## Recent Publications

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Book
Santos, J. P., and M. F. Laranjeira. Métodos Matemáticos para Físicos e Engenheiros., 2004. Abstract
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Conference Paper
Pohl, Randolf, François Nez, Luis M. P. Fernandes, Marwan Abdou Ahmed, Fernando D. Amaro, Pedro Amaro, François Biraben, João M. R. Cardoso, Daniel S. Covita, Andreas Dax, Satish Dhawan, Marc Diepold, Beatrice Franke, Sandrine Galtier, Adolf Giesen, Andrea L. Gouvea, Johannes Götzfried, Thomas Graf, Theodor W. Hänsch, Malte Hildebrandt, Paul Indelicato, Lucile Julien, Klaus Kirch, Andreas Knecht, Paul Knowles, Franz Kottmann, Julian J. Krauth, Eric-Olivier Le Bigot, Yi-Wei Liu, José A. M. Lopes, Livia Ludhova, Jorge Machado, Cristina M. B. Monteiro, Françoise Mulhauser, Tobias Nebel, Paul Rabinowitz, Joaquim M. F. dos Santos, Jose Paulo Santos, Lukas A. Schaller, Karsten Schuhmann, Catherine Schwob, Csilla I. Szabo, David Taqqu, João F. C. A. Veloso, Andreas Voss, Birgit Weichelt, and Aldo Antognini. "Laser Spectroscopy of Muonic Atoms and Ions." In Proceedings of the 12th International Conference on Low Energy Antiproton Physics (LEAP2016), 1-12. Journal of the Physical Society of Japan, 2017. Abstract
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Lopes, G., D. Tendeiro, J. P. Santos, and P. Vieira. "Monte Carlo Simulation of Radiation through the Human Retina Using Geant4.", 431-434. Vol. 41. Cham: Springer International Publishing, 2014. Abstract
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Lopes, G., D. Tendeiro, J. P. Santos, and P. Vieira. "Monte Carlo Simulation of Radiation through the Human Retina Using Geant4.", 431-434. Vol. 41. Cham: Springer International Publishing, 2014. Abstract
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Lopes, A., A. Gabriel, J. Machado, P. Ribeiro, R. Gomes, Jo M. P. o Coelho, C. O. Silva, C. P. Reis, J. P. Santos, and P. Vieira. "Multiple Source Phototherapy in Breast Cancer: A Viability Study." In 9th International Conference on Biomedical Electronics and Devices, 247-250. SCITEPRESS - Science and and Technology Publications, 2016. Abstract
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Journal Article
Amaro, Pedro, Sophie Schlesser, Mauro Guerra, Eric-Olivier Le Bigot, Jean-Michel Isac, Pascal Travers, Jose Paulo Santos, Csilla Szabo, Alexandre Gumberidze, and Paul Indelicato. "Absolute Measurement of the Relativistic Magnetic Dipole Transition Energy in Heliumlike Argon." Phys. Rev. Lett. 109 (2012): 043005. AbstractWebsite

The 1s2s 3S1 ! 1s2 1S0 relativistic magnetic dipole transition in heliumlike argon, emitted by the plasma of an electron-cyclotron resonance ion source, has been measured using a double-flat crystal x-ray spectrometer. Such a spectrometer, used for the first time on a highly charged ion transition, provides absolute (reference-free) measurements in the x-ray domain. We find a transition energy of 3104.1605(77) eV (2.5 ppm accuracy). This value is the most accurate, reference-free measurement done for such a transition and is in good agreement with recent QED predictions.

Amaro, Pedro, Sophie Schlesser, Mauro Guerra, Eric-Olivier Le Bigot, Jean-Michel Isac, Pascal Travers, Jose Paulo Santos, Csilla Szabo, Alexandre Gumberidze, and Paul Indelicato. "Absolute Measurement of the Relativistic Magnetic Dipole Transition Energy in Heliumlike Argon." Physical Review Letters 109 (2012): 043005. AbstractWebsite

The 1s2s 3S1 - 1s2 1S0 relativistic magnetic dipole transition in heliumlike argon, emitted by the plasma of an electron-cyclotron resonance ion source, has been measured using a double-flat crystal x-ray spectrometer. Such a spectrometer, used for the first time on a highly charged ion transition, provides absolute (reference-free) measurements in the x-ray domain. We find a transition energy of 3104.1605(77) eV (2.5 ppm accuracy). This value is the most accurate, reference-free measurement done for such a transition and is in good agreement with recent QED predictions.

Amaro, P., S. Schlesser, M. Guerra, E. Le Bigot, J. P. Santos, C. I. Szabo, A. Gumberidze, and P. Indelicato. "Absolute measurements and simulations of x-ray line energies of highly charged ions with a double-crystal spectrometer." T156 (2013): 014104. AbstractWebsite
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Amaro, P., S. Schlesser, M. Guerra, E. Le Bigot, J. P. Santos, C. I. Szabo, A. Gumberidze, and P. Indelicato. "Absolute measurements and simulations of x-ray line energies of highly charged ions with a double-crystal spectrometer." Physica Scripta T156 (2013): 014104. AbstractWebsite
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Guerra, M., P. Amaro, C. I. Szabo, A. Gumberidze, P. Indelicato, and J. P. Santos. "Analysis of the charge state distribution in an ECRIS Ar plasma using high-resolution x-ray spectra." Journal of Physics B: Atomic, Molecular and Optical Physics 46 (2013): 065701. AbstractWebsite

In this work, we obtained a charge state distribution inside an Ar plasma produced by an electron–cyclotron-resonance ion source. The processes that lead to the observed lines in x-ray spectra are identified and included in the simulated x-ray spectrum. The geometrical constraints of the flat double crystal spectrometer, used to measure the x-ray spectrum, are investigated as they are crucial for correctly obtaining the ion densities from the observed transition amplitudes. Multiple electron impact ionization is included, and a realistic electron velocity distribution is taken into account. The charge state distribution of the Ar ions is compared to measured extracted ionic currents.

Guerra, M., P. Amaro, C. I. Szabo, A. Gumberidze, P. Indelicato, and J. P. Santos. "Analysis of the charge state distribution in an ECRIS Ar plasma using high-resolution x-ray spectra." Journal of Physics B: Atomic, Molecular and Optical Physics 46 (2013): 065701. AbstractWebsite

In this work, we obtained a charge state distribution inside an Ar plasma produced by an electron–cyclotron-resonance ion source. The processes that lead to the observed lines in x-ray spectra are identified and included in the simulated x-ray spectrum. The geometrical constraints of the flat double crystal spectrometer, used to measure the x-ray spectrum, are investigated as they are crucial for correctly obtaining the ion densities from the observed transition amplitudes. Multiple electron impact ionization is included, and a realistic electron velocity distribution is taken into account. The charge state distribution of the Ar ions is compared to measured extracted ionic currents.

Safari, L., J. P. Santos, P. Amaro, K. Jankala, and F. Fratini. "Analytical evaluation of atomic form factors: Application to Rayleigh scattering." Journal of Mathematical Physics 56 (2015): 052105-9. AbstractWebsite
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Guimarães, D., J. P. Santos, M. L. Carvalho, M. S. Diniz, B. House, and V. M. Miller. "Analytical evidence of heterogeneous lead accumulation in the hypothalamic defence area and nucleus tractus solitarius." NeuroToxicology 44 (2014): 91-97. AbstractWebsite

Guimarães, D., J. P. Santos, M. L. Carvalho, M. S. Diniz, B. House, and V. M. Miller. "Analytical evidence of heterogeneous lead accumulation in the hypothalamic defence area and nucleus tractus solitarius." NeuroToxicology 44 (2014): 91-97. AbstractWebsite

Safari, L., P. Amaro, J. P. Santos, and F. Fratini. "Angular and polarization analysis for two-photon decay of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>s</mi></mrow>[/itex]&." Physical Review A 90 (2014): 014502. AbstractWebsite

The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the relativistic Dirac equation and second-order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W($\theta${})$\sim${}1+{cos}^{2}$\theta${}$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W($\theta${})$\sim${}1$-${}1/3{cos}^{2}$\theta${}$ while the polarizations of the emitted photons are orthogonal, where $$\theta{} is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions. Safari, L., P. Amaro, J. P. Santos, and F. Fratini. "Angular and polarization analysis for two-photon decay of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>s</mi></mrow>[/itex]&." Physical Review A 90 (2014): 014502. AbstractWebsite The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the relativistic Dirac equation and second-order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of 2s states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type W(\theta{})\sim{}1+{cos}^{2}\theta{} while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type W(\theta{})\sim{}1-{}1/3{cos}^{2}\theta{} while the polarizations of the emitted photons are orthogonal, where$$\theta${}$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.

Surzhykov, A., A. Volotka, F. Fratini, J. P. Santos, P. Indelicato, G. Plunien, Th Stöhlker, and S. Fritzsche. "Angular correlations in the two-photon decay of heliumlike heavy ions." Physical Review A 81 (2010): 042510. AbstractWebsite
The two-photon decay of heavy, helium-like ions is investigated based on second-order perturbation theory and Dirac’s relativistic equation. Special attention has been paid to the angular emission of the two photons (i.e., how the angular correlation function depends on the shell structure of the ions in their initial and final states). Moreover, the effects from the (electric and magnetic) nondipole terms in the expansion of the electron-photon interaction are discussed. Detailed calculations have been carried out for the two-photon decay of the 1s2s1S0, 1s2s3S1, and 1s2p3P0 states of helium-like Xe52+, Au77+, and U90+ ions.
Surzhykov, A., A. Volotka, F. Fratini, J. P. Santos, P. Indelicato, G. Plunien, Th Stöhlker, and S. Fritzsche. "Angular correlations in the two-photon decay of heliumlike heavy ions." Physical Review A 81 (2010): 042510. AbstractWebsite

The two-photon decay of heavy, helium-like ions is investigated based on second-order perturbation theory and Dirac’s relativistic equation. Special attention has been paid to the angular emission of the two photons (i.e., how the angular correlation function depends on the shell structure of the ions in their initial and final states). Moreover, the effects from the (electric and magnetic) nondipole terms in the expansion of the electron-photon interaction are discussed. Detailed calculations have been carried out for the two-photon decay of the 1s2s1S0, 1s2s3S1, and 1s2p3P0 states of helium-like Xe52+, Au77+, and U90+ ions.

Santos, J. P., F. Parente, and P. Indelicato. "Application of B-splines finite basis sets to relativistic two-photon decay rates of 2s level in hydrogenic ions." The European Physical Journal D 3 (1998): 43-52. AbstractWebsite

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies.

Katriel, Jacob, J. P. Marques, P. Indelicato, A. M. Costa, M. C. Martins, J. P. Santos, and F. Parente. "Approach towards the critical charge of some excited states of the Be isoelectronic series." Physical Review A 90 (2014): 052519-5. AbstractWebsite
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Sampaio, J. M., T. I. Madeira, J. P. Marques, F. Parente, A. M. Costa, P. Indelicato, J. P. Santos, M. - C. Lépy, and Y. Ménesguen. "Approaches for theoretical and experimental determinations of K-shell decay rates and fluorescence yields in Ge." Physical Review A 89 (2014): 012512. AbstractWebsite
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Sampaio, J. M., T. I. Madeira, J. P. Marques, F. Parente, A. M. Costa, P. Indelicato, J. P. Santos, M. - C. Lépy, and Y. Ménesguen. "Approaches for theoretical and experimental determinations of K-shell decay rates and fluorescence yields in Ge." Physical Review A 89 (2014): 012512. AbstractWebsite
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Santos, I., M. S. Diniz, M. L. Carvalho, and J. P. Santos. "Assessment of Essential Elements and Heavy Metals Content on Mytilus galloprovincialis from River Tagus Estuary." Biological Trace Element Research (2014). AbstractWebsite

Trace elemental content was analysed in edible tissues of Mytilus galloprovincialis collected in five different sampling areas near the mouth of river Tagus estuary in Lisbon. The concentrations of essential elements (S, K, Ca, Fe, Cu, Zn, As, Br and Sr) were determined by energy-dispersive X-ray fluorescence (EDXRF) spectrometry, while toxic elements (Cr, Cd, Hg, Se and Pb) were measured by inductively coupled plasma-atomic emission spectrometry (ICP-AES). The results show that the essential elements K and S are present at the highest concentrations in all the studied samples reaching 2,920 and 4,520 μg g(-1) (fresh weight), respectively. The highest levels of heavy metals found were in two areas close to the city for Pb and Cd, but below the maximum allowed values.

Santos, I., M. S. Diniz, M. L. Carvalho, and J. P. Santos. "Assessment of Essential Elements and Heavy Metals Content on Mytilus galloprovincialis from River Tagus Estuary." Biological Trace Element Research (2014). AbstractWebsite

Trace elemental content was analysed in edible tissues of Mytilus galloprovincialis collected in five different sampling areas near the mouth of river Tagus estuary in Lisbon. The concentrations of essential elements (S, K, Ca, Fe, Cu, Zn, As, Br and Sr) were determined by energy-dispersive X-ray fluorescence (EDXRF) spectrometry, while toxic elements (Cr, Cd, Hg, Se and Pb) were measured by inductively coupled plasma-atomic emission spectrometry (ICP-AES). The results show that the essential elements K and S are present at the highest concentrations in all the studied samples reaching 2,920 and 4,520 μg g(-1) (fresh weight), respectively. The highest levels of heavy metals found were in two areas close to the city for Pb and Cd, but below the maximum allowed values.