  We propose an experiment to measure the nuclear charge radii of light
elements with up to 20~times higher accuracy. These are essential both for
understanding nuclear physics at low energies, and for experimental and
theoretical applications in simple atomic systems. Such comparisons advance the
understanding of bound-state quantum electrodynamics and are useful for
searching for new physics beyond the Standard Model. The energy levels of
muonic atoms are highly susceptible to nuclear structure, especially to the
mean square charge radius. The radii of the lightest nuclei (with the atomic
number, $Z=1,2$) have been determined with high accuracy using laser
spectroscopy in muonic atoms, while those of medium mass and above were
determined using X-ray spectroscopy with semiconductor detectors. In this
communication, we present a new experiment, aiming to obtain precision
measurements of the radii of light nuclei $3 \leq Z \leq 10$ using
single-photon energy measurements with cryogenic microcalorimeters; a
quantum-sensing technology capable of high efficiency with outstanding
resolution for low-energy X-rays.
