### Regular Series

#### Vol. 48 (2017), No. 4, pp. 699 – 792

Production of Light Nuclei in the Thermal and Coalescence Models

Acta Phys. Pol. B 48, 707 (2017)

page 707 •

abstract

The thermal model properly describes the production yields of light nuclei in relativistic heavy-ion collisions even so the loosely bound sizable nuclei cannot exist in the dense and hot hadron gas at a chemical freeze-out. Within the coalescence model, light nuclei are formed at the latest stage of nuclear collisions — a kinetic freeze-out — due to final state interactions. After discussing the models, we derive simple analytic formulas and, using model parameters directly inferred from experimental data, we show that the thermal and coalescence model predictions are quantitatively close to each other. A possibility to falsify one of the two models is suggested.

Non-identical Particle Correlation Analysis in the Presence of Non-femtoscopic Correlations

Acta Phys. Pol. B 48, 717 (2017)

page 717 •

abstract

Femtoscopy is a technique of using correlations of two emitted particles to estimate the space-time extent of the source produced in heavy-ion collisions. Correlations of two non-identical particles have a unique additional feature of being sensitive to the difference in average emission position of the two particle types. For pion–kaon pairs, the femtoscopic signal arises from the Coulomb interaction between particles. Its strength is comparable to the magnitude of effects of non-femtoscopic origin. In this work, we identify main sources of these background correlations. We propose a robust method to estimate them and account for their influence in the femtoscopic analysis of experimental data. We validate the proposed correction method on a data sample generated with the THERMINATOR 2 model and provide a recipe for experimentalists.

Modification of $\mit \Delta$(1232) in the Neutrino Nucleus Reaction

Acta Phys. Pol. B 48, 729 (2017)

page 729 •

abstract

The remarkable observations in the pion-induced and charge-exchange reactions on a nucleus are the significant shift and broadening of the ${\mit \Delta } (1232)$-peak relative to free pion–nucleon scattering. For the forward going massless leptons, the weak process $(\nu _l,l)$ on a nucleon, according to Adler’s partially conserved axial current theorem, is connected to the pion–nucleon scattering. This mechanism is also applicable to the nucleus. Therefore, the modification of the ${\mit \Delta }$-peak in a nucleus can be seen in the $(\nu _l,l)$ reaction since it is connected to the pion–nucleus scattering. To investigate this issue quantitatively, the double differential cross sections of the forward going ejectile $l$ energy distribution in the $(\nu _l,l)$ reaction are calculated in the ${\mit \Delta }$-excitation region for both proton and nucleus. The measured pion–nucleon and pion–nucleus scattering cross sections in the quoted energy region are used in these reactions as an input. Since the $(\nu _l,l)$ reaction is connected to the pion-induced scattering, the features of the previous reaction is shown analogous to those of the latter.

Pion Fluctuation in High-energy Collisions — A Chaos-based Quantitative Estimation with Visibility Graph Technique

Acta Phys. Pol. B 48, 741 (2017)

page 741 •

abstract

We propose a new approach for studying pion fluctuation for deeper understanding of the internal dynamics, from a perspective of fractional Brownian motion (fBm)-based complex network analysis method called Visibility Graph analysis. This chaos-based, rigorous, non-linear technique is applied to study the erratic behaviour of multipion production in $\pi ^{-}$–Ag/Br interactions at 350 GeV. This method can offer reliable results with finite data points. The Power of Scale-freeness of Visibility Graph denoted by PSVG is a measure of fractality, which can be used as a quantitative parameter for the assessment of the state of a chaotic system. The event-wise fluctuation of the multipion production process can be represented by this parameter. From the analysis of the PSVG, we can quantitatively confirm that fractal behaviour of the particle production process depends on the target excitation, and the fractality decreases with the increase of target excitation.

New Solvable Potentials with Bound State Spectrum

Acta Phys. Pol. B 48, 757 (2017)

page 757 •

abstract

A new family of solvable potentials related to the Schrödinger–Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential class, which is a rather general class of solvable potentials related to the hypergeometric functions, can be generalized to even wider classes of solvable potentials. As a consequence, the non-linear Schrödinger-type equation has been obtained.

A Random Matrix Model Whose Eigenvalue Spacings Are Closely Described by the Brody Distribution

Acta Phys. Pol. B 48, 765 (2017)

page 765 •

abstract

We introduce a primitive $2 \times 2$ random matrix model with one parameter, $1 \le d \le 2$. It is shown that an ensemble of such matrices has eigenvalue spacings that transition from near-Poisson statistics, when $d = 2$, to GOE statistics for $2 \times 2$ matrices, when $d = 1$. This transition can be very closely modelled by the Brody distribution, where the Brody parameter is $q = (2-d)/d$. Exact integral forms for the complete transition are given.

Classical Mechanics and Quantum Fields in Noncommutative Phase Spaces

Acta Phys. Pol. B 48, 773 (2017)

page 773 •

abstract

In this paper, we have analyzed noncommutative (NC) structures in the case when the NC parameter is not constant. Firstly, it is a variable in the configuration space making part of the dynamics of the relativistic particle action. Secondly, through a straightforward approach, we have constructed quantum scalar fields and its algebra in an NC space-time.

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