Related Experiment Video
Updated: Feb 28, 2026
06:46
Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic
Published on: August 25, 2016
11.8K
Time-resolved X-ray scattering by electronic wave packets: analytic solutions to the hydrogen atom
Mats Simmermacher1, Niels E Henriksen, Klaus B Møller
1Department of Chemistry, Technical University of Denmark, 2800 Lyngby, Denmark. neh@kemi.dtu.dk.
Physical Chemistry Chemical Physics : PCCP
|June 20, 2017
Summary
This study details time-resolved X-ray scattering by electronic wave packets in atoms. Analytical solutions for the hydrogen atom enable efficient and accurate simulations of dynamical changes.
Area of Science:
- Atomic Physics
- Quantum Mechanics
- X-ray Scattering
Background:
- Modern pulsed X-ray sources enable time-dependent measurements of atomic and molecular dynamics.
- Interpreting these experiments requires a robust theoretical framework for non-resonant scattering.
Purpose of the Study:
- To provide a detailed theoretical description of time-resolved X-ray scattering by non-stationary electronic wave packets.
- To establish an analytical framework for simulations and benchmarks.
Main Methods:
- Application of the Waller-Hartree approximation to identify scattering signal contributions.
- Derivation of analytical expressions for scattering signals of wave packets in the hydrogen atom.
- Computation of scattering patterns for exemplary wave packets at different time points.
Main Results:
- Identification and interpretation of distinct contributions to the total differential scattering signal.
- Development of an analytical method for hydrogen atom wave packet scattering, enabling simulations without numerical integration.
- Demonstration of efficiency and accuracy benchmarks for the developed theoretical approach.
Conclusions:
- The developed theoretical framework provides a detailed understanding of time-resolved X-ray scattering by electronic wave packets.
- Analytical solutions offer an efficient and accurate method for simulating and analyzing such dynamical processes.
- Distinct features of time-resolved scattering are clearly illustrated, advancing the field of ultrafast atomic dynamics studies.
More Related Videos
08:48High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water
Published on: April 28, 2022
2.2K
11:27Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
Published on: December 8, 2016
12.8K
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
60.3K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
60.3K
02:18X-ray Crystallography
26.5K
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
26.5K
02:32The de Broglie Wavelength
33.9K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
33.9K
01:29Determination of Crystal Structures
11
In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
11
02:18The Bohr Model
81.8K
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the...
81.8K
02:28Electronic Structure of Atoms
29.4K
An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
29.4K