Charge and Energy Dependences of Ionization and Transfer for Helium in Collisions with Fast Charged Projectiles

The classical method within the independent electron model is employed to investigate （i） charge dependences of single and double ionization for helium by various charged ions A^q＋ （q = 1 - 8） at impact energies of 0.64 and 1.44 MeV/u, respectively, （ii） energy dependences of transfer ionization for helium by 0.5-3 MeV/u A^8.9＋ ions impact. The Lenz-Jensen model of the atom is applied instead of the Bohr model of the atom, and the impact-parameter dependences are also introduced into the calculations. Satisfactory agreement is found between theoretical and experimental data.     

min{max|x~n a_1 x~(n-1) a_2 x~(n-2) … a_(n-1) x a_n|}(x∈A)问题

引理1设n∈N,且n≥2则cosnθ=12n-1cosnθ q1·cos(n-2)θ q2·cos(n-4)θ …(1)(其中q1,q2,……均为与n有关的常数)说明:文[1]给出了余弦的n(n≥2,n∈N)次降幂公式:cosnθ=12n-1nk=0Ckncos(n-2k)θ.将上式整理即有:cosnθ=12n-1cosnθ 12n-1C1ncos(n-2)θ 12n-1C2ncos(n-4)θ     

Transfer Ionization of Helium in Collisions with C^q＋ and O^q＋ （q =1 - 3）

Cross-section ratios σTI/σSC of transfer ionization （TI） to single capture （SC） of C^q＋- and O^q＋-He （q = 1 - 3） collisions in the energy range of 15-440 keV/u （0.8-4.2 vBohr） are experimentally determined. It is shown that σTI/σSC strongly depends on the projectile velocity, and there is a maximum for E（keV/u）/q1/2 ≈, 150. Combining the Bohr-Lindhard model and the statistical model, a theoretical estimate is presented, in reasonable agreement with the experimental data when E（keV//u）/q^1/2 〉 35.