Treiman-Yang criterion for direct nuclear reactions

Updated evidence of the Trojan horse particle invariance for the2H(d,p)3H reaction

“…We will see how applying the conditions on the momentum distribution of the spectator, as discussed in Ref. [29], we can use the quite simple approach. This was already observed for the first time in Ref.…”

The12C(12C,α)20Ne and12C(12C,p)23Na reactions at the Gamow peak via the Trojan Horse Method

“…In Eq.1, E QF is not changed varying the projectile energy. What is done is to keep the beam energy at a fixed value and to vary the relative momentum p sx from its QF value to an upper limit given by κ xs = √ 2 μ xs B xs that represents the on-energy-shell (OES) a = (x s) bound state wave number [36]. This upper limit is usually few tens of MeV/c.…”

Recent Results of Direct Nuclear Reaction Experiments for Stellar Nucleosynthesis

“…Several attempts have been made for testing the pole-approximation of figure 1 and to select the dominant reaction mechanism intervening in the 0+N→1+2+S three-body reaction. In particular, Shapiro et al [25] demonstrated that the pole mechanism is the simplest reaction mechanism intervening in the 0+N→1+2+S reaction. The TY criterion [15,25] establishes that the amplitude of the reaction with 3 bodies in the final state should be invariant under rotation of the plane defined by the momenta of particles 1 and 2 about the sum of these momenta, in a reference frame in which the projectile or the cluster nucleus T is at rest.…”

“…In particular, Shapiro et al [25] demonstrated that the pole mechanism is the simplest reaction mechanism intervening in the 0+N→1+2+S reaction. The TY criterion [15,25] establishes that the amplitude of the reaction with 3 bodies in the final state should be invariant under rotation of the plane defined by the momenta of particles 1 and 2 about the sum of these momenta, in a reference frame in which the projectile or the cluster nucleus T is at rest. The quantities s ′ ,t ′ ,t do not change if in the anti-laboratory system (that is the system for which the momentum of particle 0 is equal 0) the momenta of the particles 1 and 2 are rotated with respect their sum, this direction corresponding to the one of the intermediate T particle momentum.…”

“…This Treiman-Yang criterion is a necessary condition for the pole mechanism of a reaction [25]. In the last 20 years, the THM was developed to study reactions of interest for nuclear astrophysics.…”