Self-similar solutions for A-dependences in relativistic nuclear collisions in the transition energy region. A.A.Baldin

One of the most important problems nowadays, formulated by a distinguished scientist S.Nagamia in 1994, is the determination of the conditions in which hadrons lose their identity, and sub-nucleonic degrees of freedom begin to play a leading role. A.M.Baldin proposed a classification of applicability of the notion “elementary particle” on the basis of the variable b ik introduced by him.

the region relates to non-relativistic nuclear physics, where nucleons can be considered as point objects; the region relates to excitation of internal degrees of freedom of hadrons; the region should, in principle, be described by quantum chromodynamics.

PDG K. Hagiwara et al.,K. Hagiwara et al., Phys. Rev. D 66, (2002) (

PDG K. Hagiwara et al.,K. Hagiwara et al., Phys. Rev. D 66, (2002) (

V.Burov at.al. Phys.Lett. B67:46,1977, PEPAN,15: ,1984

Cumulative Processes Structure of the nuclei at short distances

Self-similarity is a special symmetry of solutions which consists in that the change in the scales of independent variables can be compensated by the self-similarity transformation of other dynamical variables. This results in a reduction of the number of the variables which any physical law depend upon.

The relationship between X 1 and X 2 is described by the laws of conservation written in the form Here M n is the nucleon mass, and M 3 the mass of an emitted particle. Essentially, we are using an experimentally proved correlation depletion principle in the relative four-velocity space which enables us to neglect the relative motion of not detected particles, namely the quantity in the right-hand part of the above equation. Employing this approximation, the correlation between X1 and X2 can conveniently be written in the form In the case of production of antiparticle with mass M 3, the mass M 4 is equal to M 3 as a consequence of conservation of quantum numbers. In studying the production of protons and nuclear fragments M 4 =  M 3 as far as minimal value of  corresponds to the fact that any other additional particles are not produced. The X 1 and X 2 obtained from the minimum  are used to construct an universal description of the A-dependencies. The analysis of the experimental data shows that the A-dependence of the inclusive production cross section can be parametrized by a universal function     , were X is equal to X 1 and X 2, respectively.

Cumulative processes S.V.Boyarinov, et al. Yad. Fis., v.57, N8, (1994), O.P.Gavrishchuk et al. Nucl. Phys., A523 (1991) 589.

Twice cumulative Jim Carroll Nucl. Phys. A488 (1989) A.Shor et al. Phys. Rev. Lett. 62 (1989) A.A.Baldin et al. Nucl. Phys., A519 (1990) 407. A.A.Baldin et al. Rapid Communications JINR, 3-92 (1992) 20.

Twice cumulative A.Schroter et al. Z.Phys. A350, (1994),

Antimatter production

A.A.Baldin, E.N.Kladnitskaya, O.V. Rogachevsky, JINR Rapid Comm., (1999), N.2 [94]-99, p.20. M.Kh.Anikina, et al., Phys. Lett. B., (1997), v.397, p.30.

P.Stankus et al. Nucl. Phys. A544 (1992) p.603c-608c.

conclusion The proposed self-similar solution quantitatively describes the angular, energy and A- dependences of inclusive production cross sections of all hadrons with transverse momentum up to 2GeV. For higher transverse momenta the A- dependence becomes a function not only of X 1, X 2, but also of Р t (or m t ). The analysis of inclusive spectra for the data selected in different ways shows that multiplicity in relativistic nuclear collisions has its origin basically in independent nucleon-nucleon interactions. Thus, high multiplicity at interaction of heavy nuclei is not a satisfactory criterion for search and study of collective interactions, or detection of exotic states of nuclear matter (such as quark-gluon plasma). It is natural to consider two types of collectivity in nuclear-nuclear collisions: the first is related to production of particles in the region kinematically forbidden for single nucleon-nucleon interactions (X 1 or X 2 or both greater than unity); the second is a result of collectivity of the initial state in nucleus- nucleus collisions) – high probability of a large number of independent nucleon-nucleon interactions in the collision. The analysis of multiple experimental data on the basis of the proposed self-similarity approach allows to conclude that the effect of the collectivity of the first type drops drastically with increasing energy of colliding particles and increases with increasing mass of the produced particle.

Collective effects of the first type (cumulative) “die out” with increasing collision energy. Therefore, in order to investigate subthreshold processes, it is necessary to optimize the combination of the nucleus mass and energy to provide sufficient number of nucleons, on the one hand, and avoid extra multiplicity, on the other hand.

We must remember that what we observe is not Nature itself, but Nature which uncovers in the form in which it is revealed by our way of putting questions. Scientific work in physics consists in putting questions about Nature in the language we use, and trying to get an answer in experiment performed by the means (tools) we have. At that the words of Bohr about quantum theory come to mind: if harmony in life is sought for, one should never forget that in the game of life we are spectators and players at the same time.