Abstract In the present work, we consider the filling and thermal emptying of traps and centers in a simple one-trap-one-recombination-center model in a small system such as a quartz grain in nature, when both the excitation and thermal release of electrons are very slow. Due to the nature of the very slow process, Monte Carlo simulations appear to be a very appropriate method. However, in parallel, we have applied an approximate analytical method and found practically the same results although the Monte Carlo results showed some small fluctuations due to the statistical nature of the procedure. This is in line with the experimental results which are also expected to have statistical fluctuations. The main result found is that after a long enough time, measured in hundreds or thousands years or more, the filling of the trap reaches a plateau which, depending on the parameters, may be very significantly smaller than the concentration of the trap in question. This equilibrium value is the same if we start from very low, e.g. zero concentration or very high, above the equilibrium value. This plateau level depends strongly on the relevant parameters. However, comparing simulations with activation energies of 1.2 eV and 1.3 eV shows strong dependence of the plateau level on the energy. Similarly, we can expect strong dependence on the temperature at which the sample is held. The results reached here and shown in Fig. 1 , Fig. 2 , Fig. 3 , Fig. 4 are based on the simplest OTOR model, but similar results of approaching a plateau level which are not due to the saturation of traps may occur in more complex systems as is demonstrated by simulations based on the Bailey model for quartz which includes several traps and centers.

中文翻译：

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热释光 (TL) 和光受激发光 (OSL) 的长时间激发和衰落之间的竞争

摘要 在目前的工作中，我们在一个简单的单阱一复合中心模型中考虑了在自然界中的石英颗粒等小系统中阱和中心的填充和热排空，当激发和热释放电子非常慢。由于非常缓慢的过程的性质，蒙特卡罗模拟似乎是一种非常合适的方法。然而，与此同时，我们应用了近似分析方法并发现了几乎相同的结果，尽管由于程序的统计性质，蒙特卡罗结果显示出一些小的波动。这与预期也会有统计波动的实验结果一致。发现的主要结果是，经过足够长的时间（以数百或数千年或更长时间计算）后，陷阱的填充达到了一个平台期，取决于参数，可能比所讨论的陷阱的浓度小得多。如果我们从非常低（例如零浓度或非常高）高于平衡值开始，则该平衡值是相同的。该平台水平在很大程度上取决于相关参数。然而，将模拟与 1.2 eV 和 1.3 eV 的活化能进行比较显示平台水平对能量的强烈依赖性。类似地，我们可以预期对样品保持温度的强烈依赖性。这里得到的结果如图 1、图 2、图 3、图 4 所示，是基于最简单的 OTOR 模型，