


Everyday examples of gas ionization are such as 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 industry (e.g., radiation therapy).

Production of ions



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 potential. The study of such collisions is of fundamental importance with regard to the few-body problem (see article on few-body systems), which is one of the major unsolved problems in physics. Kinematically complete experiments,[2] 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 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.[3]


Ionization efficiency is the ratio of the number of ions formed to the number of electrons or photons used.[5][6]

Ionization energy of atoms

Figure 1. Ionization energies of neutral elements.


Semi-classical description of ionization


Quantum mechanical description of ionization


Tunnel ionization




The rate of MPI on atom with an ionization potential in a linearly polarized laser with frequency is given by


  • is the Keldysh's adiabaticity parameter,
  • ,
  • is the peak electric field of laser and
  • .

The coefficients , and are given by

The coefficient is given by


Quasi-static tunnel ionization

The quasi-static tunnelling (QST) is the ionization whose rate can be satisfactorily predicted by the ADK model,[12] i.e. the limit of the PPT model when approaches zero.[13] 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 emphasis the particle nature of light (absorbing multiple photons during ionization). This approach was adopted by Krainov model[14] based on the earlier works of Faisal[15] and Reiss.[16] The resulting rate is given by

where, is the minimum number of photons necessary to ionize the atom, , ( is the ponderomotive energy), is the double Bessel function, , where is the angle between the momentum of the electron, p, and the electric field of the laser, F, and, the symbol FT denotes the three-dimensional Fourier transformation. Finally, incorporates the Coulomb correction in the SFA model.

Atomic stabilization/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.,[17] the probability of remaining in the ground state, , is given by





Non-sequential multiple ionization

The phenomenon of non-sequential ionization (NSI) of atoms exposed to intense laser fields has been a subject of many theoretical and experimental studies since 1983. The pioneering work began with the observation of a “knee” structure on the Xe2+ ion signal versus intensity curve by L’Huillier et al.[22] From the experimental point of view, the NS double ionization refers to processes which somehow enhance the rate of production of doubly charged ions by a huge factor at intensities below the saturation intensity of the singly charged ion. Many, on the other hand, prefer to define the NSI as a process by which two electrons are ionized nearly simultaneously. This definition implies that apart from the sequential channel there is another channel which is the main contribution to the production of doubly charged ions at lower intensities. The first observation of triple NSI in argon interacting with a 1 µm laser was reported by Augst et al.[23] Later, systematically studying the NSI of all rare gas atoms, the quadruple NSI of Xe was observed.[24] The most important conclusion of this study was the observation of the following relation between the rate of NSI to any charge state and the rate of tunnel ionization (predicted by the ADK formula) to the previous charge states;

where is the rate of quasi-static tunneling to i'th charge state and are some constants depending on the wavelength of the laser (but not on the pulse duration).


The electron rescattering model was independently developed by Kuchiev,[26] Schafer et al,[27] Corkum,[28] Becker and Faisal[29] and Faisal and Becker.[30] The principal features of the model can be understood easily from Corkum's version. Corkum's model describes the NS ionization as a process whereby an electron is tunnel ionized. The electron then interacts with the laser field where it is accelerated away from the nuclear core. If the electron has been ionized at an appropriate phase of the field, it will pass by the position of the remaining ion half a cycle later, where it can free an additional electron by electron impact. Only half of the time the electron is released with the appropriate phase and the other half it never return to the nuclear core. The maximum kinetic energy that the returning electron can have is 3.17 times the ponderomotive potential ( ) of the laser. Corkum's model places a cut-off limit on the minimum intensity ( is proportional to intensity) where ionization due to re-scattering can occur.




Multiphoton ionization of inner-valence electrons and fragmentation of polyatomic molecules

The ionization of inner valance electrons are responsible for the fragmentation of polyatomic molecules in strong laser fields. According to a qualitative model[33][34] the dissociation of the molecules occurs through a three-step mechanism:



Kramers-Henneberger frame and ionization phase effects

Studying the strong field ionization of the atom in so called Kramers-Henneberger (K-H) frame[37] leads to the conclusion that the ionization efficiency strongly depends on the temporal details of the ionizing pulse but not necessarily on the field strength and the total energy of the ionizing pulse pumped into the atom.[38] The Kramers-Henneberger frame is the non-intertial frame moving with the free electron under the influence of the harmonic laser pulse. The free electron solution of the Newton equations for the electron in one dimension in the harmonic laser field

will be also harmonic

The frame comoving with this electron will be obtained by the coordinate transformation

while the added Coulomb potential will be

The full cycle time-average of that potential which is

will be the even function of and therefore having the maximum at while for that initial condition the solution will be in the K-H and it will be therefore identical to the free electron solution in the laboratory frame. The electron velocity on the other hand is phase shifted both to the field strength and to the electron position:

Therefore considering the wavelet pulses and defining the ionization as the full escape from the line segment of the length 2r (or from the spherical region in three dimensions) the full ionization happens in the classical model after the time or no ionization at all depending if the harmonic field wavelet is cut at the zero minimum or the maximum velocity.

Dissociation – distinction


See also

  • Above threshold ionization
  • Adiabatic ionization
  • Ionization chamber – Instrument for detecting gaseous ionization, used in ionizing radiation measurements
  • Ion source
  • Photoionization and photoionization mode
  • Thermal ionization
  • Electron ionization
  • Chemical ionization
  • Townsend avalanche – The chain reaction of ionization occurring in a gas with an applied electric field
Phase transitions of matter
Solid Liquid Gas
From Solid Melting Sublimation
Liquid Freezing Vaporization
Gas Deposition Condensation


  2. Schulz, Michael (2003). "Three-Dimensional Imaging of Atomic Four-Body Processes". Nature. 422 (6927): 48–51. Bibcode:2003Natur.422...48S. doi:10.1038/nature01415. PMID 12621427.
  3. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) "adiabatic ionization".
  5. Todd, J. F. J. (1991). "Recommendations for Nomenclature and Symbolism for Mass Spectroscopy (including an appendix of terms used in vacuum technology)(IUPAC Recommendations 1991)". Pure Appl. Chem. 63 (10): 1541–1566. doi:10.1351/pac199163101541.
  6. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) "ionization efficiency".
  7. Keldysh, L. V. (1965). "Ionization in the Field of a Strong Electromagnetic Wave". Soviet Phys. JETP. 20 (5): 1307.
  8. Volkov D M 1934 Z. Phys. 94 250
  9. Perelomov, A. M.; Popov, V. S.; Terent'ev, M. V. (1966). "Ionization of Atoms in an Alternating Electric Field". Soviet Phys. JETP. 23 (5): 924. Bibcode:1966JETP...23..924P.
  10. Perelomov, A. M.; Popov, V. S.; Terent'ev, M. V. (1967). "Ionization of Atoms in an Alternating Electric Field: II". Soviet Phys. JETP. 24 (1): 207. Bibcode:1967JETP...24..207P.
  11. Larochelle, S.; Talebpour, A.; Chin, S. L. (1998). "Coulomb effect in multiphoton ionization of rare-gas atoms" (PDF). Journal of Physics B: Atomic, Molecular and Optical Physics. 31 (6): 1215. Bibcode:1998JPhB...31.1215L. doi:10.1088/0953-4075/31/6/009. Archived from the original (PDF) on November 21, 2014.
  12. Ammosov, M. V.; Delone, N. B.; Krainov, V. P. (1986). "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field". Soviet Phys. JETP. 64 (6): 1191.
  13. Sharifi, S. M.; Talebpour, A; Yang, J.; Chin, S. L. (2010). "Quasi-static tunnelling and multiphoton processes in the ionization of Ar and Xe using intense femtosecond laser pulses". Journal of Physics B: Atomic, Molecular and Optical Physics. 43 (15): 155601. Bibcode:2010JPhB...43o5601S. doi:10.1088/0953-4075/43/15/155601. ISSN 0953-4075.
  14. Krainov, Vladimir P. (1997). "Ionization rates and energy and angular distributions at the barrier-suppression ionization of complex atoms and atomic ions". Journal of the Optical Society of America B. 14 (2): 425. Bibcode:1997JOSAB..14..425K. doi:10.1364/JOSAB.14.000425. ISSN 0740-3224.
  15. Faisal, F. H. M. (1973). "Multiple absorption of laser photons by atoms". Journal of Physics B: Atomic and Molecular Physics. 6 (4): L89–L92. Bibcode:1973JPhB....6L..89F. doi:10.1088/0022-3700/6/4/011. ISSN 0022-3700.
  16. Reiss, Howard (1980). "Effect of an intense electromagnetic field on a weakly bound system". Physical Review A. 22 (5): 1786–1813. Bibcode:1980PhRvA..22.1786R. doi:10.1103/PhysRevA.22.1786. ISSN 0556-2791.
  17. Story, J.; Duncan, D.; Gallagher, T. (1994). "Landau-Zener treatment of intensity-tuned multiphoton resonances of potassium". Physical Review A. 50 (2): 1607–1617. Bibcode:1994PhRvA..50.1607S. doi:10.1103/PhysRevA.50.1607. ISSN 1050-2947. PMID 9911054.
  18. De Boer, M.; Muller, H. (1992). "Observation of large populations in excited states after short-pulse multiphoton ionization". Physical Review Letters. 68 (18): 2747–2750. Bibcode:1992PhRvL..68.2747D. doi:10.1103/PhysRevLett.68.2747. PMID 10045482.
  19. Hioe, F. T.; Carrol, C. E. (1988). "Coherent population trapping in N-level quantum systems". Physical Review A. 37 (8): 3000–3005. Bibcode:1988PhRvA..37.3000H. doi:10.1103/PhysRevA.37.3000. PMID 9900034.
  20. Talebpour, A.; Chien, C. Y.; Chin, S. L. (1996). "Population trapping in rare gases". Journal of Physics B: Atomic, Molecular and Optical Physics. 29 (23): 5725. Bibcode:1996JPhB...29.5725T. doi:10.1088/0953-4075/29/23/015.
  21. Morishita, Toru; Lin, C. D. (2013). "Photoelectron spectra and high Rydberg states of lithium generated by intense lasers in the over-the-barrier ionization regime". Physical Review A. 87 (6): 63405. Bibcode:2013PhRvA..87f3405M. doi:10.1103/PhysRevA.87.063405. ISSN 1050-2947.
  22. L’Huillier, A.; Lompre, L. A.; Mainfray, G.; Manus, C. (1983). "Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 μm". Physical Review A. 27 (5): 2503. Bibcode:1983PhRvA..27.2503L. doi:10.1103/PhysRevA.27.2503.
  23. Augst, S.; Talebpour, A.; Chin, S. L.; Beaudoin, Y.; Chaker, M. (1995). "Nonsequential triple ionization of argon atoms in a high-intensity laser field". Physical Review A. 52 (2): R917–R919. Bibcode:1995PhRvA..52..917A. doi:10.1103/PhysRevA.52.R917. PMID 9912436.
  24. Larochelle, S.; Talebpour, A.; Chin, S. L. (1998). "Non-sequential multiple ionization of rare gas atoms in a Ti:Sapphire laser field". Journal of Physics B: Atomic, Molecular and Optical Physics. 31 (6): 1201. Bibcode:1998JPhB...31.1201L. doi:10.1088/0953-4075/31/6/008.
  25. Fittinghoff, D. N.; Bolton, P. R.; Chang, B.; Kulander, K. C. (1992). "Observation of nonsequential double ionization of helium with optical tunneling". Physical Review Letters. 69 (18): 2642–2645. Bibcode:1992PhRvL..69.2642F. doi:10.1103/PhysRevLett.69.2642. PMID 10046547.
  26. Kuchiev, M. Yu (1987). "Atomic antenna". Soviet Phys. JETP Lett. 45: 404–406.
  27. Schafer, K. J.; Yang, B.; DiMauro, L.F.; Kulander, K.C. (1992). "Above threshold ionization beyond the high harmonic cutoff". Physical Review Letters. 70 (11): 1599–1602. Bibcode:1993PhRvL..70.1599S. doi:10.1103/PhysRevLett.70.1599. PMID 10053336.
  28. Corkum, P. B. (1993). "Plasma perspective on strong field multiphoton ionization". Physical Review Letters. 71 (13): 1994–1997. Bibcode:1993PhRvL..71.1994C. doi:10.1103/PhysRevLett.71.1994. PMID 10054556.
  30. Faisal, F. H. M.; Becker, A. (1997). "Nonsequential double ionization: Mechanism and model formula". Laser Phys. 7: 684.
  31. Walker, B.; Sheehy, B.; Dimauro, L. F.; Agostini, P.; Schafer, K. J.; Kulander, K. C. (1994). "Precision Measurement of Strong Field Double Ionization of Helium". Physical Review Letters. 73 (9): 1227–1230. Bibcode:1994PhRvL..73.1227W. doi:10.1103/PhysRevLett.73.1227. PMID 10057657.
  32. Becker, A.; Faisal, F. H. M. (1999). "S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses". Journal of Physics B: Atomic, Molecular and Optical Physics. 32 (14): L335. Bibcode:1999JPhB...32L.335B. doi:10.1088/0953-4075/32/14/101.
  33. Talebpour, A.; Bandrauk, A. D.; Yang, J; Chin, S. L. (1999). "Multiphoton ionization of inner-valence electrons and fragmentation of ethylene in an intense Ti:sapphire laser pulse" (PDF). Chemical Physics Letters. 313 (5–6): 789. Bibcode:1999CPL...313..789T. doi:10.1016/S0009-2614(99)01075-1. Archived from the original (PDF) on November 21, 2014.
  34. Talebpour, A; Bandrauk, A D; Vijayalakshmi, K; Chin, S L (2000). "Dissociative ionization of benzene in intense ultra-fast laser pulses". Journal of Physics B: Atomic, Molecular and Optical Physics. 33 (21): 4615. Bibcode:2000JPhB...33.4615T. doi:10.1088/0953-4075/33/21/307.
  35. Mehdi Sharifi, S.; Talebpour, A.; Chin, S. L. (2008). "Ultra-fast laser pulses provide an ion source for highly selective mass spectroscopy". Applied Physics B. 91 (3–4): 579. Bibcode:2008ApPhB..91..579M. doi:10.1007/s00340-008-3038-y.
  36. Peng, Jiahui; Puskas, Noah; Corkum, Paul B.; Rayner, David M.; Loboda, Alexandre V. (2012). "High-Pressure Gas Phase Femtosecond Laser Ionization Mass Spectrometry". Analytical Chemistry. 84 (13): 5633–5640. doi:10.1021/ac300743k. ISSN 0003-2700. PMID 22670784.
  37. Henneberger, Walther C. (1968). "Perturbation method for atoms in intense laser beams". Physical Review Letters. 21 (12): 838–841. Bibcode:1968PhRvL..21..838H. doi:10.1103/physrevlett.21.838.
  38. Mathur, D.; Dota, K.; Dharmadhikari, A.K.; Dharmadhikari, J.A. (2013). "Carrier-envelope-phase effects in ultrafast strong-field ionization dynamics of multielectron systems: Xe and CS2". Physical Review Letters. 110 (8): 083602–083605. arXiv:1301.3639. Bibcode:2013PhRvL.110h3602M. doi:10.1103/PhysRevLett.110.083602. PMID 23473143.
  • The dictionary definition of ionization at Wiktionary