Regular Series

Vol. 48 (2017), No. 7, pp. 1263 – 1369

Importance of Thermodynamic Fluctuations in the Gaździcki–Gorenstein Model

Acta Phys. Pol. B 48, 1267 (2017)

page 1267 •


Effects of the standard thermodynamic fluctuations on the predictions of the Gaździcki–Gorenstein model of particle production in high-energy heavy-ions collisions are evaluated. At low numbers of participating nucleons, the corrections due to these fluctuations are found to be very significant.

Solution of the Specific Model of Five-body Problem to Investigate the Effective Alpha–Nucleon Interaction in a Partial-wave Analysis

Acta Phys. Pol. B 48, 1279 (2017)

page 1279 • See comment


In this paper, we have solved a simple specific model of the five-body problem in the framework of the Yakubovsky equations, restricted to the configurations of the alpha–nucleon types only, to investigate the effective interaction between an inert alpha-particle and a neutron. In the general case, the Yakubovsky scheme for the solution of the five-body system leads to a set of four coupled equations related to four independent configurations, which can be restricted to two coupled ones, to describe the effective alpha–nucleon structure model, namely an inert four-body alpha–core and a nucleon. Hence, in such a model, the other configurations will not be taken into account. To calculate the binding energies of the five-body system in the model of alpha–nucleon structure, the two coupled equations are represented in the momentum space on the basis of the Jacobi momenta. After an explicit evaluation of the two coupled integral equations in a partial-wave analysis, the obtained equations are the starting point for a numerical calculation as an eigenvalue equation form, using typical iteration method. In the first step to the calculations, i.e. applying some spin-independent potential models, some obtained binding energy differences between the four-body as an alpha-particle and the five-body as an alpha–nucleon systems suggest that a simple effective interaction between an inert alpha-particle and a nucleon is attractive and of about 13 MeV. In addition, the represented binding energy results with respect to the regarded spin-independent potentials are in a fair agreement with the results obtained from other methods.

Fragment Emission in \(^{32}\)S+\(^{197}\)Au Collisions at Fermi Energy

Acta Phys. Pol. B 48, 1303 (2017)

page 1303 •


Intermediate mass fragment emission from the interaction of sulphur with gold \(^{32}\)S+\(^{197}\)Au at a beam energy of 1.01 GeV (31.5 MeV \(A\)) was measured at various angles with silicon \(\Delta E\)–\(E\) telescopes. At the most forward angle \(\vartheta ={17}^\circ \), an additional \(\Delta E\) detector, an ionisation chamber was used. The measurements were successfully compared with other data of similar systems. Angle integration of cross sections was performed within the generalised moving source model. The isotopic cross sections were compared to theoretical calculations within quantum molecular dynamic and statistical multi-fragmentation models.

Classical BRST Charge and Observables in Reducible Gauge Theories

Acta Phys. Pol. B 48, 1335 (2017)

page 1335 •


We study the construction of the classical Becchi–Rouet–Stora–Tyutin (BRST) charge and observables for arbitrary reducible gauge theory. Using a special coordinate system in the extended phase space, we obtain an explicit expression for the Koszul–Tate differential and show that the BRST charge can be found by a simple iterative method. We also give a formula for the classical BRST observables.

Similarity Solutions to Burgers’ Equation in Terms of Special Functions of Mathematical Physics

Acta Phys. Pol. B 48, 1349 (2017)

page 1349 •


In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers’ equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer’s confluent hypergeometric function \({\mit \Phi }(a,b;x)\) and Bessel functions \(J_p\), showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.


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