## 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
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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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

Lead is a potent toxicant associated with adverse cardiovascular effects and hypertension in children. Yet, few studies have determined if autonomic dysfunction associated with lead exposure involves brain regions which regulate autonomic responses. Central autonomic nuclei such as the nucleus tractus solitarius (NTS) and hypothalamic defence area (HDA) may be particularly sensitive to lead infiltration because they are adjacent to ventricles and areas with semi-permeable blood-brain-barriers. To understand if autonomic nuclei are sensitive to lead accumulation Wistar rats were exposed to lead from the gestational period and lead levels were quantified in brain regions that regulate arterial pressure: the NTS and the HDA. Energy dispersive X-ray fluorescence (EDXRF) was used to quantify total brain lead levels and revealed no differences between exposed and control tissues; measured values were close to the detection limit (2μg/g). Electrothermal atomic absorption spectrometry (ETAAS) was also used, which has a greater sensitivity, to quantify lead. There was ∼2.1μg/g lead in the NTS and ∼3.1μg/g lead in the HDA of exposed rats, and no lead in the control rats. There were greater lead levels in the HDA (∼50%) as compared with the NTS. Pathology studies revealed more prominent lead granules in the HDA as compared with the NTS. Increased microglia and astrocyte activation was also noted in the NTS of lead exposed rats as compared with the HDA. Regional differences in neuro-inflammatory responses likely contribute to heterogeneous lead accumulation, with enhanced clearance of lead in the NTS. Future studies will resolve the mechanisms underpinning tissue-specific lead accumulation.

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

Lead is a potent toxicant associated with adverse cardiovascular effects and hypertension in children. Yet, few studies have determined if autonomic dysfunction associated with lead exposure involves brain regions which regulate autonomic responses. Central autonomic nuclei such as the nucleus tractus solitarius (NTS) and hypothalamic defence area (HDA) may be particularly sensitive to lead infiltration because they are adjacent to ventricles and areas with semi-permeable blood-brain-barriers. To understand if autonomic nuclei are sensitive to lead accumulation Wistar rats were exposed to lead from the gestational period and lead levels were quantified in brain regions that regulate arterial pressure: the NTS and the HDA. Energy dispersive X-ray fluorescence (EDXRF) was used to quantify total brain lead levels and revealed no differences between exposed and control tissues; measured values were close to the detection limit (2μg/g). Electrothermal atomic absorption spectrometry (ETAAS) was also used, which has a greater sensitivity, to quantify lead. There was ∼2.1μg/g lead in the NTS and ∼3.1μg/g lead in the HDA of exposed rats, and no lead in the control rats. There were greater lead levels in the HDA (∼50%) as compared with the NTS. Pathology studies revealed more prominent lead granules in the HDA as compared with the NTS. Increased microglia and astrocyte activation was also noted in the NTS of lead exposed rats as compared with the HDA. Regional differences in neuro-inflammatory responses likely contribute to heterogeneous lead accumulation, with enhanced clearance of lead in the NTS. Future studies will resolve the mechanisms underpinning tissue-specific lead accumulation.

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.

Santos, J. P., M. F. Laranjeira, and F. Parente. "Calculation of the triple to double ionization cross-section ratio of Li in the suddem approximation." Europhysics Letters 55 (2001): 479. Abstract

The triple-to-double ionization cross-section ratio of Li in the high-energy limit was computed in the sudden approximation with relativistic wave functions. Together with the calculated value of Dalgarno and Sadeghpour (Phys. Rev. A, 46 (1992) R3591), for the Li double-to-single ionization cross-section ratio, the value of 6.263x10-5 was obtained for the triple-to-single ionization cross-section ratio. This value is in full agreement with Wehlitz et al. experimental value of (6.38+-2.40)x10-5 obtained recently with synchrotron radiation (Phys. Rev. Lett., 81 (1998) 1813).

Amaro, P., A. Surzhykov, F. Parente, P. Indelicato, and J. P. Santos. "Calculation of two-photon decay rates of hydrogen-like ions by using B-polynomials." Journal of Physics A: Mathematical and Theoretical 44 (2011): 245302. AbstractWebsite
A new approach is laid out to investigate two-photon atomic transitions. It is based on the application of the finite-basis solutions constructed from the Bernstein polynomial (B-polynomial) sets. We show that such an approach provides a very promising route for the relativistic second-order (and even higher-order) calculations since it allows for analytical evaluation of the involved matrices elements. In order to illustrate possible applications of the method and to verify its accuracy, detailed calculations are performed for the 2 s 1/2 ‚Üí 1 s 1/2 transition in neutral hydrogen and hydrogen-like ions, which are compared with the theoretical predictions based on the well-established B-spline basis-set approach.