Pedro Alberto | Universidade de Coimbra (original) (raw)
Papers by Pedro Alberto
Proceedings of XV International Workshop on Hadron Physics — PoS(XVHadronPhysics)
Lecture Notes in Computer Science, 2001
Physics Letters A, 2011
We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle con... more We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.
Physical Review C, 2000
The multipole amplitudes for the N-∆(1232) electromagnetic transition are computed in the framewo... more The multipole amplitudes for the N-∆(1232) electromagnetic transition are computed in the framework of the linear σ model and the chiral chromodielectric model for small and moderate photon virtualities. The models include quark and meson degrees of freedom and the nucleon and the delta are clusters of three valence hedgehog quarks surrounded by meson clouds described by coherent states. Angular momentum and isospin projections are performed to endow model states representing the nucleon and the delta with proper quantum numbers. Recoil corrections involved in the process γ v N → ∆ are taken into account by performing linear momentum projection of the initial and final baryon states. The ratios E2/M 1 and C2/M 1 are in good agreement with the data in the two models, but the magnetic amplitude is better reproduced in the Linear Sigma Model. The ratios show little dependence with the model parameters. Both in the Linear Sigma Model and in the Chromodielectric Model the charged pions are responsible for the non-vanishing quadrupoleelectric and-coulomb amplitudes. The recoil corrections enhance the results obtained for the amplitudes without linear momentum projection, improving the comparison with experimental data. The dependence of the theoretical amplitudes with the choice of the reference frame is also studied.
Computer Physics Communications, 1999
SoftSciences project-software for learning physics and other sciences. Pedro Vieira Alberto, Carl... more SoftSciences project-software for learning physics and other sciences. Pedro Vieira Alberto, Carlos Fiolhais, Joao Paiva Computer Physics Communications 121, 593, 1999. We describe an ongoing project in Portugal aimed ...
Journal of Physics: Conference Series, 2016
Journal of Physics G: Nuclear and Particle Physics
The possibility to compute nucleon electromagnetic form factors in the time-like region by analyt... more The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions, obtained in the framework of a generic model of nucleons, has been explored. We have developed a procedure to solve analytically Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematic regions and fulfilling the first-principles requirements of analyticity and unitarity. The results obtained in the particular case of the Skyrme model are discussed and compared to data, both in space-like and time-like region.
This paper deals with the application of pattern search methods to the numerical solution of a cl... more This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular problems have no constraints and the objective function is smooth. The difficulties arise from the existence of several local minima, and especially, from the expensive function evaluation (total energy) and the possible non-availability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations and to take advantage of parallelism without the use of derivatives. Numerical results with a particular instance of this new class of pattern search methods are presented showing the promise of our approach. The new pattern search...
This paper deals with the application of pattern search methods to the numerical solution of a cl... more This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular problems have no constraints and the objective function is smooth. The difficulties arise from the existence of several local minima, and especially, from the expensive function evaluation (total energy) and the possible non-availability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations. Numerical results with a particular instance of this new class of pattern search methods and with the parallel direct search method of Dennis and Torczon are presented showing the promise of our approach.
arXiv: Nuclear Theory, 2011
Pion scattering and electro-production amplitudes have been computed in a coupled-channel framewo... more Pion scattering and electro-production amplitudes have been computed in a coupled-channel framework incorporating quasi-bound quark-model states, based on the Cloudy Bag model. All relevant low-lying nucleon resonances in the P33, P11, and S11 partial waves have been covered, including the Delta(1232), the N*(1440), N*(1535), and N*(1650). Consistent results have been obtained for elastic and inelastic scattering (two-pion, eta-N, and K-Lambda channels), as well as for electro-production. The meson cloud has been shown to play a major role, in particular in electro-magnetic observables in the P33 and P11 channels.
Brazilian Journal of Physics, 1996
Solitonic solutions with axial symmetry (in con guration and isospin spaces) are studied in the f... more Solitonic solutions with axial symmetry (in con guration and isospin spaces) are studied in the framework of the linear sigma model with quarks, and mesons. A comparison between the axial and the hedgehog solitons is presented in detail. It turns out that the axial soliton is less bound than the hedgehog. States with good angular momentum and isospin are extracted from the axial state by means of the Peierls-Yoccoz projection. The relevance of the axial ansatz is discussed in the context of a description of the angular momentum excitations of the nucleon and delta states.
arXiv: High Energy Physics - Phenomenology, 2015
The possibility to compute nucleon electromagnetic form factors in the time-like region by analyt... more The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions has been explored in the framework of the Skyrme model. We have developed a procedure to solve analytically Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematical regions and fulfilling the first-principles requirements. The results are discussed and compared to data, both in space-like and time-like region.
![Research paper thumbnail of 31 92 v 2 [ qu an tph ] 8 M ar 2 01 1 Relativistic particle in a three-dimensional box](https://attachments.academia-assets.com/78522853/thumbnails/1.jpg)
](Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısic... more Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısica Computacional, Universidade de Coimbra, P-3004-516 Coimbra, Portugal Theoretical Physics Group, Dept of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada T1K 3M4 and Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, GR-11527, Athens, Greece
Astronomische Nachrichten
European Journal of Physics
The problem of a particle in a box is probably the simplest problem in quantum mechanics which al... more The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one-and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
Journal of Geophysical Research: Solid Earth
We use empirical orthogonal function analysis (EOFA) directly on sets of Schmidt spherical harmon... more We use empirical orthogonal function analysis (EOFA) directly on sets of Schmidt spherical harmonic (SH) coefficients modeling the internal geomagnetic field or its time derivatives at different epochs. We show how to properly use the method such that the application of EOFA to either spatial or spectral domains leads to the same results, bypassing the need to work on snapshots of field charts synthesized from SHs. In case a spatial grid is required, we point out which is the best grid to use. We apply the method to the CM4 geomagnetic field model to illustrate the differences in EOFA modes obtained with and without corrections. Once the corrected main modes of secular acceleration (SA) have been singled out, we retrieve previous results showing that the 1969, 1978, and 1991 geomagnetic field acceleration jumps have the same spatial pattern. A new finding in this study is that the same spatial pattern is present in principal modes of secular variation which, once inverted, may provide the flow responsible for the jerk sequence. Another finding is the unveiling of a different spatial structure common to a second group of jerks with SA pulses around 1985 and 1996, displaying a localization very similar to SA pulses identified in 2006 and 2009 using recent satellite data. Finally, if properly handled, the EOFA can be directly applied to a grid of data values of the geomagnetic field in order to produce SH models of decorrelated modes which may help to separate different sources of the field.
AIP Conference Proceedings, 2004
Medium modification of nucleon properties are studied in the framework of the Linear Sigma Model ... more Medium modification of nucleon properties are studied in the framework of the Linear Sigma Model (LSM). The nucleon is described as a chiral soliton with 3-quarks bounded due to their interactions with sigma and pion fields. Medium effects are introduced through the coupling of the quarks to sigma and omega fields, the strengths of which are determined self-consistently in a Walecka-like model, whose fermionic nucleon mass is calculated in the framework of the LSM. The nucleon properties are presented as functions of the nuclear density.
AIP Conference Proceedings, 2004
A generalized relativistic harmonic oscillator for spin 1 2 particles is studied. The Dirac Hamil... more A generalized relativistic harmonic oscillator for spin 1 2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ S •V or ∆ V S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case Σ 0, for which pseudospin symmetry is exact.
Proceedings of XV International Workshop on Hadron Physics — PoS(XVHadronPhysics)
Lecture Notes in Computer Science, 2001
Physics Letters A, 2011
We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle con... more We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.
Physical Review C, 2000
The multipole amplitudes for the N-∆(1232) electromagnetic transition are computed in the framewo... more The multipole amplitudes for the N-∆(1232) electromagnetic transition are computed in the framework of the linear σ model and the chiral chromodielectric model for small and moderate photon virtualities. The models include quark and meson degrees of freedom and the nucleon and the delta are clusters of three valence hedgehog quarks surrounded by meson clouds described by coherent states. Angular momentum and isospin projections are performed to endow model states representing the nucleon and the delta with proper quantum numbers. Recoil corrections involved in the process γ v N → ∆ are taken into account by performing linear momentum projection of the initial and final baryon states. The ratios E2/M 1 and C2/M 1 are in good agreement with the data in the two models, but the magnetic amplitude is better reproduced in the Linear Sigma Model. The ratios show little dependence with the model parameters. Both in the Linear Sigma Model and in the Chromodielectric Model the charged pions are responsible for the non-vanishing quadrupoleelectric and-coulomb amplitudes. The recoil corrections enhance the results obtained for the amplitudes without linear momentum projection, improving the comparison with experimental data. The dependence of the theoretical amplitudes with the choice of the reference frame is also studied.
Computer Physics Communications, 1999
SoftSciences project-software for learning physics and other sciences. Pedro Vieira Alberto, Carl... more SoftSciences project-software for learning physics and other sciences. Pedro Vieira Alberto, Carlos Fiolhais, Joao Paiva Computer Physics Communications 121, 593, 1999. We describe an ongoing project in Portugal aimed ...
Journal of Physics: Conference Series, 2016
Journal of Physics G: Nuclear and Particle Physics
The possibility to compute nucleon electromagnetic form factors in the time-like region by analyt... more The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions, obtained in the framework of a generic model of nucleons, has been explored. We have developed a procedure to solve analytically Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematic regions and fulfilling the first-principles requirements of analyticity and unitarity. The results obtained in the particular case of the Skyrme model are discussed and compared to data, both in space-like and time-like region.
This paper deals with the application of pattern search methods to the numerical solution of a cl... more This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular problems have no constraints and the objective function is smooth. The difficulties arise from the existence of several local minima, and especially, from the expensive function evaluation (total energy) and the possible non-availability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations and to take advantage of parallelism without the use of derivatives. Numerical results with a particular instance of this new class of pattern search methods are presented showing the promise of our approach. The new pattern search...
This paper deals with the application of pattern search methods to the numerical solution of a cl... more This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular problems have no constraints and the objective function is smooth. The difficulties arise from the existence of several local minima, and especially, from the expensive function evaluation (total energy) and the possible non-availability of first-order derivatives. We introduce a pattern search approach that attempts to exploit the physical nature of the problem by using energy lowering geometrical transformations. Numerical results with a particular instance of this new class of pattern search methods and with the parallel direct search method of Dennis and Torczon are presented showing the promise of our approach.
arXiv: Nuclear Theory, 2011
Pion scattering and electro-production amplitudes have been computed in a coupled-channel framewo... more Pion scattering and electro-production amplitudes have been computed in a coupled-channel framework incorporating quasi-bound quark-model states, based on the Cloudy Bag model. All relevant low-lying nucleon resonances in the P33, P11, and S11 partial waves have been covered, including the Delta(1232), the N*(1440), N*(1535), and N*(1650). Consistent results have been obtained for elastic and inelastic scattering (two-pion, eta-N, and K-Lambda channels), as well as for electro-production. The meson cloud has been shown to play a major role, in particular in electro-magnetic observables in the P33 and P11 channels.
Brazilian Journal of Physics, 1996
Solitonic solutions with axial symmetry (in con guration and isospin spaces) are studied in the f... more Solitonic solutions with axial symmetry (in con guration and isospin spaces) are studied in the framework of the linear sigma model with quarks, and mesons. A comparison between the axial and the hedgehog solitons is presented in detail. It turns out that the axial soliton is less bound than the hedgehog. States with good angular momentum and isospin are extracted from the axial state by means of the Peierls-Yoccoz projection. The relevance of the axial ansatz is discussed in the context of a description of the angular momentum excitations of the nucleon and delta states.
arXiv: High Energy Physics - Phenomenology, 2015
The possibility to compute nucleon electromagnetic form factors in the time-like region by analyt... more The possibility to compute nucleon electromagnetic form factors in the time-like region by analytic continuation of their space-like expressions has been explored in the framework of the Skyrme model. We have developed a procedure to solve analytically Fourier transforms of the nucleon electromagnetic current and hence to obtain form factors defined in all kinematical regions and fulfilling the first-principles requirements. The results are discussed and compared to data, both in space-like and time-like region.
Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısic... more Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısica Computacional, Universidade de Coimbra, P-3004-516 Coimbra, Portugal Theoretical Physics Group, Dept of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada T1K 3M4 and Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, GR-11527, Athens, Greece
Astronomische Nachrichten
European Journal of Physics
The problem of a particle in a box is probably the simplest problem in quantum mechanics which al... more The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one-and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
Journal of Geophysical Research: Solid Earth
We use empirical orthogonal function analysis (EOFA) directly on sets of Schmidt spherical harmon... more We use empirical orthogonal function analysis (EOFA) directly on sets of Schmidt spherical harmonic (SH) coefficients modeling the internal geomagnetic field or its time derivatives at different epochs. We show how to properly use the method such that the application of EOFA to either spatial or spectral domains leads to the same results, bypassing the need to work on snapshots of field charts synthesized from SHs. In case a spatial grid is required, we point out which is the best grid to use. We apply the method to the CM4 geomagnetic field model to illustrate the differences in EOFA modes obtained with and without corrections. Once the corrected main modes of secular acceleration (SA) have been singled out, we retrieve previous results showing that the 1969, 1978, and 1991 geomagnetic field acceleration jumps have the same spatial pattern. A new finding in this study is that the same spatial pattern is present in principal modes of secular variation which, once inverted, may provide the flow responsible for the jerk sequence. Another finding is the unveiling of a different spatial structure common to a second group of jerks with SA pulses around 1985 and 1996, displaying a localization very similar to SA pulses identified in 2006 and 2009 using recent satellite data. Finally, if properly handled, the EOFA can be directly applied to a grid of data values of the geomagnetic field in order to produce SH models of decorrelated modes which may help to separate different sources of the field.
AIP Conference Proceedings, 2004
Medium modification of nucleon properties are studied in the framework of the Linear Sigma Model ... more Medium modification of nucleon properties are studied in the framework of the Linear Sigma Model (LSM). The nucleon is described as a chiral soliton with 3-quarks bounded due to their interactions with sigma and pion fields. Medium effects are introduced through the coupling of the quarks to sigma and omega fields, the strengths of which are determined self-consistently in a Walecka-like model, whose fermionic nucleon mass is calculated in the framework of the LSM. The nucleon properties are presented as functions of the nuclear density.
AIP Conference Proceedings, 2004
A generalized relativistic harmonic oscillator for spin 1 2 particles is studied. The Dirac Hamil... more A generalized relativistic harmonic oscillator for spin 1 2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ S •V or ∆ V S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case Σ 0, for which pseudospin symmetry is exact.