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Effective Theory of Shallow Nuclei

Effective Theory of Shallow Nuclei. U. van Kolck. University of Arizona. Supported in part by US DOE. Background by S. Hossenfelder. Outline. Introduction Effective (Field) Theories Few-nucleon systems Halo nuclei Outlook . c. N.B. On wiki page:.

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Effective Theory of Shallow Nuclei

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  1. Effective TheoryofShallow Nuclei U. van Kolck University of Arizona Supported in part by US DOE v. Kolck, Shallow Nuclei Background by S. Hossenfelder

  2. Outline • Introduction • Effective (Field) Theories • Few-nucleon systems • Halo nuclei • Outlook c N.B. On wiki page: • suggested reading • homework! v. Kolck, Shallow Nuclei

  3. MPI-Heidelberg Nuclear Chart see Bertulani’s lecture What are the nucleosynthesis reaction rates? What are the limits of nuclear existence? v. Kolck, Shallow Nuclei

  4. Nuclear scales perturbative QCD ~1 GeV see Schwenk’s lecture Chiral EFT Typical nuclei ~10 MeV ~150 MeV Contact and Halo/cluster EFTs Shallow nuclei ~1 MeV ~30 MeV TODAY v. Kolck, Shallow Nuclei

  5. In classical mechanics: bound-state size range of force e.g. square well reduced mass But… not always true in quantum mechanics! v. Kolck, Shallow Nuclei

  6. (center-of-mass frame) In quantum mechanics: elastic scattering (for simplicity) (N.B.: ) (conservation of energy) : given by certain probability amplitude – the “scattering amplitude” angular momentum Legendre polynomial partial-wave amplitude Two important properties: • Poles • Low-energy expansion bound states effective range shape parameter resonances (before any singularity) v. Kolck, Shallow Nuclei “Effective-Range Expansion” scattering length b.s.:

  7. square well, S-wave e.g. when generic fine-tuning etc. new scale emerges v. Kolck, Shallow Nuclei

  8. In the quantum world, one can have a b.s. with size much larger than the range of the force provided there is fine-tuning v. Kolck, Shallow Nuclei

  9. Feshbach resonance Chiral EFT: (incomplete) NLO Beane, Bedaque, Savage + v.K. ’02 cf. Beane + Savage. ’03 … Fukugita et al. ‘95 Lattice QCD: quenched cf. Beane, et al. ‘06 Regal + Jin ‘03 unitarity limit NN triplet scattering length Large deuteron size because v. Kolck, Shallow Nuclei

  10. c EFT : the basic idea more generally: same argument for any short-range potential same same wf tail similar observables systematic improvement: in the limit, v. Kolck, Shallow Nuclei just like multipole expansion

  11. Effective Hamiltonian fitted to 2-body data 3-body data etc. 3-body interaction no calculation in physics (except for TOE, if it exists) is ever exact “Whatever can happen will happen” Wikipedia quantum field theory v. Kolck, Shallow Nuclei

  12. Chen, Rupak + Savage ’99 fitted LO EFT NNLO EFT predicted NLO EFT Nijmegen PSA LO EFT fitted NLO EFT Nijmegen PSA predicted NNLO EFT v. Kolck, Shallow Nuclei

  13. Rupak ’01 fitted NNNNLO EFT v. Kolck, Shallow Nuclei

  14. Bedaque, Hammer + v.K. ’99 ’00 Hammer + Mehen ’01 Bedaque et al. ’03 … Bedaque + v.K. ’97 Bedaque, Hammer + v.K. ’98 … no 3-body force up to NNNNLO 3-body force already at LO fitted predicted v.Oers + Seagrave ‘67 NNLO EFT Dilg et al. ‘71 v.Oers + Seagrave ‘67 NLO EFT Kievsky et al. ‘96 LO EFT LO EFT fitted nothing predicted Dilg et al. ‘71 v. Kolck, Shallow Nuclei QED-like precision!

  15. Light nuclei Stetcu, Barrett +v.K., ‘06 LO EFT fitted to d, t, a ground-state binding energies Harmonic-oscillator basis fits works within ~10% ! see Rotureau’s lecture works within ~30% v. Kolck, Shallow Nuclei

  16. new scale leads to proliferation of shallow states (near driplines): loosely bound nucleons around tightly bound cores Halo/Cluster states separation energy core excitation energy core p n n p p p n n p n “ ” e.g. resonance at bound state at resonance at v. Kolck, Shallow Nuclei resonance at

  17. Bertulani, Hammer + v.K. ’02 fitted fitted LO NLO NLO EFT LO EFT Arndt et al. ’73 NLO EFT fitted scatt length only NNNLO EFT v. Kolck, Shallow Nuclei

  18. Higa, Hammer + v.K. ‘08 see Higa’s lecture Extra fitting parameters Bohr radius none fitted with and More fine-tuning!!! fine-tuning of 1 in 10 fine-tuning of 1 in 1000! v. Kolck, Shallow Nuclei

  19. What next Bertulani, Higa + v.K., in progress • Coulomb interaction in higher waves: e.g. • three-body states: e.g. 1) 2) • reactions: e.g. c.f. Kong + Ravndal ’99 Rotureau, in progress c.f. Bedaque, Hammer + v.K. ’99 Higa + Rupak, in progress c.f. Rupak ’01 v. Kolck, Shallow Nuclei

  20. SM Forecast QCD lattice Extrapolates to realistically small Chiral EFT Faddeev* eqs, … Extrapolate to larger and larger Contact EFT NCSM, … Halo/cluster EFT Low-energy reactions v. Kolck, Shallow Nuclei

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