Ab initio theory of light nuclei with inverse scattering NN interaction

1. Ab initio theory of light nuclei with inverse scattering NN interaction EMIN-2012: September 21, 2012 Andrey M. ShirokovMoscow State University Collaborators: V. Kulikov (Moscow State University) J. Vary and P. Maris (IowaState University) A. Mazur (Pacific NationalUniversity, Khabarovsk)

2. What are we doing?

3. Large-scale ab initio No-core Shell Model calculations What are we doing?

4. Large-scale ab initio No-core Shell Model calculations + new realistic NN interaction JISP What are we doing?

5. Ab initio:

6. Ab initio: • No model assumptions (shell model with inert core, cluster model, etc., are not ab initio)

7. Ab initio: • No model assumptions (shell model with inert core, cluster model, etc., are not ab initio) • Ab initio approaches: • Faddeev (A ≤ 4) • hyperspherical(A ≤ 6) • Green function’s Monte Carlo (A ≤ 13) • no-core shell model (A < 20) • coupled-cluster approach (around closed shells)

8. Modern NN interaction models:

9. Modern NN interaction models: • Realistic (phenomenological) meson-exchange NN potentials (Nijmegen, Bonn, Argonne) + NNN phenomenological potentials

10. Modern NN interaction models: • Realistic (phenomenological) meson-exchange NN potentials (Nijmegen, Bonn, Argonne) + NNN phenomenological potentials • EFT (ChPT) NN potentials + NNN EFT (ChPT) potentials

11. Modern NN interaction models: • Realistic (phenomenological) meson-exchange NN potentials (Nijmegen, Bonn, Argonne) + NNN phenomenological potentials • EFT (ChPT) NN potentials + NNN EFT (ChPT) potentials • JISP16 NN interaction no NNN interaction fitted to light nuclei

12. Why would be nice to avoid NNN forces?

13. Role of NNN force? • W. Polyzou and W. Glöckle theorem (Few-body Syst. 9, 97 (1990)): H=T+VijH’=T+V’ij+Vijk, where Vijand V’ijare phase-equivalent, H and H’ are isospectral. Hope:H’=T+V’ij+VijkH=T+Vij with (approximately) isospectralH and H’ . JISP type interaction seems to be NN interaction minimizing NNN force. Without NNN force calculations are simpler, calculations are faster, larger model spaces become available; hence predictions are more reliable.

14. JISP = J-matrix inverse scattering potential

15. J-matrix formalism:scattering in the oscillator basis

16. JISP NN interaction • NN interaction is a small matrix of the in the oscillator basis: 9ћΩtruncation, ћΩ = 40 MeV fast convergence of shell model calculations • Good description of NN data

17. JISP16 properties • 1992 npdata base (2514 data): χ2/datum = 1.03 • 1999 npdata base (3058 data): χ2/datum = 1.05

18. PETs

19. Ambiguity of JISP interaction • Any unitary transformation of NN Hamiltonian H generates a Phase-equivalent transformation (PET). • Simplest PETs with continuous parameters are used to fit properties of light nuclei in No-core Shell Model (NCSM) calculations.

20. JISP NN interaction • A. M. Shirokov, A. I. Mazur, S. A. Zaytsev, J. P. Vary, T. A. Weber, Phys. Rev. C 70, 044005 (2004): A ≤ 4 • A. M. Shirokov, J. P. Vary, A. I. Mazur, S. A. Zaytsev, T. A. Weber, Phys. Lett. B 621, 96 (2005): A ≤ 6 — JISP6 • A. M. Shirokov, J. P. Vary, A. I. Mazur, T. A. Weber, Phys. Lett. B 644, 33 (2007): A ≤ 16 — JISP16

21. Modern NN interaction models: • Meson-exchange NN potentials (Nijmegen, Bonn, Argonne) and EFT (ChPT) NNpotentials + NNN phenomenological or EFT (ChPT) potentials • JISP16 NN interaction good enough convergence with bare interaction bad convergence; effective interaction is needed

22. Our initial approach

27. From effective interactions to no-core full configuration calculations • Extrapolation: Egs(Nmax) = ae-bNmax+ Egs(∞) • Works with bare interaction only (e.g., JISP16) • Example: P. Maris, J. P. Vary, A. M. Shirokov, Phys. Rev. C 79, 014308 (2009)

28. Successful prediction: 14F • 1,990,061,078 basis states • each ħΩ point requires 2 to 3 hours on 7,626 quad-core compute nodes (30,504 processors in total) at the Jaguar supercomputer at ORNL

29. Successful prediction: 14F spectrum

30. Deficiency of JISP16 revealed by NCFC extrapolations

31. How it looked initially: How it looks now:

32. Improved interaction JISP162010 • Obtained by a more accurate fit to nuclear data using NCFC

33. Nuclear matter with JISP16

34. Nuclear matter • JISP162010 improves NM properties. • Strong dependence on high partial waves makes it possible to fit NM to phenomenological data without violating description of light nuclei.

35. Conclusions • Ab initio NCFC approach based on NCSM is able to describe light nuclei with A < 20. • JISP16 provides a good description of NN data and binding energies, spectra, EM transitions in light nuclei, etc., without NNN forces. • An improved version JISP162010 providing a more accurate description of nuclei is available. Later this version will be additionally fitted to nuclear matter too. • Further development: description of other observables, e.g., rms radii in heavy enough nuclei, description of heavier nuclei, design of charge-dependent version of the interaction.

36. Thank you!