[Paper Review] Electromagnetic Strength Distributions from the Ab Initio No-Core Shell Model

Christina Stumpf, Tobias Wolfgruber+1 more|arXiv (Cornell University)|Sep 20, 2017

Electromagnetic Scattering and Analysis5 references3 citations

TL;DR

This paper presents an ab initio approach combining the No-Core Shell Model (NCSM) with the Lanczos strength-function method to compute electromagnetic transition strength distributions—E0, E1, and E2—across the oxygen isotopes from 16O to 24O. Using chiral two- and three-nucleon interactions, it achieves full energy-range coverage from low-lying states to giant resonances, revealing fragmentation, fine structure, and pygmy modes, while exposing limitations in RPA-type approximations and providing quantitative constraints on nuclear interactions.

ABSTRACT

We present an ab initio approach for the description of collective excitations and transition strength distributions of arbitrary nuclei up into the sd-shell that based on the No-Core Shell Model in combination with the Lanczos strength-function method. Starting from two- and three-nucleon interactions from chiral effective field theory, we investigate the electric monopole, dipole, and quadrupole response of the even oxygen isotopes from 16-O to 24-O. The method describes the full energy range from low-lying excitations to the giant resonance region and beyond in a unified and consistent framework, including a complete description of fragmentation and fine-structure. This opens unique opportunities for understanding dynamic properties of nuclei from first principles and to further constrain nuclear interactions. We demonstrate the computational efficiency and the robust model-space convergence of our approach and compare to established approximate methods, such as the Random Phase Approximation, shedding new light on their deficiencies.

Motivation & Objective

• To develop a first-principles ab initio framework for computing electromagnetic transition strength distributions across the sd-shell, including low-lying excitations and giant resonances.
• To overcome the limitations of approximate methods like RPA and SRPA by providing a fully consistent, converged description from first principles.
• To test the predictive power of modern chiral nuclear interactions (NN+3N) by comparing computed strength distributions to experimental data.
• To investigate the emergence of pygmy dipole and quadrupole resonances in neutron-rich oxygen isotopes.
• To assess the role of ground-state correlations and non-localities in determining resonance energies beyond mean-field expectations.

Proposed method

• The No-Core Shell Model (NCSM) is used to solve the nuclear many-body problem with chiral two- and three-nucleon interactions, employing a harmonic oscillator basis truncated at $N_{\text{max}}$.
• Importance truncation is applied to control the factorial growth of basis dimensions and improve convergence.
• The Lanczos strength-function method is applied to the ground-state eigenvector to compute transition strength distributions efficiently and with high convergence.
• The method enables direct calculation of strength functions across the full energy spectrum, including fragmentation and fine structure, without relying on continuum approximations.
• Isospin decomposition is used to identify neutron-dominated low-lying $2^+$ states contributing to the E2 strength, indicating pygmy quadrupole character.
• The approach is validated by convergence tests with increasing $N_{\text{max}}$ and compared to RPA and SRPA approximations.

Experimental results

Research questions

• RQ1 How do ab initio calculations of electromagnetic strength distributions in oxygen isotopes compare to experimental data, particularly for the isoscalar giant monopole resonance?
• RQ2 To what extent do modern chiral interactions (NN+3N) reproduce the observed systematics of E1 and E2 strength distributions across the oxygen isotopic chain?
• RQ3 Why do predicted resonance energies for E0, E1, and E2 modes lie too high despite the interactions reproducing incompressibility and ground-state radii?
• RQ4 What is the role of low-lying, neutron-dominated $2^+$ states in the E2 strength distribution, and how does this relate to the pygmy quadrupole resonance?
• RQ5 How do the deficiencies of RPA and SRPA manifest in the context of ab initio benchmark calculations?

Key findings

• The NNLO$_{\text{sat}}$ interaction predicts a centroid energy of 19.8 MeV for the isoscalar E0 giant monopole resonance in 16O, which is too high compared to the experimental value of 13.5 MeV, despite reproducing nuclear matter incompressibility.
• The isovector E1 strength distribution broadens toward 20O and narrows toward 24O, with increasing low-energy strength consistent with the emergence of pygmy dipole resonances.
• The dipole polarizability increases from 0.48 fm³ for 16O to 1.09 fm³ for 24O under the NNLO$_{\text{sat}}$ interaction, though all values remain below the experimental 0.58 fm³ for 16O.
• Low-lying $2^+$ states in 18O and beyond contribute significantly to the isoscalar E2 strength, indicating a pygmy quadrupole resonance, with strong neutron dominance confirmed via isospin decomposition.
• The NN+3N(400) interaction underestimates ground-state radii by ~10%, leading to a relative shift in strength distributions compared to NNLO$_{\text{sat}}$, which is tuned to reproduce experimental radii.
• The Lanczos method demonstrates robust convergence with $N_{\text{max}}$, enabling reliable strength function calculations across the full energy range without continuum approximations.