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Particles, Volume 7, Issue 4 (December 2024) – 4 articles

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9 pages, 1116 KiB  
Article
Hurst Exponent and Event-by-Event Fluctuations in Relativistic Nucleus–Nucleus Collisions
by Anastasiya I. Fedosimova, Khusniddin K. Olimov, Igor A. Lebedev, Sayora A. Ibraimova, Ekaterina A. Bondar, Elena A. Dmitriyeva and Ernazar B. Mukanov
Particles 2024, 7(4), 918-926; https://doi.org/10.3390/particles7040055 (registering DOI) - 15 Oct 2024
Viewed by 245
Abstract
A joint study of multi-particle pseudo-rapidity correlations and event-by-event fluctuations in the distributions of secondary particles and fragments of the target nucleus and the projectile nucleus was carried out in order to search for correlated clusters of secondary particles. An analysis of the [...] Read more.
A joint study of multi-particle pseudo-rapidity correlations and event-by-event fluctuations in the distributions of secondary particles and fragments of the target nucleus and the projectile nucleus was carried out in order to search for correlated clusters of secondary particles. An analysis of the collisions of the sulfur nucleus with photoemulsion nuclei at an energy of 200 A·GeV is presented based on experimental data obtained at the SPS at CERN. The analysis of multi-particle correlations was performed using the Hurst method. A detailed analysis of each individual event showed that in events of complete destruction of a projectile nucleus with a high multiplicity of secondary particles, long-distance multi-particle pseudo-rapidity correlations are observed. The distribution of average pseudo-rapidity in such events differs significantly from others, as it is much narrower, and its average value is noticeably shifted towards lower values <η>. Full article
(This article belongs to the Special Issue Feature Papers for Particles 2023)
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Figure 1

Figure 1
<p>(<b>a</b>) A schematic representation of a nuclear interaction. (<b>b</b>) Dependence of the number of fragments of the target nucleus <span class="html-italic">N</span><sub>h</sub> and the multiplicity of <span class="html-italic">s</span>-particles <span class="html-italic">n</span><sub>s</sub> for interactions of S+Em at 200 A·GeV.</p>
Full article ">Figure 2
<p>Multiplicity of <span class="html-italic">s</span>-particles for events with different numbers of multi-charged fragments: (<b>a</b>) <span class="html-italic">N</span><sub>f</sub> = 1 S+Em 200 A·GeV; (<b>b</b>) <span class="html-italic">N</span><sub>f</sub> = 0 S+Em 200 A·GeV; (<b>c</b>) <span class="html-italic">N</span><sub>f</sub> = 1 S+Em 3.7 A·GeV; (<b>d</b>) <span class="html-italic">N</span><sub>f</sub> = 0 S+Em 3.7 A·GeV.</p>
Full article ">Figure 3
<p>Average pseudo-rapidity distribution of S+Em 200 A·GeV for events with different numbers of <span class="html-italic">s</span>-particles and multi-charged fragments <span class="html-italic">N</span><sub>f</sub>: (<b>a</b>) all events; (<b>b</b>) all events with <span class="html-italic">N</span><sub>f</sub> = 1; (<b>c</b>) <span class="html-italic">N</span><sub>f</sub> = 0 and <span class="html-italic">n</span><sub>s</sub> &lt; 200; (<b>d</b>) <span class="html-italic">N</span><sub>f</sub> = 0 and <span class="html-italic">n</span><sub>s</sub> ≥ 200.</p>
Full article ">Figure 4
<p>Hurst exponent at different pseudo-rapidity intervals in S+Em at 200 A·GeV interactions for events with <span class="html-italic">N</span><sub>f</sub> = 0 and a multiplicity of <span class="html-italic">n</span><sub>s</sub> &gt; 200 and <span class="html-italic">n</span><sub>s</sub> &lt; 200.</p>
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19 pages, 1025 KiB  
Review
Some Singular Spacetimes and Their Possible Alternatives
by Andrew DeBenedictis
Particles 2024, 7(4), 899-917; https://doi.org/10.3390/particles7040054 (registering DOI) - 14 Oct 2024
Viewed by 331
Abstract
In this review, we begin with a historical survey of some singular solutions in the theory of gravitation, as well as a very brief discussion of how black holes could physically form. Some possible scenarios which could perhaps eliminate these singularities are then [...] Read more.
In this review, we begin with a historical survey of some singular solutions in the theory of gravitation, as well as a very brief discussion of how black holes could physically form. Some possible scenarios which could perhaps eliminate these singularities are then reviewed and discussed. Due to the vastness of the field, its coverage is not exhaustive; instead, the concentration is on a small subset of topics such as possible quantum gravity effects, non-commutative geometry, and gravastars. A simple singularity theorem is also reviewed. Although parts of the manuscript assume some familiarity with relativistic gravitation or differential geometry, the aim is for the broad picture to be accessible to non-specialists of other physical sciences and mathematics. Full article
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Figure 1

Figure 1
<p>An excerpt from K. Schwarzschild’s original paper [<a href="#B7-particles-07-00054" class="html-bibr">7</a>]. <b>Please note</b> that <span class="html-italic">R</span> in Schwarzschild’s paper is analogous to <span class="html-italic">r</span> in this manuscript. Note that negative values of <span class="html-italic">r</span> in this figure are allowed by extension, taking us down to <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (the singularity). As we can see in this figure, there is a <math display="inline"><semantics> <msup> <mi>C</mi> <mn>2</mn> </msup> </semantics></math> coordinate transformation between Schwarzschild’s <span class="html-italic">R</span> coordinate and Schwarzschild’s <span class="html-italic">r</span> coordinate (<math display="inline"><semantics> <mrow> <mo>∂</mo> <mi>R</mi> <mo>/</mo> <mo>∂</mo> <mi>r</mi> <mo>=</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>/</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>r</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <mi>R</mi> <mo>/</mo> <msup> <mrow> <mo>(</mo> <mo>∂</mo> <mi>r</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>2</mn> <msup> <mi>α</mi> <mn>3</mn> </msup> <mi>r</mi> <mo>/</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>α</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>r</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> <mrow> <mn>5</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>∂</mo> <mi>r</mi> <mo>/</mo> <mo>∂</mo> <mi>R</mi> <mo>=</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>/</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>R</mi> <mn>3</mn> </msup> <mo>−</mo> <msup> <mi>α</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <mi>r</mi> <mo>/</mo> <msup> <mrow> <mo>(</mo> <mo>∂</mo> <mi>R</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mo>−</mo> <mn>2</mn> <msup> <mi>α</mi> <mn>3</mn> </msup> <mi>R</mi> <mo>/</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>R</mi> <mn>3</mn> </msup> <mo>−</mo> <msup> <mi>α</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> <mrow> <mn>5</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>), save for at the singular point <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mo>−</mo> <mi>α</mi> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>), which Schwarzschild did not consider. Figure included with the kind permission of the Berlin-Brandenburg Academy of Sciences and Humanities—Academy Library—Shelfmark: Z 350—19,161 (Akademiearchiv, Berlin-Brandenburgischen Akademie der Wissenschaften).</p>
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<p>An excerpt from Michell’s original 1784 paper [<a href="#B19-particles-07-00054" class="html-bibr">19</a>]. “If there should really exist in nature any bodies, whose density is not less than that of the sun, and whose diameters are more than 500 times the diameter of the sun, since their light could not arrive at us; or if there should exist any other bodies of a somewhat smaller size, which are not naturally luminous; of the existence of bodies under either of these circumstances, we could have no information from sight; yet, if any other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability, as this might afford a clue to some of the apparent irregularities of the revolving bodies, which would not be easily explicable on any other hypothesis; but as the consequences of such a supposition are very obvious, and the consideration of them somewhat beside my present purpose, I shall not prosecute them any further.” Copyright status: Not in copyright.</p>
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<p>The Hamiltonian evolution of the <math display="inline"><semantics> <msub> <mi>E</mi> <mn>3</mn> </msub> </semantics></math> factor in the classical and quantum corrected scenarios. The classical evolution (red), which is the Schwarzschild metric with a small cosmological constant, behaves as <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>=</mo> <msup> <mi>τ</mi> <mn>2</mn> </msup> </mrow> </semantics></math>, and there is a singularity (<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) at <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. The quantum-corrected evolution (black) avoids <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and has no corresponding singularity. Parameters: <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.274</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>Λ</mo> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math>. The full results are discussed in [<a href="#B39-particles-07-00054" class="html-bibr">39</a>].</p>
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<p>The Hamiltonian evolution of the <math display="inline"><semantics> <msub> <mi>E</mi> <mn>3</mn> </msub> </semantics></math> factor in regular Hamiltonian mechanics (red) and the noncommutative theory (black) for a spherical black hole. The singularity in the regular scenario at <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (signaled by <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) is pushed indefinitely into negative <math display="inline"><semantics> <mi>τ</mi> </semantics></math> values. Parameters: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>Λ</mo> <mo>=</mo> <mo>−</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.274</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mn>0.3</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>0.1</mn> </mrow> </semantics></math>. Full results may be found in [<a href="#B44-particles-07-00054" class="html-bibr">44</a>].</p>
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<p>The radial pressure <math display="inline"><semantics> <msubsup> <mi>T</mi> <mrow> <mspace width="0.277778em"/> <mspace width="0.277778em"/> <mspace width="0.166667em"/> <mn>1</mn> </mrow> <mn>1</mn> </msubsup> </semantics></math> for a gravastar which is locally de Sitter at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and essentially Schwarzschild at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>&gt;</mo> <msup> <mi>r</mi> <mo>∗</mo> </msup> </mrow> </semantics></math>, taken as the boundary of the star. Since Schwarzschild is vacuum, this means the pressure must smoothly vanish at <math display="inline"><semantics> <msup> <mi>r</mi> <mo>∗</mo> </msup> </semantics></math>. As stated in the main text, it is demanded that in the atmosphere this pressure is monotonically decreasing. Full results may be found in [<a href="#B64-particles-07-00054" class="html-bibr">64</a>,<a href="#B65-particles-07-00054" class="html-bibr">65</a>].</p>
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12 pages, 357 KiB  
Article
Cross-Sections of Neutral-Current Neutrino Scattering on 94,96Mo Isotopes
by T. S. Kosmas, R. Sahu and V. K. B. Kota
Particles 2024, 7(4), 887-898; https://doi.org/10.3390/particles7040053 - 4 Oct 2024
Viewed by 446
Abstract
In our recent publications, we presented neutral-current ν–nucleus cross-sections for the coherent and incoherent channels for some stable Mo isotopes, assuming a Mo detector medium, within the context of the deformed shell model. In these predictions, however, we have not included the [...] Read more.
In our recent publications, we presented neutral-current ν–nucleus cross-sections for the coherent and incoherent channels for some stable Mo isotopes, assuming a Mo detector medium, within the context of the deformed shell model. In these predictions, however, we have not included the contributions in the cross-sections stemming from the stable 94,96Mo isotopes (abundance of 94Mo 9.12% and of 96Mo 16.50%). The purpose of the present work is to perform detailed calculations of ν94,96Mo scattering cross-sections, for a given energy Eν of the incoming neutrino, for coherent and incoherent processes. In many situations, the Eν values range from 15 to 30 MeV, and in the present work, we used Eν = 15 MeV. Mo as a detector material has been employed by the MOON neutrino and double-beta decay experiments and also from the NEMO neutrinoless double-beta decay experiment. For our cross-section calculations, we utilize the Donnelly–Walecka multipole decomposition method in which the ν–nucleus cross-sections are given as a function of the excitation energy of the target nucleus. Because only the coherent cross-section is measured by current experiments, it is worth estimating what portion of the total cross-section represents the measured coherent rate. This requires the knowledge of the incoherent cross-section, which is also calculated in the present work. Full article
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Figure 1

Figure 1
<p>HF single-particle spectra for <sup>94</sup>Mo corresponding to lowest energy prolate and oblate configurations. In the figure, circles represent protons and crosses represent neutrons. The HF energy E in MeV, mass quadrupole moment Q in units of the square of the oscillator length parameter and the total azimuthal quantum number K are given in the figure.</p>
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<p>The ground band and a few other low-lying levels observed in <sup>94</sup>Mo are compared with the DSM predictions. The experimental data are taken from [<a href="#B42-particles-07-00053" class="html-bibr">42</a>].</p>
Full article ">Figure 3
<p>HF single-particle spectra for <sup>96</sup>Mo corresponding to lowest energy prolate and oblate configurations. In the figure, circles represent protons and crosses represent neutrons. The HF energy E in MeV, mass quadrupole moment Q in units of the square of the oscillator length parameter and the total azimuthal quantum number K are given in the figure.</p>
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<p>The ground band and a few other low-lying levels observed in <sup>96</sup>Mo are compared with the DSM predictions. The experimental data are taken from [<a href="#B42-particles-07-00053" class="html-bibr">42</a>].</p>
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<p>The differential cross-section as a function of the excitation energy <math display="inline"><semantics> <mi>ω</mi> </semantics></math> for <sup>94</sup>Mo at incoming neutrino energy <math display="inline"><semantics> <mrow> <msub> <mi>ϵ</mi> <mi>ν</mi> </msub> <mo>=</mo> <mn>15</mn> </mrow> </semantics></math> MeV for different excited states. The contribution of the excitation to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </semantics></math> state is represented by red, to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>2</mn> <mo>+</mo> </msup> </mrow> </semantics></math> by blue, to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>1</mn> <mo>−</mo> </msup> </mrow> </semantics></math> by black, and to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>2</mn> <mo>−</mo> </msup> </mrow> </semantics></math> by cyan.</p>
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<p>The differential cross-section as a function of the excitation energy <math display="inline"><semantics> <mi>ω</mi> </semantics></math> for <sup>96</sup>Mo at incoming neutrino energy <math display="inline"><semantics> <mrow> <msub> <mi>ϵ</mi> <mi>ν</mi> </msub> <mo>=</mo> <mn>15</mn> </mrow> </semantics></math> MeV for different excited states. Figure is generated with the data taken from ref. [<a href="#B18-particles-07-00053" class="html-bibr">18</a>]. The contribution of the excitation to the <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </semantics></math> state is represented by blue, to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>2</mn> <mo>+</mo> </msup> </mrow> </semantics></math> by red, to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>1</mn> <mo>−</mo> </msup> </mrow> </semantics></math> by cyan, and to <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <msup> <mn>2</mn> <mo>−</mo> </msup> </mrow> </semantics></math> by black.</p>
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8 pages, 285 KiB  
Article
Implications of the Spin-Induced Accretion Disk Truncation on the X-ray Binary Broadband Emission
by Theodora Papavasileiou, Odysseas Kosmas and Theocharis Kosmas
Particles 2024, 7(4), 879-886; https://doi.org/10.3390/particles7040052 - 1 Oct 2024
Viewed by 379
Abstract
Black hole X-ray binary systems consist of a black hole accreting mass from its binary companion, forming an accretion disk. As a result, twin relativistic plasma ejections (jets) are launched towards opposite and perpendicular directions. Moreover, multiple broadband emission observations from X-ray binary [...] Read more.
Black hole X-ray binary systems consist of a black hole accreting mass from its binary companion, forming an accretion disk. As a result, twin relativistic plasma ejections (jets) are launched towards opposite and perpendicular directions. Moreover, multiple broadband emission observations from X-ray binary systems range from radio to high-energy gamma rays. The emission mechanisms exhibit thermal origins from the disk, stellar companion, and non-thermal jet-related components (i.e., synchrotron emission, inverse comptonization of less energetic photons, etc.). In many attempts at fitting the emitted spectra, a static black hole is often assumed regarding the accretion disk modeling, ignoring the Kerr metric properties that significantly impact the geometry around the usually rotating black hole. In this work, we study the possible implications of the spin inclusion in predictions of the X-ray binary spectrum. We mainly focus on the most significant aspect inserted by the Kerr geometry, the innermost stable circular orbit radius dictating the disk’s inner boundary. The outcome suggests a higher-peaked and hardened X-ray spectrum from the accretion disk and a substantial increase in the inverse Compton component of disk-originated photons. Jet-photon absorption is also heavily affected at higher energy regimes dominated by hadron-induced emission mechanisms. Nevertheless, a complete investigation requires the full examination of the spin contribution and the resulting relativistic effects beyond the disk truncation. Full article
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Figure 1

Figure 1
<p>The total luminosity emitted by the accretion disk (<b>left</b> panel) and the respective inverse Compton (IC) component of the spectral distribution for different values of the black hole spin (<b>right</b> panel).</p>
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<p>The emitted luminosity of the jet due to proton synchrotron emission (<b>left</b> panel) and proton collisions (<b>right</b> panel) after photon–photon interactions with the emission from the accretion disk for different black hole spins.</p>
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