vol. 51, p. 2015 (15 pages)

•abstract

A simple model of alpha decay with the Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to the power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of the Green’s function representation and numerical solution of the time-dependent Schrödinger equation. The numerical results confirm power law with exponent \(n=3\) after the turnover into the non-exponential decay regime. Moreover, oscillations of non-escape probability are observed in the intermediate stage of the process. The simple alpha-decay model is compared to the results of the Rothe–Hintschich–Monkman experiment which was the first experimental proof of violation of the exponential law.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2015/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2015

DOI

https://doi.org/10.5506/APhysPolB.51.2015

cite as

Acta Phys. Pol. B **51**, 2015 (2020)

vol. 51, p. 2031 (10 pages), funded by SCOAP^{3}

abstract

We investigate the Bhabha scattering with the Seiberg–Witten expended noncommutative Standard Model scenario to the first order of the noncommutativity parameter \({\mit \Theta }_{\mu \nu }\). This study is based on the definition of the noncommutativity parameter that we have assumed. We explore the noncommutative scale \({\mit \Lambda }_{_\mathrm {NC}}\geq 0.8\) TeV considering different machine energy ranging from 0.5 TeV to 1.5 TeV.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2031/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2031

DOI

https://doi.org/10.5506/APhysPolB.51.2031

cite as

Acta Phys. Pol. B **51**, 2031 (2020)

vol. 51, p. 2041 (13 pages)

•abstract

We study the relativistic quantum dynamics of spin-\(0\) massive charged particle in a Gödel-type space-time with electromagnetic interactions. We solve the Klein–Gordon equation subject to a uniform magnetic field in the Som–Raychaudhuri space-time with a cosmic string. In addition, we include a magnetic quantum flux into the relativistic quantum system, and obtain the energy eigenvalues and analyze an analogue of the Aharonov–Bohm (AB) effect.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2041/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2041

DOI

https://doi.org/10.5506/APhysPolB.51.2041

cite as

Acta Phys. Pol. B **51**, 2041 (2020)

vol. 51, p. 2055 (10 pages)

•abstract

In (\(1+1\)) space-time dimensions, we can have two particles that are Weyl and Majorana particles at the same time — 1D Weyl–Majorana particles. That is, the right-chiral and left-chiral parts of the two-component Dirac wave function that satisfies the Majorana condition, in the Weyl representation, describe these particles, and each satisfies their own Majorana condition. Naturally, the nonzero component of each of these two two-component wave functions satisfies a Weyl equation. We investigate and discuss this issue and demonstrate that for a 1D Weyl–Majorana particle in a box, the nonzero components and, therefore, the chiral wave functions only admit the periodic and antiperiodic boundary conditions. From the latter two boundary conditions, we can only construct four boundary conditions for the entire Dirac wave function. Then, we demonstrate that these four boundary conditions are also included within the most general set of self-adjoint boundary conditions for a 1D Majorana particle in a box.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2055/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2055

DOI

https://doi.org/10.5506/APhysPolB.51.2055

cite as

Acta Phys. Pol. B **51**, 2055 (2020)

vol. 51, p. 2065 (17 pages)

•abstract

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz-invariant Lagrangian consistent with a space-like four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2065/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2065

DOI

https://doi.org/10.5506/APhysPolB.51.2065

cite as

Acta Phys. Pol. B **51**, 2065 (2020)

vol. 51, p. 2083 (14 pages)

•abstract

The Dirac formalism allowing to deal with systems subject to constrains is applied to find the commutation relations that should be imposed on the canonical variables of the effective two-dimensional field theory of massless fields obtained by defining the recently introduced Bagger–Lambert–Gustavsson (BLG) three-dimensional theory of a membrane system on the compactified \({\mathbb R}^{1,1}\times S^1\)space. The obtained set of constrains is of second class in the Dirac classification and should, therefore, be quantized through the introduction of the Dirac brackets which we write down in the explicit form.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2083/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2083

DOI

https://doi.org/10.5506/APhysPolB.51.2083

cite as

Acta Phys. Pol. B **51**, 2083 (2020)

vol. 51, p. 2097 (9 pages), funded by SCOAP^{3}

abstract

In this paper, we investigate the effect on energy resolution from changing the angle and the position of incidence photon for a \(5 \times 5\) crystal matrix built with (\(25 \times 25 \times 200\)) mm\(^{3}\) LYSO scintillating crystals. Those crystals have been proposed for the electromagnetic calorimeter of the Turkish Accelerator Center-Particle Factory (TAC-PF) detector. The energy resolution was obtained as \(\sigma _{E}/E = 0.42\% / \sqrt {E/{\mathrm {GeV}}} \oplus 1.60\%\) at the center of the matrix in the energy range of 50 MeV to 2 GeV. When we examined the dependence of the energy resolution on the incidence angle of the photon, resolution began to deteriorate at angles greater than \(2^{\circ }\) on the \(5 \times 5\) crystal matrix. Moreover, energy resolution at the corners of the central crystal was worse than at the center of the central crystal by a factor of 1.3 at 50 MeV and 1.1 at 2 GeV.

direct link to the full text (pdf)

https://www.actaphys.uj.edu.pl/R/51/11/2097/pdf

link to the articles list

https://www.actaphys.uj.edu.pl/R/51/11/2097

DOI

https://doi.org/10.5506/APhysPolB.51.2097

cite as

Acta Phys. Pol. B **51**, 2097 (2020)

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