Reference Quadrupole Moments of Transition Elements from Lamb Shifts in Muonic Atoms

TL;DR

This paper introduces a new method using muonic x-ray spectroscopy with cryogenic microcalorimeters to measure electric quadrupole moments of light transition elements with high precision, aiding nuclear and quantum chemistry research.

Contribution

It proposes a novel experimental approach combining advanced detectors and theoretical calculations to accurately determine quadrupole moments from Lamb shift measurements.

Findings

Feasibility demonstrated through calculations and simulations.

Uncertainty in quadrupole moments can be reduced by up to tenfold.

Method enables rapid, precise measurements within a day.

Abstract

We present a novel method for accurately measuring the absolute electric quadrupole moments of light transition elements $(23 \leq Z \leq 30 )$. Our approach is based on performing precision muonic x-ray spectroscopy of the $2s-2p$ manifold, which is also referred to as the Lamb shift. These transitions are too weak to be detected with dispersive methods and too overlapping to be resolved by solid-state detectors. Here, we propose the use of cryogenic microcalorimeters, which possess high efficiency and excellent energy resolution in the relevant energy regime, coupled with state-of-the-art theoretical calculations. We demonstrate the feasibility of this approach by performing extensive calculations and realistic simulations. In this way, we establish that the uncertainty in the absolute moment, which is transferred to the quadrupole moments of all isotopes in the chain, could be reduced by up to an order of magnitude within a day of measurement. These precise reference quadrupole moments serve as valuable inputs for nuclear structure studies and for benchmarking state-of-the-art quantum chemistry calculations in open-shell elements.