Ab initio theory of light nuclei with inverse scattering NN

interaction

EMIN-2012: September 21, 2012 Andrey M. Shirokov

Moscow State University Collaborators: V. Kulikov (Moscow State University)J. Vary and P. Maris (Iowa State University) A. Mazur (Pacific National University, Khabarovsk)

What are we doing?

What are we doing?

Large-scale ab initio No-core Shell Model calculations

What are we doing?

Large-scale ab initio No-core Shell Model calculations + new realistic NN interaction JISP

Ab initio:

Ab initio:• No model assumptions (shell model with inert core,

cluster model, etc., are not ab initio)

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)

Modern NN interaction models:

Modern NN interaction models:

• Realistic (phenomenological) meson-exchange NN potentials (Nijmegen, Bonn, Argonne)

+ NNN phenomenological potentials

Modern NN interaction models:

• Realistic (phenomenological) meson-exchange NN potentials (Nijmegen, Bonn, Argonne)

+ NNN phenomenological potentials• EFT (ChPT) NN potentials + NNN EFT (ChPT) potentials

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

Why would be nice to avoid NNN forces?

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’ .

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.

JISP = J-matrix inverse scattering potential

J-matrix formalism:scattering in the oscillator basis

JISP NN interaction

• NN interaction is a small matrix of the in the oscillator basis:

9ћΩ truncation, ћΩ = 40 MeV fast convergence of shell model calculations• Good description of NN data

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

PETs

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.

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

Modern NN interaction models:

• Meson-exchange NN potentials (Nijmegen, Bonn, Argonne) and EFT (ChPT) NN potentials

+ NNN phenomenological or EFT (ChPT) potentials

• JISP16 NN interaction good enough convergence with bare

interaction

bad convergence; effective interaction is needed

Our initial approach

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)

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

Successful prediction: 14F spectrum

• Deficiency of JISP16 revealed by NCFC extrapolations

How it looked initially:

How it looks now:

Improved interaction JISP162010

• Obtained by a more accurate fit to nuclear data using NCFC

Nuclear matter with JISP16

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.

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.

Thank you!