## Recent Publications

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A
Amaro, P., J. P. Santos, F. Parente, A. Surzhykov, and P. Indelicato. "Resonance effects on the two-photon emission from hydrogenic ions." Physical Review A (Atomic, Molecular, and Optical Physics) 79 (2009): 062504. AbstractWebsite
A theoretical study of the all two-photon transitions from initial bound states with ni=2,3 in hydrogenic ions is presented. High-precision values of relativistic decay rates for ions with nuclear charge in the range 1<=Z<=92 are obtained through the use of finite basis sets for the Dirac equation constructed from B splines. We also report the spectral (energy) distributions of several resonant transitions, which exhibit interesting structures, such as zeros in the emission spectrum, indicating that two-photon emission is strongly suppressed at certain frequencies. We compare two different approaches (the line profile approach and the QED approach based on the analysis of the relativistic two-loop self-energy) to regularize the resonant contribution to the decay rate. Predictions for the pure two-photon contributions obtained in these approaches are found to be in good numerical agreement.
Amaro, P., C. I. Szabo, S. Schlesser, A. Gumberidze, E. G. Kessler, A. Henins, E. O. Le Bigot, M. Trassinelli, J. M. Isac, P. Travers, M. Guerra, J. P. Santos, and P. Indelicato. "A vacuum double-crystal spectrometer for reference-free X-ray spectroscopy of highly charged ions." Radiation Physics and Chemistry 98 (2014): 132-149. AbstractWebsite

Amaro, P., F. Fratini, S. Fritzsche, P. Indelicato, J. P. Santos, and A. Surzhykov. "Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogenlike ions." Physical Review A 86 (2012): 042509. AbstractWebsite

The spontaneous two-photon emission in hydrogenlike ions is investigated within the framework of second- order perturbation theory and Dirac’s equation. Special attention is paid to the angular correlation of the emitted photons as well as to the degree of linear polarization of one of the two photons, if the second is just observed under arbitrary angles. Expressions for the angular correlation and the degree of linear polarization are expanded in powers of cosine functions of the two-photon opening angle, whose coefficients depend on the atomic number and the energy sharing of the emitted photons. The effects of including higher (electric and magnetic) multipoles upon the emitted photon pairs beyond the electric-dipole approximation are also discussed. Calculations of the coefficients are performed for the transitions 2s1/2 → 1s1/2, 3d3/2 → 1s1/2, and 3d5/2 → 1s1/2, along the entire hydrogen isoelectronic sequence (1 Z 100).

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., J. P. Santos, F. Parente, A. Surzhykov, and P. Indelicato. "Resonance effects on the two-photon emission from hydrogenic ions." Physical Review A 79 (2009): 062504. AbstractWebsite

A theoretical study of the all two-photon transitions from initial bound states with ni=2,3 in hydrogenic ions is presented. High-precision values of relativistic decay rates for ions with nuclear charge in the range 1<=Z<=92 are obtained through the use of finite basis sets for the Dirac equation constructed from B splines. We also report the spectral (energy) distributions of several resonant transitions, which exhibit interesting structures, such as zeros in the emission spectrum, indicating that two-photon emission is strongly suppressed at certain frequencies. We compare two different approaches (the line profile approach and the QED approach based on the analysis of the relativistic two-loop self-energy) to regularize the resonant contribution to the decay rate. Predictions for the pure two-photon contributions obtained in these approaches are found to be in good numerical agreement.

Amaro, P., J. P. Marques, P. Indelicato, T. K. Mukherjee, J. K. Saha, L. C. Tribedi, and J. P. Santos. "Double KK excited states in highly charged sulphur ." Journal of Physics: Conference Series 635 (1981): 022071. Abstract
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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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Amaro, P., F. Fratini, S. Fritzsche, P. Indelicato, J. P. Santos, and A. Surzhykov. "Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogenlike ions." Phys. Rev. A 86 (2012): 042509. AbstractWebsite

The spontaneous two-photon emission in hydrogenlike ions is investigated within the framework of second- order perturbation theory and Dirac’s equation. Special attention is paid to the angular correlation of the emitted photons as well as to the degree of linear polarization of one of the two photons, if the second is just observed under arbitrary angles. Expressions for the angular correlation and the degree of linear polarization are expanded in powers of cosine functions of the two-photon opening angle, whose coefficients depend on the atomic number and the energy sharing of the emitted photons. The effects of including higher (electric and magnetic) multipoles upon the emitted photon pairs beyond the electric-dipole approximation are also discussed. Calculations of the coefficients are performed for the transitions 2s1/2 → 1s1/2, 3d3/2 → 1s1/2, and 3d5/2 → 1s1/2, along the entire hydrogen isoelectronic sequence (1

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.
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., 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.

Amaro, Pedro, Filippo Fratini, Laleh Safari, Aldo Antognini, Paul Indelicato, Randolf Pohl, and Jose Paulo Santos. "Quantum interference shifts in laser spectroscopy with elliptical polarization." Physical Review A 92 (2015): 062506-5. AbstractWebsite
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Amaro, Pedro, Beatrice Franke, Julian J. Krauth, Marc Diepold, Filippo Fratini, Laleh Safari, Jorge Machado, Aldo Antognini, Franz Kottmann, Paul Indelicato, Randolf Pohl, and Jose Paulo Santos. "Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3." Physical Review A 92 (2015): 022514-7. AbstractWebsite
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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, P., C. I. Szabo, S. Schlesser, A. Gumberidze, E. G. Kessler, A. Henins, E. O. Le Bigot, M. Trassinelli, J. M. Isac, P. Travers, M. Guerra, J. P. Santos, and P. Indelicato. "A vacuum double-crystal spectrometer for reference-free X-ray spectroscopy of highly charged ions." Radiation Physics and Chemistry 98 (2014): 132-149. AbstractWebsite

Amaro, P., and Csilla I. Szabo. A vacuum double-crystal spectrometer for reference-free highly charged ions X-ray spectroscopy. Submitted to Radiation Physics and Chemistry, Radiat. Phys. Chem. ed., 2012. Abstract
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Amaro, Pedro, Filippo Fratini, Laleh Safari, Jorge Machado, Mauro Guerra, Paul Indelicato, and Jose Paulo Santos. "Relativistic evaluation of the two-photon decay of the metastable 1s22s2p 3P0 state in berylliumlike ions with an effective-potential model." Physical Review A 93 (2016): 032502-8. AbstractWebsite

The two-photon $1{s}^{2}2s2p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}\ensuremath{\rightarrow}1{s}^{2}{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ transition in berylliumlike ions is investigated theoretically within a fully relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum, can affect the forbidden $E1M1$ decay rate. For this purpose, we include the electronic correlation via an effective local potential and within a single-configuration-state model. Due to its experimental interest, evaluations of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected at the present level of accuracy in the evaluation of the decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by up to 20%. By performing a fully relativistic $jj$-coupling calculation, we find a decrease of the decay rate by two orders of magnitude compared to nonrelativistic $LS$-coupling calculations, for the selected heavy ions.

B
Benis, E. P., S. Doukas, T. J. M. Zouros, P. Indelicato, F. Parente, C. Martins, J. P. Santos, and J. P. Marques. "Evaluation of the effective solid angle of a hemispherical deflector analyser with injection lens for metastable Auger projectile states." Nuclear Inst. and Methods in Physics Research, B 365 (2015): 457-461. AbstractWebsite

Nuclear Inst. and Methods in Physics Research, B, 365 (2015) 457-461. doi:10.1016/j.nimb.2015.07.006

C
Cardoso, Pedro, Pedro Amaro, Jose Paulo Santos, Joaquim T. de Assis, and Maria Luisa Carvalho. "Determination of Nickel and Manganese Contaminants in Pharmaceutical Iron Supplements using Energy Dispersive X-ray Fluorescence." Applied Spectroscopy (2016). AbstractWebsite

In this study, we investigate the capability of energy dispersive X-ray fluorescence (EDXF) spectrometry in a triaxial geometry apparatus as a fast and nondestructive determination method of both dominant and contaminant elements in pharmaceutical iron supplements. The following iron supplements brands with their respective active ingredients were analyzed: Neutrofer fólico (iron gylcinate), Anemifer (iron(II) sulfate monohydrate), Noripurum (iron(III)-hydroxide polymaltose complex), Sulferbel (iron(II) sulfate monohydrate), and Combiron Fólico (carbonyl iron). Although we observe a good agreement between the iron content obtained by the present method and that indicated in the supplement's prescribed dose, we observe contamination by manganese and nickel of up to 180 μg and 36 μg, respectively. These contents correspond to 7.2% and 14.4% of the permitted daily exposure of manganese and nickel, respectively, for an average adult individual as determined by the European Medicine Agency (EMEA). The method was successfully validated against the concentrations of several certified reference materials of biological light matrices with similar concentrations of contaminants. Moreover, we also validated our method by comparing the concentrations with those obtained with the inductively coupled plasma-atomic emission technique.

Costa, A. M., M. C. Martins, J. P. Santos, P. Indelicato, and F. Parente. "Relativistic calculation of Kβ hypersatellite energies and transition probabilities for selected atoms with 13<=Z<=80." Journal of Physics B: Atomic and Molecular Physics 39 (2006): 2355-2366. AbstractWebsite
Energies and transition probabilities of Kβ hypersatellite lines are computed using the Dirac–Fock model for several values of Z throughout the periodic table. The influence of the Breit interaction on the energy shifts from the corresponding diagram lines and on the Kβh1/Kβh3 intensity ratio is evaluated. The widths of the double-K hole levels are calculated for Al and Sc. The results are compared to experiment and to other theoretical calculations.
Costa, A. M., M. C. Martins, J. P. Santos, P. Indelicato, and F. Parente. "Relativistic calculation of Kα hypersatellite line energies and transition probabilities for selected atoms with 12<=Z<=80." Journal of Physics B: Atomic, Molecular and Optical Physics 40 (2007): 57. AbstractWebsite
The transition probabilities of Kα hypersatellite lines and energy shifts with respect to the corresponding diagram lines are computed using the Dirac–Fock model for several values of atomic number Z throughout the periodic table. The influence of the Breit interaction on the Kα1h/Kα2h line intensity ratio, Kα1h and Kα2h line energy shifts and Kα1h to Kα2h line energy splitting is evaluated. Double-K shell hole threshold values for selected elements with 23 ⩽Z⩽ 30, calculated within the same approach, are compared with available experimental results.
Costa, A. M., M. C. Martins, J. P. Santos, P. Indelicato, and F. Parente. "Relativistic calculation of Kβ hypersatellite energies and transition probabilities for selected atoms with 13 ≤ Z ≤ 80." Journal of Physics B: Atomic and Molecular Physics 39 (2006): 2355-2366. AbstractWebsite

Energies and transition probabilities of Kβ hypersatellite lines are computed using the Dirac–Fock model for several values of Z throughout the periodic table. The influence of the Breit interaction on the energy shifts from the corresponding diagram lines and on the Kβh1/Kβh3 intensity ratio is evaluated. The widths of the double-K hole levels are calculated for Al and Sc. The results are compared to experiment and to other theoretical calculations.Al_Sc_Mg_Ti

Costa, A. M., M. C. Martins, J. P. Santos, P. Indelicato, and F. Parente. "Relativistic calculation of K&alpha; hypersatellite line energies and transition probabilities for selected atoms with 12 ≤ Z ≤ 80." Journal of Physics B: Atomic, Molecular and Optical Physics 40 (2007): 57. AbstractWebsite

The transition probabilities of K&alpha; hypersatellite lines and energy shifts with respect to the corresponding diagram lines are computed using the Dirac&ndash;Fock model for several values of atomic number <I>Z</I> throughout the periodic table. The influence of the Breit interaction on the K&alpha;<SUB>1</SUB><SUP>h</SUP>/K&alpha;<SUB>2</SUB><SUP>h</SUP> line intensity ratio, K&alpha;<SUB>1</SUB><SUP>h</SUP> and K&alpha;<SUB>2</SUB><SUP>h</SUP> line energy shifts and K&alpha;<SUB>1</SUB><SUP>h</SUP> to K&alpha;<SUB>2</SUB><SUP>h</SUP> line energy splitting is evaluated. Double-K shell hole threshold values for selected elements with 23 &les;<I>Z</I>&les; 30, calculated within the same approach, are compared with available experimental results.

Costa, A. M., M. C. Martins, J. P. Santos, P. Indelicato, and F. Parente. "Dirac-Fock Transition Energies and Radiative and Radiationless Transition Probabilities for Ar8+ to Ar16+ Ion Levels with K-Shell Hole." Atomic Data and Nuclear Data Tables 79 (2001): 223-239. Abstract
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D
Diepold, Marc, Luis M. P. Fernandes, Jorge Machado, Pedro Amaro, Marwan Abdou-Ahmed, Fernando D. Amaro, Aldo Antognini, François Biraben, Tzu-Ling Chen, Daniel S. Covita, Andreas J. Dax, Beatrice Franke, Sandrine Galtier, Andrea L. Gouvea, Johannes Götzfried, Thomas Graf, Theodor W. Hänsch, Malte Hildebrandt, Paul Indelicato, Lucile Julien, Klaus Kirch, Andreas Knecht, Franz Kottmann, Julian J. Krauth, Yi-Wei Liu, Cristina M. B. Monteiro, Françoise Mulhauser, Boris Naar, Tobias Nebel, François Nez, Jose Paulo Santos, Joaquim M. F. dos Santos, Karsten Schuhmann, Csilla I. Szabo, David Taqqu, João F. C. A. Veloso, Andreas Voss, Birgit Weichelt, and Randolf Pohl. "Improved x-ray detection and particle identification with avalanche photodiodes." Review of Scientific Instruments 86 (2015): 053102-7. AbstractWebsite
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