Rydberg Ionization Spectroscopy
Encyclopedia

Rydberg states

Atoms and molecules have ionization energy
Ionization potential
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...

 thresholds associated with the energy required to remove an electron from the ionic core. (The Rydberg formula
Rydberg formula
The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on November 5, 1888.-History:...

 describes the energy level series of a Rydberg atom
Rydberg atom
thumb|right|300px|Figure 1: Energy levels in atomic [[lithium]] showing the Rydberg series of the lowest 3 values of [[Angular momentum#Angular momentum in quantum mechanics|orbital angular momentum]] converging on the first ionization energy....

.) Rydberg series describe the energy levels associated with almost removing an electron from the ionic core. Each Rydberg series converges on an ionization energy threshold associated with a particular ionic core configuration. These quantized Rydberg energy levels can be associated with the quasiclassical Bohr atomic picture. The closer you get to the ionization threshold energy
Threshold energy
In particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle...

, the more "near threshold Rydberg states" there are. As the electron is promoted to higher energy levels, the spatial excursion of the electron from the ionic core increases and the system is more like the Bohr model
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...

 picture. (That is, the ionic core interaction with the Rydberg looks more like the interaction between the proton and the electron in the hydrogen atom
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...

. This can be refined by including a correction in the Rydberg formula associated with the presence of the ionic core called the quantum defect
Quantum defect
The term quantum defect is ambiguous. Various meanings are discussed below. Characteristic is that the defect deals with the loss on the smallest energy scale of light: that of the quantum.-Quantum defect in laser science:...

.) One way to visualize this system classically is to think of the electron as comet far removed from the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

 that represents the ionic core. The angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

 of a comet determines if it has a highly elliptical orbit
Highly Elliptical Orbit
A highly elliptical orbit is an elliptic orbit with a low-altitude perigee and a high-altitude apogee. It is a type of high Earth orbit....

 that is more likely to interact with the core of the system or a more nearly circular orbit
Circular orbit
A circular orbit is the orbit at a fixed distance around any point by an object rotating around a fixed axis.Below we consider a circular orbit in astrodynamics or celestial mechanics under standard assumptions...

 that is much less likely to interact with core. This is also true for the orbital angular momentum
Azimuthal quantum number
The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital...

 of a Rydberg state electron interacting with an ionic core.

Resonance ionization spectroscopy – RIS

The ionization threshold energy of atoms and small molecules are typically larger than the photon energies that are most easily available experimentally. However, it can be possible to span this ionization threshold energy if the photon energy is resonant with an intermediate electronically excited state. While it is often possible to observe the lower Rydberg levels in conventional spectroscopy of atoms and small molecules, Rydberg states
Rydberg states
The Rydberg states of an atom are electronically excited states with energies that follow the Rydberg formula as they converge on an ionic state with an ionization energy. Although the Rydberg formula was developed to describe atomic energy levels, it has been used to describe many other systems...

 are even more important in laser ionization experiments. Laser spectroscopic experiments often involve ionization through a photon energy resonance at an intermediate level, with an unbound final electron state and an ionic core. On resonance for phototransitions permitted by selection rules, the intensity of the laser in combination with the excited state lifetime makes ionization an expected outcome. This RIS approach and variations permit very sensitive detection of specific species.

Low Rydberg levels and REMPI

High photon intensity experiments can involve multiphoton processes with the absorption of integer multiples of the photon energy. In experiments that involve a multiphoton resonance, the intermediate is often a Rydberg state, and the final state is often an ion. The initial state of the system, photon energy, angular momentum and other selection rules can help in determining the nature of the intermediate state. This approach is exploited in Resonance Enhanced Multiphoton Ionization Spectroscopy (REMPI
REMPI
Resonance Enhanced Multi-Photon Ionization is a technique applied to the spectroscopy of atoms and small molecules. In practice, a tunable laser can be used to access an excited intermediate state. The selection rules associated with a two-photon or other multi-photon photoabsorption are different...

). An advantage of this spectroscopic technique is that the ions can be detected with almost complete efficiency and even resolved for their mass. It is also possible to gain additional information by performing experiments to look at the energy of the liberated photoelectron in these experiments. (Robert N. Compton and Philip M. Johnson pioneered the development of REMPI
REMPI
Resonance Enhanced Multi-Photon Ionization is a technique applied to the spectroscopy of atoms and small molecules. In practice, a tunable laser can be used to access an excited intermediate state. The selection rules associated with a two-photon or other multi-photon photoabsorption are different...

.)

Near-threshold Rydberg levels

The same approach that produces an ionization event can be used to access the dense manifold of near-threshold Rydberg states with laser experiments. These experiments often involve a laser operating at one wavelength to access the intermediate Rydberg state and a second wavelength laser to access the near-threshold Rydberg state region. Because of the photoabsorption selection rules, these Rydberg electrons are expected to be in highly elliptical angular momentum states. It is the Rydberg electrons excited to nearly circular angular momentum states that are expected to have the longest lifetimes. The conversion between a highly elliptical and a nearly circular near-threshold Rydberg state might happen in several ways, including encountering small stray electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

s.

ZEKE

Zero electron kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 (ZEKE) was developed with the idea of collecting only the resonance ionization photoelectrons that have extremely low kinetic energy. The technique involves waiting for a period of time after a resonance ionization experiment and then pulsing an electric field to collect the lowest energy photoelectrons in a detector. Typically, ZEKE experiments utilize two different tunable lasers. One laser photon energy is tuned to be resonant with the energy of an intermediate state. (This may be resonant with an excited state at a multiphoton transition.) Another photon energy is tuned to be very close to the ionization threshold energy. The technique worked extremely well and demonstrated energy resolution that was significantly better than the laser bandwidth. It turns out that it was not the photoelectrons that were detected in ZEKE. The delay between the laser and the electric field pulse selected the longest lived and most circular Rydberg states closest to the energy of the ion core. The population distribution of surviving very long-lived near threshold Rydberg states is narrower than the laser energy bandwidth. The electric field pulse stark shifts the near-threshold Rydberg states and vibrational autoionization occurs. ZEKE has provided a significant advance in the study of the vibrational spectroscopy of molecular ions. Klaus Müller-Dethlefs originated ZEKE spectroscopy.

MATI

Mass analyzed threshold ionization (MATI) was developed with idea of collecting the mass of the ions in a ZEKE experiment. MATI would have offered no advantage if low kinetic photoelectrons were detected. Because MATI also exploits vibrational autoionization of very near-threshold Rydberg states, it also can offer better resolution than the laser bandwidth in addition to allowing unambiguous determination of the mass of the ion. This information can be indispensable in understanding a variety of systems.

PIRI

Photo-induced Rydberg ionization (PIRI) was developed following REMPI
REMPI
Resonance Enhanced Multi-Photon Ionization is a technique applied to the spectroscopy of atoms and small molecules. In practice, a tunable laser can be used to access an excited intermediate state. The selection rules associated with a two-photon or other multi-photon photoabsorption are different...

 experiments on electronic autoionization of low-lying Rydberg states of carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

. In REMPI
REMPI
Resonance Enhanced Multi-Photon Ionization is a technique applied to the spectroscopy of atoms and small molecules. In practice, a tunable laser can be used to access an excited intermediate state. The selection rules associated with a two-photon or other multi-photon photoabsorption are different...

 photoelectron experiments, it was determined that a two-photon ionic core photoabsorption process (followed by prompt electronic autoionization) could dominate the direct single photon absorption in the ionization of some Rydberg states of carbon dioxide. These sorts of two excited electron systems had already been under study in the atomic physics
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

, but there the experiments involved very high order Rydberg states. PIRI works because electronic autoionization can dominate direct photoionization (photoionisation). The circularized near-threshold Rydberg state is more likely to undergo a core photoabsorption than to absorb a photon and directly ionize the Rydberg state. PIRI extends the near-threshold spectroscopic techniques to allow access to the electronic states (including dissociative molecular states and other hard to study systems) as well as the vibrational states of molecular ions.
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