The Trojan Horse Method (THM) lays its foundations on the cluster structure of light nuclei which are usually used as “Trojan horses”. Many of them were successfully employed in the last decades to shed light to numerous astrophysical problems. Cluster structure and dynamics also suggest a series of tests which may be performed in order to strengthen the basis of the method. Among them pole invariance was investigated for three different situations. In fact, the cross sections for the \(^6\)Li(d, \(\alpha )^4\)He, \(^2\)H(d,p)\(^3\)H and \(^7\)Li(p, \(\alpha )^4\)He binary reactions were measured for several break-up schemes and analyzed within the framework of the Plane Wave Impulse Approximation (PWIA). The indirect results extracted by using different Trojan Horse nuclei (e.g. \(^2\)H, \(^3\)He, \(^6\)Li) were compared with each other as well as with direct measurements of the corresponding astrophysical reactions. The very good agreement obtained confirms the applicability of the pole approximation and of the pole invariance method, namely the independence of binary indirect cross section on the chosen Trojan Horse nucleus, at least for the cases investigated. Moreover, we can verify that the effect of using a charged or a neutral particle as a spectator implies negligible corrections consistent with the experimental errors. In addition, the dynamics of clusters inside the Trojan Horse nucleus and their fingerprints on the measured momentum distribution play a key role for THM applications. In this article we will therefore discuss also these assertions studied in different systems(\(^2\)H, \(^3\)He, \(^6\)Li, \(^9\)Be, \(^{14}\)N) and in particular for the deuteron case the relative impact of s and d waves in the momentum distribution will also be examined.

特洛伊木马方法（THM）的基础是通常被称为“特洛伊木马”的轻核的簇结构。在过去的几十年中，他们中的许多人被成功雇用，以阐明许多天体物理学问题。群集结构和动力学还建议进行一系列测试，以增强该方法的基础。其中针对三种不同情况研究了极不变性。实际上，\（^ 6 \） Li（d，\（\ alpha）^ 4 \） He，\（^ 2 \） H（d，p）\（^ 3 \） H和\的横截面（^ 7 \） Li（p，\（\ alpha）^ 4 \）测量了几种分解方案的二元反应，并在平面波脉冲近似（PWIA）框架内进行了分析。通过使用不同的特洛伊木马核（例如\（^ 2 \） H，\（^ 3 \） He，\（^ 6 \）提取的间接结果Li）相互比较，并直接测量了相应的天体物理反应。获得的非常好的一致性证实了极点逼近和极点不变性方法的适用性，即至少在所研究的情况下，所选特洛伊木马核的二元间接截面的独立性。此外，我们可以验证使用带电或中性粒子作为旁观者的效果意味着与实验误差一致的可忽略不计的校正。此外，特洛伊木马核内部簇的动态及其在测量动量分布上的指纹对于THM应用也起着关键作用。因此，在本文中，我们还将讨论在不同系统（\（^ 2 \） H，\（^ 3 \） He，\（^ 6 \） Li，\（^ 9 \） Be，\（^ {14} \） N），特别是在氘核的情况下，s和d波的相对影响动量分布也将被检查。