Clusters and their fundamental role for Trojan Horse Method
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.