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Solution of the Deuteron using Perturbation Theory

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. The Deuteron.

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Solution of the Deuteron using Perturbation Theory

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  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. B. Long slides (08) What is EFT? A classical example Ex. Multipole expansions in Electrodynamics Unknown Charge distribution R r0 Symmetries of E&M Power counting Low energy constants (LECs) Based on dimensional analysis Systematic low-energy approximation

  4. The Deuteron Hamiltonian long-range ~ short-range Tensor term Central 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 Nagels etal., Phys. Rev. D (1978) van Kolck et al., Phys Rev. C (1996) NLO has been done. Results very complicated.

  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

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