1. Solution of the Deuteron using Perturbation Theory (ongoing work with R. S. Azevedo and Prof. Bira van Kolck) University of Arizona Undergraduate Symposium - 2009 Pedro H. S. de Bruin Outline: The Deuteron EFT Perturbative Solution Conclusion

2. The Deuteron Only bound-state in the two-nucleon system Weak binding: B ≈ 2.22 MeV Large size: ≈ 46 MeV, Quantum Numbers: I = 0, S = 1 and J = 1

3. What is EFT? A classical example r0r0 R Unknown Charge distribution Low energy constants (LECs) Power counting Based on dimensional analysis Symmetries of E&M Systematic low-energy approximation Ex. Multipole expansions in Electrodynamics B. Long slides (08)

4. The Deuteron Hamiltonian long-range ~ short-range Central term Tensor term j = total angular momentum

5. Schroedinger Equation Very complicated!

6. Perturbative Solution Observables independent of cutoff

7. Leading Order Normalization Condition:

8. Next-to-Leading Order

9. Sharp Cutoff Oscillates rapidly Jackiw (1991)

10. Gaussian Cutoff NLO has been done. Results very complicated. Nagels et al., Phys. Rev. D (1978) van Kolck et al., Phys Rev. C (1996)

11. Conclusion and Outlook EFT for the deuteron Perturbative solution of the deuteron in LO and NLO What Next: Numerical fit to scattering data LO: fitted to NLO: fitted to To be compared with numerical non-perturbative solution