ATTRACTIVE INTER - PARTICLE FORCE IN VAN DER WAALS MODEL OF MULTICOMPONENT HADRON GAS IN THE GRAND CANONICAL ENSEMBLE
Ya.D. Krivenko-Emetov1,2
1Institute for Nuclear Research, National Academy of Sciences of Ukraine
2National Technical University of Ukraine, 03056 Kyiv
For the last decade, statistical models of hadron gas are actively used to describe Large Hadron Collider (LHC) data on yield of particles in nucleus-nuclear a lot of (A + A) collisions at significant energies. The van der Waals model (VdW) with allowance for hadron repulsions at short distances proved to be particularly effective among these models. This is due to the fact that taking into account the repulsion effect leads to the prevention of undesirably large values of particle number densities at high temperatures. And also to the fact that in the collisions of heavy high-energy ions in LHC a large number of different species of particles are formed. The number of these particles is not fixed. Therefore, the model uses the formalism of the Grand Canonical Ensemble(GCE) in which thermodynamic quantities depend not on the number of particles but on chemical potentials. Over the years, various versions of VdW models have been proposed and applied to fit experimental data on the ratio of number of particles in A + A collisions at LHC energies. Tens or even hundreds of hadrons of different species can be a yield born depending on collision energy. These different hadrons will be denoted by the index "i".
Among these models we can distinguish the model proposed in [1]. In this model the intrinsic volume of the
i-th kind of hadrons is expressed in terms of the radius of the hard core 
, we the repulsion of two
different species of particles "i" and "j" is expressed
respectively in terms of the radius 
. The introduction of phenomenological parameters
and markedly
changes the yield of the number of particles
and is confirmed basically by experimental results. However, the VdW model has
not been properly develops in the case when there are attraction forces between
particles. Taking this fact into account would help us to describe more subtle
effects in dependence of hadronic gas pressure on the density.
We can generalize this approach taking into account the attractive
long-distance interaction 
(where 
n(r) - density) with sharp coordinate
dependences [2-3].
Next we do this for a multicomponent gas of particles, and so on. For multicomponent systems we have double sums that can be transformed into a multidimensional integral, having the saddle points
etc. In particular, it would be
good to make the transition from theory to experiment at CERN for the nucleus-nucleus
collisions. First, we must do this in the case of
a non-relativistic limit with a conserved number of particles without
creating new ones (conservation of the number of particle 
). Then we must make the
transition to the relativistic nucleus-nucleus reactions
at high energy densities. Other development applications may be related to dynamics for calculating kinetic coefficients such as viscosity, thermal conductivity, and diffusion.
1. M. I. Gorenstein, A. P. Kostyuk, and Ya.D. Krivenko - J. Phys. G –1999.–Vol. 25. – P. 75-83.
2. Krivenko-Emetov Ya.D. "Interparticle attractive forces account of the multicomponent hadron gas in the grand canonical ensenble"/ XXIV annual scientific conference of Institute for Nuclear Research of National Academy of Sciences of Ukraine; 258 p; 2017; p.; Book of abstract of 15th annual scientific conference of Institute for Nuclear Research of National Academy of Sciences of Ukraine; 240 p; 2018; p. 34-36; Available from Ukrainian INIS Centre (2018).
3. Volodymyr Vovchenko, Anton Motornenko, Paolo Alba, Mark I. Gorenstein, Leonid M. Satarov, and Horst Stoecker Multicomponent van der Waals equation of state: Applications in nuclear and hadronic physics /Phys. Rev. C 96, 045202 – Published 10 October 2017
