Ionization or ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules, electrons, positrons, protons, antiprotons, and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.
Uses Everyday examples of gas ionization occur within a fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Müller counter or the ionization chamber. The ionization process is widely used in a variety of equipment in fundamental science (e.g., mass spectrometry) and in medical treatment (e.g., radiation therapy). It is also widely used for air purification, though studies have shown harmful effects of this application.
Production of ions
Negatively charged ions are produced when a free electron collides with an atom and is subsequently trapped inside the electric potential barrier, releasing any excess energy. The process is known as electron capture ionization.
Positively charged ions are produced by transferring an amount of energy to a bound electron in a collision with charged particles (e.g. ions, electrons or positrons) or with photons. The threshold amount of the required energy is known as ionization energy. The study of such collisions is of fundamental importance with regard to the few-body problem, which is one of the major unsolved problems in physics. Kinematically complete experiments, i.e. experiments in which the complete momentum vector of all collision fragments (the scattered projectile, the recoiling target-ion, and the ejected electron) are determined, have contributed to major advances in the theoretical understanding of the few-body problem in recent years.
Adiabatic ionization Adiabatic ionization is a form of ionization in which an electron is removed from or added to an atom or molecule in its lowest energy state to form an ion in its lowest energy state.
The Townsend discharge is a good example of the creation of positive ions and free electrons due to ion impact. It is a cascade reaction involving electrons in a region with a sufficiently high electric field in a gaseous medium that can be ionized, such as air. Following an original ionization event, due to such as ionizing radiation, the positive ion drifts towards the cathode, while the free electron drifts towards the anode of the device. If the electric field is strong enough, the free electron gains sufficient energy to liberate a further electron when it next collides with another molecule. The two free electrons then travel towards the anode and gain sufficient energy from the electric field to cause impact ionization when the next collisions occur; and so on. This is effectively a chain reaction of electron generation, and is dependent on the free electrons gaining sufficient energy between collisions to sustain the avalanche.Glenn F Knoll. Radiation Detection and Measurement, third edition 2000. John Wiley and sons,
Ionization efficiency is the ratio of the number of ions formed to the number of electrons or photons used.
Ionization energy of atoms
The trend in the ionization energy of atoms is often used to demonstrate the periodic behavior of atoms with respect to the atomic number, as summarized by ordering atoms in Mendeleev's table. This is a valuable tool for establishing and understanding the ordering of electrons in atomic orbitals without going into the details of wave functions or the ionization process.
An example is presented in the figure to the right. The periodic abrupt decrease in ionization potential after rare gas atoms, for instance, indicates the emergence of a new shell in alkali metals. In addition, the local maximums in the ionization energy plot, moving from left to right in a row, are indicative of s, p, d, and f sub-shells.
Semi-classical description of ionization
Classical physics and the Bohr model of the atom can qualitatively explain photoionization and collision-mediated ionization. In these cases, during the ionization process, the energy of the electron exceeds the energy difference of the potential barrier it is trying to pass. The classical description, however, cannot describe tunnel ionization since the process involves the passage of electron through a classically forbidden potential barrier.
Quantum mechanical description of ionization The interaction of atoms and molecules with sufficiently strong laser pulses or with other charged particles leads to the ionization to singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can be calculated using quantum mechanics. (There are classical methods available also, like the Classical Trajectory Monte Carlo Method (CTMC), but it is not overall accepted and often criticized by the community.). Two quantum mechanical methods exist: perturbative and non-perturbative. Methods like time-dependent coupled-channel or time independent close coupling – where the wave function is expanded in a finite basis set – are examples of non-perturbative methods and numerous options exist e.g. B-splines, generalized Sturmians or Coulomb wave packets. Another non-perturbative method is to solve the corresponding Schrödinger equation fully numerically on a lattice.
In general, analytic solutions are not available, and the approximations required for manageable numerical calculations do not provide acceptably accurate results. However, when the laser intensity is sufficiently high, the detailed structure of the atom or molecule can be ignored and an analytic solution for the ionization rate is possible.
Tunnel ionization
Tunnel ionization is ionization due to quantum tunneling. In classical ionization, an electron must have enough energy to make it over the potential barrier, but quantum tunneling allows the electron simply to go through the potential barrier instead of going all the way over it because of the wave nature of the electron. The probability of an electron's tunneling through the barrier drops off exponentially with the width of the potential barrier. Therefore, an electron with a higher energy can make it further up the potential barrier, leaving a much thinner barrier to tunnel through and thus a greater chance to do so. In practice, tunnel ionization is observable when the atom or molecule is interacting with near-infrared strong laser pulses. This process can be understood as a process by which a bounded electron, through the absorption of more than one photon from the laser field, is ionized. This picture is generally known as multiphoton ionization (MPI).
Keldysh modeled the MPI process as a transition of the electron from the ground state of the atom to the Volkov states.Volkov D M 1934 Z. Phys. 94 250 In this model the perturbation of the ground state by the laser field is neglected and the details of atomic structure in determining the ionization probability are not taken into account. The major difficulty with Keldysh's model was its neglect of the effects of Coulomb interaction on the final state of the electron. As it is observed from figure, the Coulomb field is not very small in magnitude compared to the potential of the laser at larger distances from the nucleus. This is in contrast to the approximation made by neglecting the potential of the laser at regions near the nucleus. Perelomov et al. included the Coulomb interaction at larger internuclear distances. Their model (which we call the PPT model) was derived for short range potential and includes the effect of the long range Coulomb interaction through the first order correction in the quasi-classical action. Larochelle et al. have compared the theoretically predicted ion versus intensity curves of rare gas atoms interacting with a Ti:Sapphire laser with experimental measurement. They have shown that the total ionization rate predicted by the PPT model fit very well the experimental ion yields for all rare gases in the intermediate regime of the Keldysh parameter.
The rate of MPI on atom with an ionization potential in a linearly polarized laser with frequency is given by
where is the Keldysh parameter, , is the peak electric field of the laser and . The coefficients , and are given by
The coefficient is given by
where
Quasi-static tunnel ionization The quasi-static tunneling (QST) is the ionization whose rate can be satisfactorily predicted by the ADK model, i.e. the limit of the PPT model when approaches zero. The rate of QST is given by
As compared to the absence of summation over n, which represent different above threshold ionization (ATI) peaks, is remarkable.
Strong field approximation for the ionization rate The calculations of PPT are done in the E-gauge, meaning that the laser field is taken as electromagnetic waves. The ionization rate can also be calculated in A-gauge, which emphasizes the particle nature of light (absorbing multiple photons during ionization). This approach was adopted by Krainov model based on the earlier works of Faisal and Reiss. The resulting rate is given by
where:
with being the ponderomotive energy, is the minimum number of photons necessary to ionize the atom, is the double Bessel function,
with the angle between the momentum of the electron, p, and the electric field of the laser, F, FT is the three-dimensional Fourier transform, and incorporates the Coulomb correction in the SFA model.
Population trapping In calculating the rate of MPI of atoms only transitions to the continuum states are considered. Such an approximation is acceptable as long as there is no multiphoton resonance between the ground state and some excited states. However, in real situation of interaction with pulsed lasers, during the evolution of laser intensity, due to different Stark shift of the ground and excited states there is a possibility that some excited state go into multiphoton resonance with the ground state. Within the dressed atom picture, the ground state dressed by photons and the resonant state undergo an avoided crossing at the resonance intensity . The minimum distance, , at the avoided crossing is proportional to the generalized Rabi frequency, coupling the two states. According to Story et al., the probability of remaining in the ground state, , is given by
where is the time-dependent energy difference between the two dressed states. In interaction with a short pulse, if the dynamic resonance is reached in the rising or the falling part of the pulse, the population practically remains in the ground state and the effect of multiphoton resonances may be neglected. However, if the states go onto resonance at the peak of the pulse, where , then the excited state is populated. After being populated, since the ionization potential of the excited state is small, it is expected that the electron will be instantly ionized.
In 1992, de Boer and Muller showed that Xe atoms subjected to short laser pulses could survive in the highly excited states 4f, 5f, and 6f. These states were believed to have been excited by the dynamic Stark shift of the levels into multiphoton resonance with the field during the rising part of the laser pulse. Subsequent evolution of the laser pulse did not completely ionize these states, leaving behind some highly excited atoms. We shall refer to this phenomenon as "population trapping".