solution of the deuteron using perturbation theory
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
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
What is EFT? A classical example
r0R
Unknown
Charge
distribution
Low energy
constants
(LECs)
Power counting
Based on dimensional analysis
Symmetries
of E&M
)(R
Systematic low-energy approximation
Ex. Multipole expansions in Electrodynamics
B. Long slides (08)
The Deuteron Hamiltonian
long-range ~ short-range
Central term
Tensor term
j = total angular momentum
Schroedinger Equation
Very complicated!
Perturbative Solution
Observables independent of cutoff
Leading Order
Normalization Condition:
Next-to-Leading Order
Sharp Cutoff
Oscillates rapidly
Jackiw (1991)
Gaussian Cutoff
NLO has been done. Results very complicated.
Nagels et al., Phys. Rev. D (1978)van Kolck et al., Phys Rev. C (1996)
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