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NN- JISP: NN- s- p- ab initio
, 24 2006
A. () J. Vary and T. Weber (Iowa State University) A. Ma . ()


Ab initio:
· (, ) · Ab initio : · ; · ; · Green function's Monte Carlo; · no-core shell model; · coupled-cluster approach


Coupled cluster approach:


:
· : · Monte Carlo shell model · m-scheme + Lanczos ( no-core shell model);


m-scheme + Lanczos:
· : , "" J, L .. · Translationary invariant SM ( , J, L ..)



no-core SM ( m, J, L ..); J .



·

, J.


Lanczos itterations:

· ,


Lanczos itterations:


No-core shell model:


Effective interactions:
· "" ( ) ( ): G- . · No-core SM: Lee­Suzuki transformation, .. ab initio NN-, "" NN-.


Lee­Suzuki transformation:


Highlights
JISP = J-matrix inverse scattering potential PETs = phase-equivalent transformations No-core shell model: ab initio approach No three-nucleon forces Results for nuclei with A



ab exitu

16


J-matrix formalism:
scattering in the oscillator basis


PETs


ab initio ab exitu
· JISP16: J-matrix inverse scattering 9h NN potential with h = 40 MeV fitted to nuclei up through 16O · Only simplest PETs generated by 2x2 unitary matrix U are used · Ab exitu approach: · PETs: sd wave - fitting deuteron properties (rms radius and quadrupole moment) various p and one of d waves - fitting few levels of 6Li and binding energy of 16O in relatively small model spaces · All the rest NCSM results (other nuclei, larger model spaces) are ab initio


JISP16 properties
· 1992 np data base (2514 data): 2/datum = 1.03 · 1999 np data base (3058 data): 2/datum = 1.05





















Role of NNN force?
· W. Polyzou and W. GlЖckle 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.


Conclusions
· · JISP16 provides a realistic description of two-body and many-body properties, comparable with modern realistic NN + NNN forces Convergence of NCSM calculations with JISP16 is faster, even the bare JISP16 calculation convergence is reasonable, I.e. the results are more reliable. A confidence region of the binding energy predictions can be obtained for many nuclei by comparing the bare and effective interaction results


Plans
· · · · JISP16 improvement by the fit to the same nuclei Charge-dependent JISP16 Extending the calculations to the sd shell Scattering calculations: NCSM + J-matrix