Tochtli Yépez-Mart́ınez, ∗ Peter O. Hess, † and Osvaldo Civitarese ‡ Instituto de Educación Media... more Tochtli Yépez-Mart́ınez, ∗ Peter O. Hess, † and Osvaldo Civitarese ‡ Instituto de Educación Media Superior de la Ciudad de México, Plantel Benito Juárez, Av. Zacatlán, esq. Cempasúchil S/N. Pueblo de San Lorenzo Tezonco, C.P. 09790, Alcald́ıa Iztapalapa. Ciudad de México, México. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior S/N, A.P. 70-543, 04510 M ́exico D.F. Mexico. and Frankfurt Institute for Advanced Studies, J. W. von Goethe University, Hessen, Germany 3 Departamento de F́ısica, Universidad Nacional de La Plata, C.C. 67 (1900), La Plata, Argentina. (Dated: September 1, 2021)
The 2ν ββ decay half-lives of six nuclei, whose decays were previously reported as theoretically ... more The 2ν ββ decay half-lives of six nuclei, whose decays were previously reported as theoretically forbidden, are calculated by including the pairing interaction, which mixes different occupations and opens up the possibility of the decay. All allowed channels for the 0ν ββ decay are also computed. The estimated 2ν ββ half-lives suggest that measurements in 244 Pu may find positive signals, and that planned experiments would succeed in detecting the ββ 2ν decay in 160 Gd. Limits for the zero neutrino mode, in the analyzed deformed emitters, are predicted.
The onset of instabilities, in the standard proton-neutron quasiparticle random phase approximati... more The onset of instabilities, in the standard proton-neutron quasiparticle random phase approximation ͑QRPA͒, is investigated by using different boson mappings and trial states belonging to a representation of coherent states. The model describes pairing and proton-neutron interactions. It is shown that an exact mapping of the Hamiltonian is needed to describe correctly the QRPA phase transition, i.e., that the algebra of all operators participant in the Hamiltonian should be preserved by the boson mapping. Spurious components of the wave functions, which appear if the Pauli principle is violated, are isolated by construction.
The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the mo... more The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the most difficult to implement in many-fermion systems, which are common in nuclear physics. To investigate the consequences of ignoring the PEP, we discuss several algebraic models in nuclear structure physics, in particular cluster models. Sometimes they tend to ignore the Pauli Exclusion Principle for practical reasons, leading to flawed interpretations. Though at first sight there seems to be an agreement to experiment, often it is due to the limited number of states known experimentally. We discuss several models which include or not the PEP, illustrating through their differences the importance of the PEP. This contribution is also a review of recently published results.
After a short review on the possible experimental observations to verify pseudocomplex General Re... more After a short review on the possible experimental observations to verify pseudocomplex General Relativity, neutron stars as a particular object of interest are investigated. Dark energy is added to the structure of a neutron star, while for the nuclear part the chiral SU(3) model is used. For the coupling of matter to dark energy a special assumption is made. The consequences are discussed. We show that neutron stars of up to six solar masses are obtained, which already behave similar to a black hole.
The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16 O, assumed to consist of a sy... more The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16 O, assumed to consist of a system of four α-clusters. For the 4-α cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4α-particles. A phenomenological Hamiltonian is used, justifying the name Semi in the SACM. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that the 16 O shows evidence of a tetrahedral structure, which can be explained easily by symmetry arguments. We show that PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy.
The observation predictions of the pseudocomplex General Relativity, related to the structure of ... more The observation predictions of the pseudocomplex General Relativity, related to the structure of an accretion disk, are compared to the reported observations of the Event Horizon Telescope.
We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an... more We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV .
The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vac... more The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vacuum fluctuations near a black hole. These vacuum fluctuations are treated as a dark energy. A parameter is introduced to account for these fluctuations. It is zero for the standard theory and acquires a maximal value, just before there would be no event horizon. The existence of an event horizon not only depends on the value of this parameter, but also on the spin of the black hole. In addition, we study the existence of a light-ring. We also elaborate on the relation of the appearance and vanishing of the event horizon and light-ring to phase transitions.
We present a generalized variational procedure oriented to the algebraic solution of many-body Ha... more We present a generalized variational procedure oriented to the algebraic solution of many-body Hamiltonians expressed in bosonic and fermionic variables. The method specializes in the nonperturbative regime of the solutions. As an example, we focus on the application of the method to nonperturbative QCD.
A review will be presented on the algebraic extension of the standard Theory of Relativity (GR) t... more A review will be presented on the algebraic extension of the standard Theory of Relativity (GR) to the pseudocomplex formulation (pc-GR). The pc-GR predicts the existence of a dark energy outside and inside the mass distribution, corresponding to a modification of the GR-metric. The structure of the emission profile of an accretion disc changes also inside a star. Discussed are the consequences of the dark energy for cosmological models, permitting different outcomes on the evolution of the universe.
An r-dependent term is added to the metric for the study of extensions of the Theory of General R... more An r-dependent term is added to the metric for the study of extensions of the Theory of General Relativity (GR). The stability of the Schwarzschild solution is investigated with and without the presence of this additional term. Polar (Zerilli) and axial (Regge-Wheeler) modes are studied and the differences discussed. The main conclusion is that, with an r-dependent term in the metric, the axial and polar modes remain stable. Assuming that GR describes the data of the gravitational wave events, in the modified theory, axial modes involve larger masses, which might change the interpretation of the source of the gravitational wave events observed.
The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12 C as a system of three αclust... more The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12 C as a system of three αclusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12 C nucleus can effectively be treated as a two-cluster system 8 Be+α. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0 + 2 → 2 + 1) transition requires a mixing of SU (3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.
The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a ... more The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle–hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like [Formula: see text], as well as the pion ([Formula: see text]).
Tochtli Yépez-Mart́ınez, ∗ Peter O. Hess, † and Osvaldo Civitarese ‡ Instituto de Educación Media... more Tochtli Yépez-Mart́ınez, ∗ Peter O. Hess, † and Osvaldo Civitarese ‡ Instituto de Educación Media Superior de la Ciudad de México, Plantel Benito Juárez, Av. Zacatlán, esq. Cempasúchil S/N. Pueblo de San Lorenzo Tezonco, C.P. 09790, Alcald́ıa Iztapalapa. Ciudad de México, México. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior S/N, A.P. 70-543, 04510 M ́exico D.F. Mexico. and Frankfurt Institute for Advanced Studies, J. W. von Goethe University, Hessen, Germany 3 Departamento de F́ısica, Universidad Nacional de La Plata, C.C. 67 (1900), La Plata, Argentina. (Dated: September 1, 2021)
The 2ν ββ decay half-lives of six nuclei, whose decays were previously reported as theoretically ... more The 2ν ββ decay half-lives of six nuclei, whose decays were previously reported as theoretically forbidden, are calculated by including the pairing interaction, which mixes different occupations and opens up the possibility of the decay. All allowed channels for the 0ν ββ decay are also computed. The estimated 2ν ββ half-lives suggest that measurements in 244 Pu may find positive signals, and that planned experiments would succeed in detecting the ββ 2ν decay in 160 Gd. Limits for the zero neutrino mode, in the analyzed deformed emitters, are predicted.
The onset of instabilities, in the standard proton-neutron quasiparticle random phase approximati... more The onset of instabilities, in the standard proton-neutron quasiparticle random phase approximation ͑QRPA͒, is investigated by using different boson mappings and trial states belonging to a representation of coherent states. The model describes pairing and proton-neutron interactions. It is shown that an exact mapping of the Hamiltonian is needed to describe correctly the QRPA phase transition, i.e., that the algebra of all operators participant in the Hamiltonian should be preserved by the boson mapping. Spurious components of the wave functions, which appear if the Pauli principle is violated, are isolated by construction.
The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the mo... more The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the most difficult to implement in many-fermion systems, which are common in nuclear physics. To investigate the consequences of ignoring the PEP, we discuss several algebraic models in nuclear structure physics, in particular cluster models. Sometimes they tend to ignore the Pauli Exclusion Principle for practical reasons, leading to flawed interpretations. Though at first sight there seems to be an agreement to experiment, often it is due to the limited number of states known experimentally. We discuss several models which include or not the PEP, illustrating through their differences the importance of the PEP. This contribution is also a review of recently published results.
After a short review on the possible experimental observations to verify pseudocomplex General Re... more After a short review on the possible experimental observations to verify pseudocomplex General Relativity, neutron stars as a particular object of interest are investigated. Dark energy is added to the structure of a neutron star, while for the nuclear part the chiral SU(3) model is used. For the coupling of matter to dark energy a special assumption is made. The consequences are discussed. We show that neutron stars of up to six solar masses are obtained, which already behave similar to a black hole.
The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16 O, assumed to consist of a sy... more The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16 O, assumed to consist of a system of four α-clusters. For the 4-α cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4α-particles. A phenomenological Hamiltonian is used, justifying the name Semi in the SACM. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that the 16 O shows evidence of a tetrahedral structure, which can be explained easily by symmetry arguments. We show that PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy.
The observation predictions of the pseudocomplex General Relativity, related to the structure of ... more The observation predictions of the pseudocomplex General Relativity, related to the structure of an accretion disk, are compared to the reported observations of the Event Horizon Telescope.
We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an... more We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV .
The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vac... more The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vacuum fluctuations near a black hole. These vacuum fluctuations are treated as a dark energy. A parameter is introduced to account for these fluctuations. It is zero for the standard theory and acquires a maximal value, just before there would be no event horizon. The existence of an event horizon not only depends on the value of this parameter, but also on the spin of the black hole. In addition, we study the existence of a light-ring. We also elaborate on the relation of the appearance and vanishing of the event horizon and light-ring to phase transitions.
We present a generalized variational procedure oriented to the algebraic solution of many-body Ha... more We present a generalized variational procedure oriented to the algebraic solution of many-body Hamiltonians expressed in bosonic and fermionic variables. The method specializes in the nonperturbative regime of the solutions. As an example, we focus on the application of the method to nonperturbative QCD.
A review will be presented on the algebraic extension of the standard Theory of Relativity (GR) t... more A review will be presented on the algebraic extension of the standard Theory of Relativity (GR) to the pseudocomplex formulation (pc-GR). The pc-GR predicts the existence of a dark energy outside and inside the mass distribution, corresponding to a modification of the GR-metric. The structure of the emission profile of an accretion disc changes also inside a star. Discussed are the consequences of the dark energy for cosmological models, permitting different outcomes on the evolution of the universe.
An r-dependent term is added to the metric for the study of extensions of the Theory of General R... more An r-dependent term is added to the metric for the study of extensions of the Theory of General Relativity (GR). The stability of the Schwarzschild solution is investigated with and without the presence of this additional term. Polar (Zerilli) and axial (Regge-Wheeler) modes are studied and the differences discussed. The main conclusion is that, with an r-dependent term in the metric, the axial and polar modes remain stable. Assuming that GR describes the data of the gravitational wave events, in the modified theory, axial modes involve larger masses, which might change the interpretation of the source of the gravitational wave events observed.
The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12 C as a system of three αclust... more The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12 C as a system of three αclusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12 C nucleus can effectively be treated as a two-cluster system 8 Be+α. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0 + 2 → 2 + 1) transition requires a mixing of SU (3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.
The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a ... more The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle–hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like [Formula: see text], as well as the pion ([Formula: see text]).
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