nn interaction jisp16: current status and prospect bonn, september 1, 2009 andrey m. shirokov moscow...
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NN interaction JISP16: Current status and prospect
Bonn, September 1, 2009
Andrey M. ShirokovMoscow State University & Iowa State University
Collaborators: V. Kulikov (Moscow State University)J. Vary, T. Weber, and P. Maris (Iowa State University) A. Mazur, E. Mazur and S. Zaytsev (Pacific National University)
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JISP
= J-matrix inverse scattering potential
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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).
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J-matrix formalism:scattering in the oscillator basis
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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
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JISP16 properties
• 1992 np data base (2514 data): 2/datum = 1.03• 1999 np data base (3058 data): 2/datum = 1.05
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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.
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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
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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)
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Improved interaction JISP16-09
• Obtained by a more accurate fit to nuclear data
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Nuclear matter with JISP16
Thanks to Scott Bogner!
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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.
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NN interaction JISP16 is used without NNN forces
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Why would be nice to avoid NNN forces?
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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 Vij and V’ij are 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.
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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.
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Thank you!