# Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

## TL;DR

This paper analyzes the spectral statistics of molecular resonances in erbium isotopes, finding they are close to semi-Poisson distribution, which suggests intermediate spectral behavior between order and chaos, with implications for experimental resonance detection.

## Contribution

The study applies recent spectral surmises and analysis methods to experimental data, providing new insights into the resonance distribution in erbium isotopes without requiring spectrum unfolding.

## Key findings

- Resonances are close to semi-Poisson distribution.
- Analysis supports previous claims of missing resonances.
- Results suggest intermediate spectral behavior between Poisson and GOE.

## Abstract

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium $^{166}$Er and $^{168}$Er isotopes, produced as a function of magnetic field($B$) by Frisch et al. [Nature 507, (2014) 475], utilizing some recently derived surmises which interpolate between Poisson and GOE and without unfolding. Supplementing this with an analysis using unfolded spectrum, it is shown that the resonances are close to semi-Poisson distribution. There is an earlier claim of missing resonances by Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can be tested by more precise measurements in future experiments.