Model space truncation in shell-model fits

TL;DR

This study investigates how truncating the shell-model space affects nuclear binding energies and spectra, showing that refitting interaction parameters can largely recover the original energies with minimal residual error.

Contribution

It demonstrates that a small number of parameter adjustments can effectively compensate for space truncation effects in shell-model calculations.

Findings

Truncation significantly impacts binding energies but less so on excitation energies.

Refitting a few parameters recovers about 90% of the energy shifts.

Residual errors after refitting are comparable to empirical experimental errors.

Abstract

We carry out an interacting shell-model study of binding energies and spectra in the $sd$-shell nuclei to examine the effect of truncation of the shell-model spaces. Starting with a Hamiltonian defined in a larger space and truncating to the $sd$ shell, the binding energies are strongly affected by the truncation, but the effect on the excitation energies is an order of magnitude smaller. We then refit the matrix elements of the two-particle interaction to compensate for the space truncation, and find that it is easy to capture 90% of the binding energy shifts by refitting a few parameters. With the full parameter space of the two-particle Hamiltonian, we find that both the binding energies and the excitation energy can be fitted with remaining residual error about 5% of the average error from the truncation. Numerically, the rms initial error associated with our Hamiltonian is 3.4 MeV and the remaining residual error is 0.16 MeV. This is comparable to the empirical error found in $sd$-shell interacting shell model fits to experimental data\cite{br06}.