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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

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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

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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)

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

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Schroedinger Equation Very complicated!

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Perturbative Solution Observables independent of cutoff

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Leading Order Normalization Condition:

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Next-to-Leading Order

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Sharp Cutoff Oscillates rapidly Jackiw (1991)

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

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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

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