## 1 Introduction  
The demand for renewable energy from natural sources, like sunlight and wind, is rapidly increasing all over the world. The development of high-performance storage devices, like lithium rechargeable batteries, is important for stably using these renewable energies [1]. The lithium rechargeable batteries, as storage devices, must be high capacity, safe to use, and have a long lifetime. Increasing the size of the cell is important to achieve high capacity; observing the lithium reaction in situ and in operando in a local region in commercialized rechargeable cells is important for a long lifetime and ensuring safety. So far, various experimental techniques for observing lithium rechargeable batteries have been reported using synchrotron X-rays and neutron and electron particle beams, and also, the electronic and geometric structures of the materials have been characterized using various length and time scales [2]. Recent cryo-electron microscopy techniques have achieved characterization of the electrode materials toward the realization of next-generation batteries [3; 4; 5; 6]. These studies clearly visualize lithium dendrites.  
Among them, Compton scattering imaging is a promising technique for non-destructively observing the structure of the matter in a local region [7]. Compton scattering imaging is an experimental technique that uses high-energy X-rays. High-energy X-rays have high matter penetration power, which allows large-scale non-destructive construction measurement. High-energy X-rays can be used to measure light elements, as incoherent scattering (Compton) effects are enhanced with the interaction between photons and electrons. These advantages of Compton scattering imaging have been applied to a variety of fields, including the medical and security fields [8; 9]. However, these studies have been mainly performed using a proportional counter, such as a flat-panel detector and linear array detectors, and do not analyze the energy of Compton scattering X-ray photons.  
We have been developing a method for non-destructively and quantitatively monitoring lithium ions in the cell using Compton scattering imaging combined with a synchrotron-based high-energy X-ray and energy-dispersive-type detector. Thus far, we have applied this technique to the commercial lithium primary cell CR2032 under discharge, where, by measuring the Compton scattering intensities, the migration of lithium ions from the anode to the cathode was visualized as the difference in the electron density, and the structural changes due to the volume expansion of the electrodes were revealed [10]. These results showed that the difference in the Compton scattering intensities produced by the difference in the electron density enabled the non-destructive estimation of the matter in the cell. Additionally, the change in the lithium concentration with the charge and discharge of the cell could be quantitatively determined from the line-shape of the Compton scattering X-ray energy spectrum, called the Compton profile, using line-shape parameter analysis, also known as S-parameter analysis [11]. Lithium compositions in the commercial lithium rechargeable battery VL2020 at the cathode and anode were simultaneously obtained while cycling [12]. S-parameter analysis was also used to show the dependency of the cycle rate on the lithiation state in the VL2020 cell [13] and to non-destructively identify the difference between the fresh and aged 18650-type cells with micrometer-scale spatial resolution [14]. However, the Compton scattering X-ray intensity and the S-parameter analysis were performed individually. Therefore, in this study, we non-destructively identified the degradation state of the commercial coin-type cell by combining both the Compton scattering X-ray intensities and S-parameter analysis methods.