[en] In the calculations of the many-nucleon bound states, using the realistic nucleon-nucleon potential, and a three- and four-nucleon potential, the Exact Many-Body Nuclear Cluster Model (EMBNCM) was found to give accurate results, that converege much more rapidly, than those obtained by the Faddeev equation calculations. With the use of realistic nucleon-nucleon potentials, and many-nucleon potentials, containing strong tensor, Majorana, and repulsive core components, the many-body cluster structure of 16O, 27Al, 44Ti, and 48Ti is discussed. In 27Al(p,x)Na reactions we assume that two different nuclear cluster structures of 27Al, gives us two different isotopes of Na: 22Na and 24Na. But the most important result is the existence of two different permutations symmetries of 27Al. Using new method for calculation of nuclear cluster structure of 27Al, we have found two different nuclear cluster structures of 27Al: 24Na+3He and 25Na+d. The internal nuclear cluster wave functions of different nuclear cluster models (nuclear cluster isomers) of the same isotope are not equivalent, if we take into account Many-Body Nuclear Forces, such as 3BF and 4BF. The core clusters of 16O, 27Al, 44Ti, and 48Ti nuclei have a trigonal-pyramide Td, D2d, and C3v symmetry, while exterior clusters in 16O and 27Al[(24Na +3 He)model] nuclei have a trigonal symmetry C2v, and D3h. We have developed a new system of Jacobi coordinates for our EMBNCM model with the symmetry above. The new computer code for determination of direct nuclear cluster reactions has been written in Mathematica 5 programming language. We have found a high level of dependence of the nuclear cluster wave functions from the center of mass and cluster effects

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