## 1 Introduction  
The use of delayed luminescence in dating ceramic objects dates back to the Sixties of the past century. It is based on dosimetric principles; in practice, the first type of delayed luminescence, thermoluminescence (TL), uses the light emitted obtained by heating a sample as a measurement of the previously absorbed radiation dose by the sample under study, since its last heating to high temperature. In the next section, a few details are given to better describe the phenomenon. The linear relationship between emitted light and accumulated dose is fundamental in making TL a very good dosimetric technique. It is currently used to measure the exposure to radiation of professionals working in radiation fields, such as radiologists. Of course, in these cases the materials used are tailored to present an intense emission as a consequence to radiation exposure, well suited to be detected, as it is detailed in the following. On the contrary, in the application of TL to dating, the material to be used cannot be chosen. In many ceramics and bricks, quartz is contained in relatively large amounts and acts as a good natural dosimeter [1]. Other minerals, such as feldspars, could be good dosimeters, even if some problems are often present, such as the lack of stability of the source of TL signal in time, the so-called \"anomalous fading\" [2]. In order to date a ceramic by TL, the total absorbed dose since the last heating that generally corresponds to its making in a kiln can be determined by comparing the light emitted due to the exposure to the natural radiation environment in the centuries to artificial irradiations in laboratory. It must be noted that different radiation doses can be accumulated in different samples of the same age, depending on the dose rate, that is, the higher the dose rate, the more intense the natural irradiation. Therefore, the intensity of the mentioned natural radiation environment must be measured. This can generally be achieved by determining the amount of radioactivity of the sample itself and of the surrounding environment. These measurements and the connected experimental troubles are briefly described in the next sections. In the last decades, many applications of TL dating have demonstrated their feasibility in determining with acceptable precision the sequence in an archaeological stratigraphy or in determining the various phases of construction, modification and restoration in a historical building. The basic idea of dating by TL can be applied, in principle, to the material remaining in the interior of a bronze statue after its casting, the so-called clay core. In favourable cases, this material behaves like a ceramic and the procedures used for dating ceramics can be also applied to clay cores. This is extremely important, considering that, with very few exceptions that are not treated here, metal objects cannot be dated by absolute techniques. In this work, the application of TL dating to clay cores is introduced and the specific difficulties deriving from the characteristics of this material, together with the complex determination of the radiation environment, are commented on. Very few cases of application of TL to the dating of clay cores are present in the literature [3,4], mainly due to the many sources of uncertainty mentioned above and to the difficulties in correctly managing the experimental data. The first application of TL techniques to clay cores dates back to 1974, when [PERSON] [3] succeeded in testing the authenticity of core materials from a Bronze Horse of the New York Metropolitan Museum of Art. Other examples of TL applied to clay core are reported, still in the field of authenticity test [5]. In the last decades a few interesting studies of TL dating were carried out in our laboratory (_Lupa Capitolina_, the horse bronze statue from Musei Capitolini and the [PERSON] statue); they are re-considered in this work aiming at obtaining more accurate results by applying new statistical approaches.