From Wikipedia, the free encyclopedia
  (Redirected from Ionized)
Jump to: navigation, search

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons. Ionization results from the interaction of an atom or a molecule with a sub atomic particle or electromagnetic waves on the short wavelength end of the electromagnetic spectrum which have enough kinetic energy to cause ionization.

Ionization can occur in the absence of an external influence by internal conversion process, through which an excited nucleus transfers its energy to one of the inner-shell electrons and ejects it with high kinetic energy.


Everyday examples of gas ionisation are such as within a fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Muller counter or the ionisation chamber. The ionization process is widely used in a variety of equipment in fundamental science and in such as mass spectroscopy and radiotherapy.

Production of ions[edit]



Positively charged ions are produced by transferring sufficient amount of energy to a bound electron. The threshold amount of the required energy is known as ionization potential.

The Townsend avalanche 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 ionisation event, due to such as ionising 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 ionisation 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.[1]

Ionization energy of atoms[edit]

Figure 1. Ionization energies of neutral elements.


Semi-classical description of ionization[edit]


Quantum mechanical description of ionization[edit]


Tunnel ionization[edit]




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

 W_{PPT}=|C_{n^{*}l^{*}}|^{2}\sqrt{\frac{6}{\pi}}f_{lm}E_{i}(2(2E_i)^{\frac{3}{2}}/F)^{n^{*2}-|m|-3/2}(1+\gamma)^{2})^{|m/2|+3/4}A_{m}(\omega, \gamma)e^{-(2(2E_i)^{\frac{3}{2}}/F)g(\gamma)}

where  \gamma= \frac{\omega F}{\sqrt {2E_i}} is the Keldysh's adiabaticity parameter,  n^{*}=\sqrt{2E_i}/Z^{2} ,  F is the peak electric field of laser and  l^{*}=n^{*}-1 . The coefficients  f_{lm} ,  g(\gamma) and  C_{n^{*}l^{*}} are given by

 f_{lm}= \frac{(2l+1)(l+|m|)^{!}}{2^{m}|m|^{!}(l-|m|)^{!}}
 g(\gamma)=\frac{3}{2\gamma} (1+\frac{1}{2\gamma^{2}}\sinh^{-1}(\gamma)-\frac{\sqrt{1+\gamma^{2}}}{2\gamma})
|C_{n^{*}l^{*}}|^{2}= \frac{2^{2n^{*}}}{n^{*}\Gamma(n^{*}+l^{*}+1)\Gamma(n^{*}l^{*})}

The coefficient  A_{m}(\omega, \gamma) is given by

 A_{m}(\omega, \gamma)=\frac{4}{3\pi}\frac{1}{|m|^{!}}\frac{\gamma^{2}}{1+\gamma^{2}}\sum_{n>v}^{\infty}w_{m}(\sqrt{\frac{2\gamma}{\sqrt{1+\gamma^{2}}}(n-v)}e^{-(n-v)\alpha(\gamma)})


 w_{m}(x)=e^{-x^{2}}\int_0^x (x^2-y^2)^m e^{y^2}\,dy
 \alpha(\gamma)= 2(\sinh^{-1}(\gamma)-\frac{\gamma}{\sqrt{1+\gamma^{2}}})
 v= \frac{E_i}{\omega}(1+\frac{2}{\gamma^{2}})

Quasi-static tunnel ionization[edit]

The quasi-static tunnelling (QST) is the ionization whose rate can be satisfactorily predicted by the ADK model,[7] i.e. the limit of the PPT model when  \gamma approaches zero.[8] The rate of QST is given by


As compared to  W_{PPT} the absence of summation over n, which represent different above threshold ionization (ATI) peaks, is remarkable.

Strong field approximation for the ionization rate[edit]

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[9] based on the earlier works of Faisal[10] and Reiss.[11] The resulting rate is given by

 W_{KRA}= \sum_{n=N}^{n=\infty} 2 \pi \omega^{2} p (n-n_\mathrm{osc})^2 \int d \Omega |FT (I_{KAR} \Psi ( \mathbf{r}))|^2 J_n^2 (n_f, \frac{n_\mathrm{osc}}{2})

where,  N=[n_i + n_\mathrm{osc}] is the minimum number of photons necessary to ionize the atom,  n_{i} =E_i/\omega ,  n_\mathrm{osc} = U_{p} / \omega (  U_p is the ponderomotive energy),  J_{n} (u, v) is the double Bessel function,  p = \sqrt{ 2 \omega (n-n_\mathrm{osc}- n_i)} ,  n_{f} = 2 \sqrt { n_\mathrm{osc} / \omega} p cos(\theta) where  \theta 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,  I_{KAR} = (\frac {2 Z^2}{n^2 F r})^n incorporates the Coulomb correction in the SFA model.

Atomic stabilization/population trapping[edit]

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 m photons and the resonant state undergo an avoided crossing at the resonance intensity I_r. The minimum distance, V_m, at the avoided crossing is proportional to the generalized Rabi frequency, \Gamma(t)=\Gamma_m I(t)^{m/2} coupling the two states. According to Story et al.,[12] the probability of remaining in the ground state, P_g, is given by

P_g=\exp\left(-\frac{2\pi W_m^2}{dW/dt}\right)





Non-sequential multiple ionization[edit]

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.[17] 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  A+L -> A^+ + L -> A^{++} there is another channel  A+L-> A^{++} 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.[18] Later, systematically studying the NSI of all rare gas atoms, the quadruple NSI of Xe was observed.[19] 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  W_{ADK}(A^{i+}) is the rate of quasi-static tunneling to i’th charge state and \alpha_n(\lambda) 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,[21] Schafer et al,[22] Corkum,[23] Becker and Faisal[24] and Faisal and Becker.[25] The principle 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 ( U_p ) of the laser. Corkum's model places a cut-off limit on the minimum intensity ( U_p is proportional to intensity) where ionization due to re-scattering can occur.

Feynman diagram for the process of double ionization in an atom through re-scattering mechanism.


Kuciev did not include the Coulomb effects on the dynamics of the ionized electron. This resulted in the underestimation of the double ionization rate by a huge factor. Obviously, in the approach of Becker and Faisal (which is equivalent to Kuchiev's model in spirit), this drawback does not exist. In fact, their model is more exact and does not suffer from the large number of approximations made by Kuchiev. Their calculation results perfectly fit with the experimental results of Walker et al.[26] Becker and Faisal[27] have been able to fit the experimental results on the multiple NSI of rare gas atoms using their model. As a result the electron re-scattering can be taken as the main mechanism for the occurrence of the NSI process.

Multiphoton ionization of inner-valence electrons and fragmentation of polyatomic molecules[edit]

The ionization of inner valance electrons are responsible for the fragmentation of polyatomic molecules in strong laser fields. According to a qualitative model[28][29] the dissociation of the molecules occurs through a three-step mechanism:



Dissociation – distinction[edit]


See also[edit]


  2. ^ Keldysh L V (1965). "Ionization in the Field of a Strong Electromagnetic Wave". Soviet Phys. JETP 20 (5): 1307. 
  3. ^ Volkov D M 1934 Z. Phys. 94 250
  4. ^ Perelomov A M, Popov V S and Terent'ev M V (1966). "Ionization of Atoms in an Alternating Electric Field". Soviet Phys. JETP 23 (5): 924. Bibcode:1966JETP...23..924P. 
  5. ^ Perelomov A M, Popov V S and Terent'ev M V (1967). "Ionization of Atoms in an Alternating Electric Field: II". Soviet Phys. JETP 24 (1): 207. Bibcode:1967JETP...24..207P. 
  6. ^ Larochelle S, Talebpour A and Chin S L (1998). "Coulomb effect in multiphoton ionization of rare-gas atoms". Journal of Physics B: Atomic, Molecular and Optical Physics 31 (6): 1215. Bibcode:1998JPhB...31.1215L. doi:10.1088/0953-4075/31/6/009. 
  7. ^ Ammosov M V, Delone N B and Krainov V P (1986). "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field". Soviet Phys. JETP 64 (6): 1191. 
  8. ^ 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. 
  9. ^ 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. 
  10. ^ 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. 
  11. ^ 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. 
  12. ^ 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. 
  13. ^ 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. 
  14. ^ Hioe F T and 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. 
  15. ^ Talebpour A, Chien C Y and 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. 
  16. ^ 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). Bibcode:2013PhRvA..87f3405M. doi:10.1103/PhysRevA.87.063405. ISSN 1050-2947. 
  17. ^ L’Huillier A., Lompre L A, Mainfray G, and 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. 
  18. ^ Augst S, Talebpour A, Chin S L, Beaudoin Y and 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. 
  19. ^ 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. 
  20. ^ Fittinghoff D N, Bolton P R, Chang B, and 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. 
  21. ^ Kuchiev M Yu (1987). Soviet Phys. JETP Lett. 45: 404. 
  22. ^ 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. 
  23. ^ 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. 
  24. ^ Becker, Andreas; Faisal, Farhad H M (1996). "Mechanism of laser-induced double ionization of helium". Journal of Physics B: Atomic, Molecular and Optical Physics 29 (6): L197–L202. Bibcode:1996JPhB...29L.197B. doi:10.1088/0953-4075/29/6/005. ISSN 0953-4075. 
  25. ^ Faisal F H M and Becker A (1997). Laser Phys. 7: 684. 
  26. ^ Walker B, Sheehy B, Dimauro L F, Agostini P, Schafer K J, and 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. 
  27. ^ 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. 
  28. ^ 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". Chemical Physics Letters 313 (5–6): 789. Bibcode:1999CPL...313..789T. doi:10.1016/S0009-2614(99)01075-1. 
  29. ^ 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. 
  30. ^ S. Mehdi Sharifi, A. Talebpour, S.L. Chin, Ultra-fast laser pulses provide an ion source for highly selective mass spectroscopy, Applied Physics B, 2008, 91:579-581

External links[edit]