interaction between C.M. of fragments • Use appropriate asymptotic function • Distinguish between p & n channels in coupled w.f. • (½ ½,½ -½;T 0) vs. (½ -½,½ ½;T 0) • Add ISB to code Exclusive reactions in few-body systems

26. Results Exclusive reactions in few-body systems

27. ISB Results (4He*) • Benchmark ISB calculation • Interesting new results (wait for publication) Kievskyet al., J.Phys.G35,063101(2008) Exclusive reactions in few-body systems

28. Results with MT I-III + Coulomb Few-body Method Mechanism for specific problem Nuclear Model Converged? Stability Accuracy Independent Tests Solution Compare with Experiment Exclusive reactions in few-body systems

29. Results With AV18+UIX Exclusive reactions in few-body systems

30. Results With AV18+UIX Exclusive reactions in few-body systems

31. Results With AV18+UIX Exclusive reactions in few-body systems

32. Results With AV18+UIX Exclusive reactions in few-body systems

33. Results With AV18+UIX Exclusive reactions in few-body systems

34. Results With AV18+UIX Incl. CS: Add K=20 Exclusive reactions in few-body systems

35. Results With AV18+UIX Exclusive reactions in few-body systems

36. Summary • Exclusive reactions, e.g. 4He photodisintegration • are of interest, but are hard to calculate • Require state-of-the-art forces, which complicate the calculation • Our tool, based on exclusive LIT, enables: • ab initio calculation of reactions (even beyond 3-body breakup) • including state-of-the-art NN + 3N forces • isospin symmetry breaking (ISB) • Preliminary results indicate: • Tensor and L2 terms have a large effect • 3NF effect in the FSI • ISB effect: R(p/n) ~> 1 , opposite than latest experiment suggests Exclusive reactions in few-body systems