Sample of collision participants in nuclear collisions.
MC procedure to define collision participants.
The inelastic hadron–nucleus interactions at ultra–relativistic energies are considered as independent hadron–nucleon collisions. It was shown long time ago [AA78] for the hadron–nucleus collision that such a picture can be obtained starting from the Regge–Gribov approach [MA76], when one assumes that the hadron-nucleus elastic scattering amplitude is a result of reggeon exchanges between the initial hadron and nucleons from target–nucleus. This result leads to simple and efficient MC procedure [S86][ANS90] to define the interaction cross sections and the number of the nucleons participating in the inelastic hadron–nucleus collision:
We should randomly distribute \(B\) nucleons from the target-nucleus on the impact parameter plane according to the weight function \(T([\vec{b}^{B}_{j}])\). This function represents probability density to find sets of the nucleon impact parameters \([\vec{b}^{B}_{j}]\), where \(j=1,2,...,B\).
For each pair of projectile hadron \(i\) and target nucleon \(j\) with choosen impact parameters \(\vec{b}_{i}\) and \(\vec{b}^{B}_{j}\) we should check whether they interact inelastically or not using the probability \(p_{ij}(\vec{b}_{i}-\vec{b}^{B}_{j},s)\), where \(s_{ij}=(p_{i}+p_{j})^2\) is the squared total c.m. energy of the given pair with the \(4\)–momenta \(p_{i}\) and \(p_{j}\), respectively.
In the Regge–Gribov approach [MA76] the probability for an inelastic collision of pair of \(i\) and \(j\) as a function at the squared impact parameter difference \(b_{ij}^2=(\vec{ b}_i-\vec{ b}_j^B)^2 \) and \(s\) is given by
where
is the probability to find the \(n\) cut Pomerons or the probability for \(2n\) strings produced in an inelastic hadron-nucleon collision. These probabilities are defined in terms of the (eikonal) amplitude of hadron–nucleon elastic scattering with Pomeron exchange:
The quantities \(z(s)\) and \(\lambda (s)\) are expressed through the parameters of the Pomeron trajectory, \(\alpha _P^{^{\prime }}=0.25 \mbox{ GeV}^{-2}\) and \(\alpha _P(0)=1.0808\), and the parameters of the Pomeron-hadron vertex \(R_P\) and \(\gamma _P\):
respectively, where \(s_0\) is a dimensional parameter.
In Eqs. (227),(228) the so–called shower enhancement coefficient \(c\) is introduced to determine the contribution of diffractive dissociation [MA76]. Thus, the probability for diffractive dissociation of a pair of nucleons can be computed as
where
The Pomeron parameters are found from a global fit of the total, elastic, differential elastic and diffractive cross sections of the hadron–nucleon interaction at different energies.
For the nucleon-nucleon, pion-nucleon and kaon-nucleon collisions the Pomeron vertex parameters and shower enhancement coefficients are found: \(R^{2N}_{P}=3.56 \mbox{ GeV}^{-2}\), \(\gamma^{N}_P=3.96 \mbox{ GeV}^{-2}\), \(s^{N}_{0} = 3.0 \mbox{ GeV}^{2}\), \(c^{N}=1.4\) and \(R^{2\pi}_{P} = 2.36 \mbox{ GeV}^{-2}\), \(\gamma^{\pi}_P = 2.17 \mbox{ GeV}^{-2}\), and \(R^{2K}_{P} = 1.96 \mbox{ GeV}^{-2}\), \(\gamma^{K} _P = 1.92 \mbox{ GeV}^{-2}\), \(s^{K}_{0} = 2.3 \mbox{ GeV}^{2}\), \(c^{\pi}=1.8\).
Separation of hadron diffraction excitation.
For each pair of target hadron \(i\) and projectile nucleon \(j\) with choosen impact parameters \(\vec{b}_{i}\) and \(\vec{b}^{B}_{j}\) we should check whether they interact inelastically or not using the probability
If interaction will be realized, then we have to consider it to be diffractive or nondiffractive with probabilities
and