Collaborators: V. Kulikov (Moscow State University)

1. NN interaction JISP16: Current status and prospectBonn, September 1, 2009Andrey M. ShirokovMoscow State University & Iowa State University Collaborators: V. Kulikov (Moscow State University) J. Vary, T. Weber, and P. Maris (IowaState University) A. Mazur, E. Mazur and S. Zaytsev(Pacific National University)

2. JISP = J-matrix inverse scattering potential

3. J-matrix: • Scattering theory in L2 basis: oscillator basis or Laguerre basis • First in atomic physics: H. A. Yamani, L. Fishman, J. Math. Phys. 16 410 (1975). • In nuclear physics (oscillator basis): G. F. Filippov and I. P. Okhrimenko, Sov. J. Nucl. Phys. 32, 480 (1980) • Inverse scattering: S. A. Zaytsev, Theor. Math. Phys. 115, 575 (1998); A. I. Mazur, S. A. Zaytsev, J. P. Vary, T. A. Weber, Phys. Rev. C 70, 044005 (2004).

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

5. JISP NN interaction • NN interaction is a small matrix of the in the oscillator basis: 9ћ truncation, ћ = 40 MeV  fast convergence of shell model calculations • Good description of NN data

6. JISP16 properties • 1992 np data base (2514 data): 2/datum = 1.03 • 1999 np data base (3058 data): 2/datum = 1.05

7. 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.

8. 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, S. A. Zaytsev, T. A. Weber, Phys. Lett. B 644, 33 (2007): A ≤ 16 — JISP16

14. From effective interactions to full configuration calculations • Extrapolation: Egs(Nmax) = ae-bNmax+ Egs() • Works with bare interaction only • Example: P. Maris, J. P. Vary, A. M. Shirokov, Phys. Rev. C 79, 014308 (2009)

16. Improved interaction JISP16-09 • Obtained by a more accurate fit to nuclear data

17. Nuclear matter with JISP16 Thanks to Scott Bogner!

18. Nuclear matter • JISP16-09 improves NM properties. • Strong dependence on high partial waves makes it possible to fit NM to phenomenological data without violating description of light nuclei.

19. NN interaction JISP16 is used without NNN forces

20. Why would be nice to avoid NNN forces?

21. 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) isospectral H and H’ . JISP16 seems to be NN interaction minimizing NNN force. Without NNN force calculations are simpler, calculations are faster, larger model spaces become available.

22. Conclusions • JISP16 provides a good description of NN data and binding energies, spectra, EM transitions in light nuclei, etc., without NNN forces. • An improved version JISP16-09 providing a more accurate description of nuclei will be available soon. 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.

23. Thank you!