Natural Line Shape Research Articles

Precision resonance energy scans with the PANDA experiment at FAIR

.This paper summarises a comprehensive Monte Carlo simulation study for precision resonance energy scan measurements. Apart from the proof of principle for natural width and line shape measurements of very narrow resonances with PANDA, the achievable sensitivities are quantified for the concrete example of the charmonium-like X(3872) state discussed to be exotic, and for a larger parameter space of various assumed signal cross-sections, input widths and luminosity combinations. PANDA is the only experiment that will be able to perform precision resonance energy scans of such narrow states with quantum numbers of spin and parities that differ from J^{PC} = 1^{--}.

Data analysis techniques, differential cross sections, and spin density matrix elements for the reaction γp→ϕp

High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γp→ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (s) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (ϕ→K+K−) and neutral- (ϕ→KS0KL0) KK¯ decay modes of the ϕ. Further, for the charged mode, we differentiate between the cases where the final K− track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed ϕ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide s bins for the charged- and the neutral-modes, respectively. Possible effects from K+Λ* channels with pKK¯ final states are discussed. These present results constitute the most precise and extensive ϕ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.29 MoreReceived 11 March 2014Corrected 23 June 2014DOI:https://doi.org/10.1103/PhysRevC.89.055208©2014 American Physical Society

Frequency stabilization of a 369 nm diode laser by nonlinear spectroscopy of Ytterbium ions in a discharge

We demonstrate stabilization of an ultraviolet diode laser via Doppler-free spectroscopy of Ytterbium ions in a discharge. Our technique employs polarization spectroscopy, which produces a natural dispersive lineshape whose zero-crossing is largely immune to environmental drifts, making this signal an ideal absolute frequency reference for Yb+ ion trapping experiments. We stabilize an external-cavity diode laser near 369 nm for cooling Yb+ ions, using amplitude modulated polarization spectroscopy and a commercial PID feedback system. We achieve stable, low-drift locking with a standard deviation of measured laser frequency ∼ 400 kHz over 10 minutes, limited by the instantaneous linewidth of the diode laser. These results and the simplicity of our optical setup makes our approach attractive for stabilization of laser sources in atomic physics applications.

On the gauge of the natural lineshape

We use a general formulation of non-relativistic quantum electrodynamics in which the gauge freedom is carried by the arbitrary transverse component of the Green’s function for the divergence operator to calculate the natural lineshape of spontaneous emission, thus discerning the full dependence of the result on the choice of gauge. We also use a representation of the Hamiltonian in which the virtual field associated with the atomic ground state is explicitly absent. We consider two processes by which the atom is excited; the first is resonant absorption of incident radiation with a sharp line. This treatment is then adapted to derive a resonance fluorescence rate associated with the Lamb line in atomic hydrogen. Second we consider the atom’s excitation due to irradiation with a laser pulse treated semi-classically. An experiment could be used to reveal which of the calculated lineshape distributions is closest to the measured one. This would provide an answer to a question of fundamental importance; how does one best describe atom–radiation interactions with the canonical formalism?

Interaction of a single-photon wave packet with an excited atom

The interaction of a single-photon wave packet with an initially excited two-level atom in free space is studied in semiclassical and quantum approaches. It is shown that the final state of the field does not contain doubly occupied modes. The process of the atom's transition to the ground state may be accelerated, decelerated or even reversed by the incoming photon, depending on parameters. The spectrum of emitted radiation is close to the sum of the spectrum of the incoming single-photon wave packet and the natural line shape, with small and complicated deviations.

Recombination rate coefficients for KLL dielectronic satellite lines of Fe XXV and Ni XXVII

The unified method for total electron–ion recombination is extended to study the dielectronic satellite (DES) lines. These lines, formed from radiative decay of autoionizing states, are highly sensitive temperature diagnostics of astrophysical and laboratory plasma sources. The computation of the unified recombination rates is based on the relativistic Breit–Pauli R-matrix method and the close coupling approximation. As such unified recombination cross sections (σRC) include both the resonant and the non-resonant background contributions and the DES spectra correspond directly to resonances in σRC. Extending the theoretical formulation developed earlier (Nahar and Pradhan 2006 Phys. Rev. A 73 062718–1) we present recombination rate coefficients for the 22 satellite lines of KLL complexes of helium-like Fe XXV and Ni XXVII. The isolated resonance approximation, commonly used throughout plasma modeling, treats these resonances essentially as bound features except for dielectronic capture into, and autoionization out of, these levels. A line profile or cross section shape is often assumed. On the other hand, by including the coupling between the autoionizing and continuum channels, the unified method gives the intrinsic spectrum of DES lines which includes not only the energies and strengths, but also the natural line or cross section shapes. A formulation is presented to derive autoionization rates from unified resonance strengths and enable correspondence with the isolated resonance approximation. While the rates compare very well with existing rates for the strong lines to <20%, the differences for weaker DES lines are larger. We also illustrate the application of the present results to the analysis of Kα complexes observed in high-temperature x-ray emission spectra of Fe XXV and Ni XXVII. There are considerable differences with previous results in the total KLL intensity for Fe XXV at temperatures below the temperature of maximum abundance in coronal equilibrium.

Systematic multiconfiguration Dirac-Fock method study of the K-X-ray spectra of silicon

Extensive multiconfiguration Dirac-Fock calculations with the inclusion of the transverse Breit interaction and QED corrections have been performed for silicon to explain the influence of removing electrons from L and M shells on the shapes and parameters (the average Kα and Kβ transition energies and the values of Kβ/Kα intensity ratio) of its K-X-ray spectra. For Kα diagram lines and for certain L- and M-satellite lines the theoretical stick spectra (line positions with their relative intensities) have been presented. Moreover for each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response.

Theoretical predictions of the structure of M-X-ray lines of heavy atoms

Extensive multiconfiguration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on gold and thorium to elucidate the structure of various satellite (additional vacancies in N and/or O shells) and hypersatellite (additional vacancies in M or M and N shells) Mα1,2 (M5N6,7) and Mβ1 (M4N6) lines in its X-ray spectra. For every calculated type of Mα1,2 and Mβ 1 lines the theoretical stick spectra (line positions with their relative intensities) have been presented. Moreover for each type of lines two theoretical spectra have been predicted: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results will be very helpful in quantitative interpretation of a very complex origin of Mα 1,2 and Mβ 1 line structures in various high-resolution X-ray spectra of heavy atoms induced by different light and heavy projectiles.

Natural line shape

Natural line shape

Astrophysics: decoding the cosmos

Preface. Acknowledgments. Introduction. Appendix: dimensions, units and equations. PART I THE SIGNAL OBSERVED. 1 Defining the signal. 1.1 The power of light - luminosity and spectral power. 1.2 Light through a surface - flux and flux density. 1.3 The brightness of light - intensity and specific intensity. 1.4 Light from all angles - energy density and mean intensity. 1.5 How light pushes - radiation pressure. 1.6 The human perception of light - magnitudes. 1.7 Light aligned - polarization. Problems. 2 Measuring the signal. 2.1 Spectral filters and the panchromatic universe. 2.2 Catching the signal - the telescope. 2.3 The Corrupted signal - the atmosphere. 2.4 Processing the signal. 2.5 Analysing the signal. 2.6 Visualizing the signal. Problems. Appendix: refraction in the Earth's atmosphere. PART II MATTER AND RADIATION ESSENTIALS. 3 Matter essentials. 3.1 The Big Bang. 3.2 Dark and light matter. 3.3 Abundances of the elements. 3.4 The gaseous universe. 3.5 The dusty Universe. 3.6 Cosmic rays. Problems. Appendix: the electron/proton ratio in cosmic rays. 4 Radiation essentials. 4.1 Black body radiation. 4.2 Grey bodies and planetary temperatures. Problems. Appendix: derivation of the Planck function. 4.A.1 The statistical weight. 4.A.2 The mean energy per state. 4.A.3 The specific energy density and specific intensity. PART III THE SIGNAL PERTURBED. 5 The interaction of light with matter. 5.1 The photon redirected - scattering. 5.2 The photon lost - absorption. 5.3 The wavefront redirected - refraction. 5.4 Quantifying opacity and transparency. 5.5 The opacity of dust - extinction. Problems. 6 The signal transferred. 6.1 Types of energy transfer. 6.2 The equation of transfer. 6.3 Solutions to the equation of transfer. 6.4 Implications of the LTE solution. Problems. 7 The interaction of light with space. 7.1 Space and time. 7.2 Redshifts and blueshifts. 7.3 Gravitational refraction. 7.4 Time variability and source size. Problems. PART IV THE SIGNAL EMITTED. 8 Continuum emission. 8.1 Characteristics of continuum emission - thermal and non-thermal. 8.2 Bremsstrahlung (free-free) emission. 8.3 Free-bound (recombination) emission. 8.4 Two-photon emission. 8.5 Synchrotron (and cyclotron) radiation. 8.5.4 Synchrotron sources - spurs, bubbles, jets, lobes and relics. 8.6 Inverse Compton radiation. Problems. 9 Line emission. 9.1 The richness of the spectrum - radio waves to gamma rays. 9.2 The line strengths, thermalization, and the critical gas density. 9.3 Line broadening. 9.4 Probing physical conditions via electronic transitions. 9.5 Probing physical conditions via molecular transitions. Problems. PART V THE SIGNAL DECODED. 10 Forensic astronomy. 10.1 Complex spectra. 10.2 Case studies - the active, the young, and the old. 10.3 The messenger and the message. Problems. Appendix A: Mathematical and geometrical relations. A.1 Taylor series. A.2 Binomial expansion. A.3 Exponential expansion. A.4 Convolution. A.5 Properties of the ellipse. Appendix B: Astronomical geometry. B.1 One-dimensional and two-dimensional angles. B.2 Solid angle and the spherical coordinate system. Appendix C: The hydrogen atom. C.1 The hydrogen spectrum and principal quantum number. C.2 Quantum numbers, degeneracy, and statistical weight. C.3 Fine structure and the Zeeman effect. C.4 The l 21 cm line of neutral hydrogen. Appendix D: Scattering processes. D.1 Elastic, or coherent scattering. D.1.1 Scattering from free electrons - Thomson scattering. D.1.2 Scattering from bound electrons I: the oscillator model. D.1.3 Scattering from bound electrons II: quantum mechanics. D.1.4 Scattering from bound electrons III: resonance scattering and the natural line shape. D.1.5 Scattering from bound electrons IV: Rayleigh scattering. D.2 Inelastic scattering - Compton scattering from free electrons. D.3 Scattering by dust. Appendix E: Plasmas, the plasma frequency, and plasma waves. Appendix F: The Hubble relation and the expanding Universe. F.1 Kinematics of the Universe. F.2 Dynamics of the Universe. F.3 Kinematics, dynamics and high redshifts. Appendix G: Tables and Figures. References. Index.

Theoretical Study of the Accuracy Limits of Optical Resonance Frequency Measurements

The principal limits for the accuracy of the resonance frequency measurements set by the asymmetry of the natural resonance line shape are studied and applied to the recent accurate frequency measurements in the two-photon 1s-2s resonance and in the one-photon 1s-2p resonance in a hydrogen atom. This limit for 1s-2s resonance is found to be approximately 10(-5) Hz compared to the accuracy achieved in experiment +/-46 Hz. In the case of a deuterium atom the limit is essentially larger: 10(-2) Hz. For 1s-2p resonance the accuracy limit is 0.17 MHz while the uncertainty of the recent frequency measurement is about 6 MHz.

Theoretical multicon.guration Dirac-Fock method study on the structure of L-X-ray satellite and hypersatellite lines of zirconium

Detailed multicon.guration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on zirconium to elucidate the structure of various M-, N-shell satellite and L-shell hypersatellite Lα1,2 (L3M4,5) and Lβ1(L2M4) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The results are very helpful in reliable interpretation of various high-resolution L-X-ray spectra of zirconium target bombarded by different light and heavy projectiles.

Structure of L-X-ray satellite and hypersatellite lines of palladium

Extensive multiconfiguration Dirac–Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on palladium to elucidate the structure of various satellite (additional vacancies in M and/or N shells) and hypersatellite (additional vacancies in L or L and M shells) L α 1 , 2 ( L 3 M 4 , 5 ) and L β 1 ( L 2 M 4 ) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results will be absolutely essential to carry out quantitative interpretation of very complicated structure of L α 1 , 2 and L β 1 satellite and hypersatellite lines in various high-resolution L-X-ray spectra of palladium target bombarded by different light and heavy projectiles.

Structure of M-X-ray satellite and hypersatellite lines of thorium

Very extensive multiconfiguration Dirac–Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on thorium to elucidate the structure of various satellite (additional vacancies in N and/or O shells) and hypersatellite (additional vacancies in M or M and N shells) M α 1 , 2 ( M 5 N 6 , 7 ) and M β 1 ( M 4 N 6 ) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained theoretical results will be very helpful in reliable and quantitative interpretation of various experimental M-X-ray spectra of thorium target bombarded by different light and heavy projectiles (such as O and Ne ions).

Possibility of extraction of various KL0M1 and KL1M0 satellite lines in the x-ray spectra of medium-Z and heavy atoms

Predictions about the shapes of the K x-ray spectra of medium-Z and heavy atoms have been made on the basis of the results of theoretical multiconfiguration Dirac–Fock calculations (with the inclusion of the transverse Breit interaction and QED corrections) for various KL0M1 x-ray satellite lines of Pd, Tb, Ta and Th. The construction of theoretical stick and synthesized (the sum of the Lorentzian natural line shapes) K x-ray spectra (including also diagram and KL1M0 satellite lines) has enabled foreseeing such details of experimental spectra as the overlapping and visibility of particular groups of lines. The energy regions possibly best for the extraction of the satellite contributions in the measured K x-ray spectra have been indicated for each studied element. The effect of additional single ionization of the different subshells of the M shell on the structure and shapes of the spectra of various K x-ray lines has been investigated in detail for Pd, Tb, Ta and Th. It has been found that in the KL0M1 satellite spectra the shapes of the bands mainly resemble the shapes of the corresponding K x-ray diagram lines (but they are wider than the latter). For each element, the biggest average energy shifts with respect to the diagram lines are observed for a given kind of the KL0M1 lines mostly in the case of removing a 3p electron in the initial state, whereas the smallest shifts are caused by removing a 3d electron. Our study can enable the correct quantitative interpretation of the K x-ray spectra of different multiply ionized medium-Z and heavy atoms (induced in collisions with light or heavy ions) and can be instrumental in planning various new experiments involving the determination of the M- and L-shell ionization probability.

Comparison of the structure of various KL0M1 and KL1M0 x-ray satellite lines of lead

Multiconfiguration Dirac–Fock calculations (with the inclusion of the transverse Breit interaction and QED corrections) have been performed for various Pb K x-ray lines. The calculated positions and intensities of many electric dipole, electric quadrupole and magnetic dipole KL0M1 and KL1M0 x-ray satellite lines have been analysed. On the basis of theoretically constructed stick and synthesized (the sum of the Lorentzian natural line shapes) K x-ray spectra, the effect of the additional single ionization of different subshells of the M shell on the shapes and structure of Pb K x-ray spectra has been investigated and compared with the effect of the single L-shell ionization. It has been found that in the KL0M1 satellite spectra the sticks are less scattered and the shapes of the bands are narrower and smoother than in the KL1M0 spectra. The much weaker influence of an additional M-shell hole on the K x-ray spectra than of an L-shell hole is also reflected in very small values of the energy shifts (with respect to the corresponding diagram lines) of the KL0M1 satellite lines in comparison with those of the KL1M0 lines. This study provides an exhaustive set of data, enabling not only the correct quantitative analysis of many experimental Pb K x-ray spectra (induced in collisions with various projectiles), but also predictions concerning the K x-ray spectra of multiply ionized Pb or other heavy atoms, which can be helpful in designing new experiments.

Systematic Dirac–Fock method study of the X-ray spectra accompanying the ionization in collision processes: The structure of the Kβ2L0Mr lines

Extensive single-configuration Dirac–Fock (DF) calculations (within the multiconfiguration DF method) with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on Mo and Pd to elucidate the structure of the Kβ2L0Mr satellite lines in their X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results can be used to determine the M-shell ionization probability in collisions via the theoretical analysis of Kβ2 spectra of Mo and Pd induced by different energetic light and heavy ions.

Structure of variousKL1x-ray satellite lines of heavy atoms

Multiconfiguration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out for Pd, Sn, Tb, Ta, Pb, and Th in order to obtain positions and intensities of various electric dipole, electric quadrupole, and magnetic dipole $K$ x-ray diagram lines and of their $K{L}^{1}$ satellites. Theoretically constructed stick spectra have been presented together with synthesized spectra (the sum of the Lorentzian natural line shapes) for each studied element. Taking into account the existence of an $L$-shell hole in the $2s$ or $2p$ subshell, the effect of additional $L$-shell ionization on the shapes and structure of the $K$ x-ray spectra has been examined. It has been observed that generally with increasing atomic number $Z$ the shapes of particular satellite line groups tend to become smoother and to differ less from the shapes of appropriate diagram lines. Relations between the values of energy shifts of various satellite lines for each element and the changes of these relations with $Z$ have also been studied. Additionally, the relations between the intensities of different diagram lines for each element have been systematically analyzed, likewise the changes with $Z$ of the role of particular diagram lines. This study can be helpful in reliable and quantitative interpretation of many experimental $K$ x-ray spectra of Pd, Sn, Tb, Ta, Pb, and Th induced in collisions with various projectiles.

Influence of the thermal motion on the line shape and position of resonances in collinear fast beam laser spectroscopy

We derive the spectral line shape for collinear fast beam laser spectroscopy. As initial condition we take a thermally distributed ensemble into account. While the thermal velocity distribution of the fast ensemble has an asymmetric structure due to the acceleration by the electrostatic field, under typical experimental conditions the convolution with the natural line shape preserves the Lorentz profile with negligible broadening. However, the spectral line as a whole experiences a small shift depending on the temperature of the source and the acceleration .

High resolution in heteronuclear 1H–13C NMR experiments by optimizing spectral aliasing with one‐dimensional carbon data

AbstractIn the chemistry literature it is common to provide NMR data on both proton and carbon spectra based on one‐dimensional experiments, but often only proton spectra are assigned. The absence of a complete attribution of the carbons is in good part due to the difficulty in reaching the necessary resolution in the carbon dimension of two‐dimensional experiments. It has already been shown that high‐resolution heteronuclear spectra can be acquired within nearly the same acquisition time using a violation of the Nyquist condition. For a spectral width reduction by a given factor k, the resolution increases by the same factor as long as it is not limited by relaxation. The price to pay for such an improvement is a k‐fold ambiguity in the chemical shift of the signal along the folded or aliased dimension. The computer algorithm presented in this paper takes advantage of the peak list stemming from one‐dimensional spectra in order to calculate spectral widths for which the ambiguities in the aliased dimension of heteronuclear experiments are eliminated or at least minimized. The resolution improvement factor is only limited by the natural lineshape and reaches a typical value higher than 100. The program may be set to run automatically on spectrometers equipped with automatic sample changers. Applications to short‐range HSQC experiments and long‐range HMBC spectra of steroids, carbohydrates, a peptide and a mixture of isomers are shown as examples. Copyright © 2002 John Wiley &amp; Sons, Ltd.