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

¹ Department of Physics, Presidency University - 86/1 College Street, Kolkata 700 073, India
² Department of Applied Physics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda - Vadodara 390 001, India
³ Physical Research Laboratory - Navarangpura, Ahmedabad 380009, India
⁴ Physics Department, University of South Africa - P.O.Box 392, Pretoria 0003, South Africa

Received: 20 May 2017
Accepted: 10 July 2017

Abstract

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium ¹⁶⁶Er and ¹⁶⁸Er 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.