PHYSICAL 8 EVIEW A VOLUME 13, NUMBER 5 MAY 1976 Electron capture and stripping cross sections for Tl and K ions and atoms in H~ Ignacio Alvarez and Carmen Cisneros Instituto de Fisica, Mexico 20, D.I. C. F. Barnett and J. A. Ray Oak Ridge Nationa/ I aboratoxy, Oak Ridge, Tennessee 37830 (Received 18 December 1975) Electron capture cross sections (0&0) and stripping or loss cross sections (0{jf 0'f2 002) have been measured for 50- to 600-keV Tlo +' and K '+' passing through H2 gas. Equilibrium frac- tions were measured by increasing the H2 target gas density until the fraction was indepen- dent of the initial charge state. All capture and loss cross sections increased in this energy range. The equilibrium fractions were dependent only on the particle velocity and were inde- pendent of the incident-particle electronic structure. I. INTRODUCTION Diagnostics of high-temperature plasmas depend strongly on atomic phenomena. These atomic pro- cesses used in measuring plasma parameters can be divided into two el, asses, passive and active. In passive investigations, use is made of optical or particle emission from the plasma. Examples of passive methods include optical line radiation, bremsstrahlung, and neutral particles emitted by the plasma. In active diagnostics an external beam of particles or photons is used to probe the plasma properties. An ingenious active method to probe the plasmais the heavy-ion beam probe proposed and developed by Jobes and Hickok. ' A singly charged ion beam with sufficient momentum to cross the magnetic field containing the plasma is projected through the pla, sma. At some point in the plasma the doubly charged ions are formed by collisions with elec- trons and positively charged particles. If the beam dynamics is chosen correctly, a detector line can be found such that as the ion beam is de- flected in a transverse direction across the plas- ma, the doubly charged ions formed on this line will. intersect at a position external to the plasma. By placing an electrostatic analyzer at this cross- over point, the change in the final and initial ion energy is determined, which gives the plasma po- tential at the point of formation of the doubly charged ion. The doubly charged ion beam intensi- ty gives the plasma density, which can be made absolute if the pertinent cross sections are known. It is believed that the electron ionization cross section of the incident ion is the predominate cross section. Of equal importance may be charge-ex- change or stripping cross section of the heavy ion. A summary of experimental results of charge- transfer processes involving heavy ions at ener- gies less than 1 MeV has been published by Alli- son' and at higher energies by Betz. ' A summary of the various experimental techniques has been made by Barnett and Gilbody. ' Theoretical compu- tations of charge changing processes for heavy particles are very difficult; a limited number of cases have been reviewed by Mapleton. ' No theory exists which predicts accurately the capture and loss cross sections where the particle velocity is less than the orbital electron velocity. Two ap- proximate theories have been developed by Firsov' and Fleischmann. ' According to Firsov's original ideas the process- es of energy transfer in two-atom collisions are due mainly to an electron flux crossing a hypothet- ical plane located midway along and perpendicular to the line joining their centers. Hence a momen- tum transfer is observed. Firsov calculated the electron flux by assuming a spherical distribution of electron velocities at every point in space and integrating over the Firsov plane, using statistical theory. He assumed that this energy was distrib- uted among all electrons of the system and was used up in the ionization process. If the excitation energy is greater than the ionization energy, ioni- zation occurs with a high probability. In this manner, Firsov obtained a formulation which gives a universal dependence of the cross section for the removal of electrons for any col- liding pair as a function of their relative velocity. He developed the following expressions: (z, = &J,[(u iu, )'~' — 1]', 23x106E; cm 3. 7 x10 '6 0 (z +z )5/3 s+~ & 0 (z +z P/3 where g. is the total electron production cross sec-