Charge State Distribution of Recoil 16 O from 4 He( 12 C , 16 O) g in Astrophysical interest

1. Charge State Distribution of Recoil 16O from 4He(12C, 16O)g in Astrophysical interest 劉盛進A、相良建至B、寺西高B、 藤田訓裕B、山口祐幸B、　 松田沙矢香B、三鼓達輝B、岩崎諒B、Maria T. RosaryB、櫻井誠A 神户大学理学研究科A 九州大学理学府物理学専攻B 2011-12-03

2. introduction • Astrophysics. • 4He(12C,16O)g Ecm=2.4 MeV,1.5MeV Succeeded !! Total S-factor of 4He+12C 16O+g 16O1+,2+,….8+ The fraction of 16Oq+?? 16Oq+ detector • For the recoils 16Oq+, to determine 4He(12C,16O)g total cross section, fraction of 16Oq+ should be precisely known. Kyushu U. Investigation: charge exchange processes and charge state distribution of Oxygen though Helium gas. Ruhr U. extrapolation

3. Features of ion-atom collision q-1 Charge distribution q-2 q+1 Charge exchange e- e- physical processes: Capture, Ionization, Excitation,….. (Auger)

4. Ionization of Projectile, Aq+ A(q+1)+ (initial) (final) For a collision, from an initial state i to a final state f, ionization cross section is given: • Scattering amplitude • Effective charge of target(He): Ejection electron energy: • Projectile velocity: n • Minimum momentum transfer: qmin=（Ip+e）/n • Ip is binding energy of the projectile electron, e is energy of the ejected electron, • For the initial state(nlm) of ionized electron, the Schrodinger equation at multi-electrons system : PWBA: plan wave Born Approximation , • Projectile in initial and final states is represented by plane wave, (~exp(iqr)). • Perturbation of the projectile orbits is neglected. • Screening effect is taken into account. • projectile assumed to linearly without deviation of trajectory. • The final state: to solve radial equation in coulomb field

5. Capture of Projectile, Aq+ A(q-1)+ (initial) (final) • electron exchange is neglected. • The corresponding trajectory may be uniquely distinguished by an impact parameter and a velocity. • Nuclear and nuclear interaction is neglected. The H-like wave functions of an optical electron in the initial and final states: : electron initial state : electron final state : corresponding eigen-energies Impact parameter treatment

6. Possibility>1 16O6+ 16O7+ 16O5+16O4+ Ionization cross section Capture cross section F.M.Martine et al. PRA,1965(1971) Arseny: adiabatic approximation, low energy CDW: Continuum distorted wave approximation, high energy

7. Non-equili. equili. Equilibrium Charge State Distributions Variation of the charge state distribution: Gain Loss , Equilibrium distribution: All fractions reach a certain value and keep constant. Cross sections of ionization and capture are required

8. Results • Evolution of fraction against thickness 3+，100% 3+，100% Equili. Distri. Equili. Distri. He He The thickness evolution of fraction at 7.2 MeV and 4.5 MeV Equilibrium distribution can be obtained

9. Charge state distribution Mean charge state: The results of calculation deviated from the experimental results and shift to left. Reflecting the shape of experimental data well but mean charge state is smaller.

10. Data from TRIUMF Lab. (energy: 2.2MeV --- 14 MeV) Shift to left.!!

11. Enhanced ionization cross section • Blue curve: Calculation (σion. ×2) • Red curve: Experiment • Black curve: Calculation (σion. ×1) If ionization cross section is enhanced 2 times, calculation agrees with experimental data

12. Enhanced ionization cross section Date from TRIUNF Lab. • Blue curve: Calculation (σion. ×2) • Red curve: Experiment • Black curve: Calculation (σion. ×1) Ionization cross section is enhanced 2 times

13. Discussion Polarization effect Proj. Ion Proj. Ion Targ. atom • And excited state effects may play an important role in ionization of projectile. (Probability: Pexcited >Pdirect) • Ionization cross section: Ioni. Ioni. 2s 2s 1s 1s ground--excited --ionized Ground state 16O5+ Excited state 16O5+ • Theory Correction PWBA: Polarization effect • Perturbation of projectile orbits. • Result: a reduction in electron binding energy and increase the ionization probability

14. Conclusion • Comparison between theory and experiment. • Theory reflected experiment data but mean charge state was smaller • Try to correct theory (σion. ×2) and almost agreed well with experimental data. • Future: • Theory Correction (polarization effect and excited effect) • Prediction of non-equilibrium distribution at various energy • Measurement of 4He(12C, 16O)gat low energy :1.15MeV, 1.0MeV,…… • Charge exchange and charge distribution have been calculated • Ionization cross section: PWBA • Capture cross section: Impact Parameter Model

15. Thank you for attendance

16. Projectile Target r2 r’’1 r’1 R Z1 Z2 Proj. electron Target Electron 1 Target Electron 2 Hamiltonian: Interaction potential:

17. Projectile as a plane wave: Initial state:exp(-ikR) Final state: exp(-ik’R) q=k’-k (momentum transfer) Ionized electron state Initial state: fifinal state: ff The state of atom electron j1s1s(r’1, r’’2) ,jn’l’(r’1, r’’2)

18. M: reduced mass, v initial velocity, v’ the final velocity Summation of the states of target atom : Summation of the states of projectile: According the quantum transition, the cross section

19. The closure condition: Minimum momentum transfer:qmin=Ip+e+ △ET Ip is binding energy of the projectile electron, e is energy of the ejected electron, △ET is the excitation energy of the target electron

20. Scattering amplitude: F factor For the nlm initial state, the Hamiltonian at multi-electorns system : Spherical function: The final state: to solve radial equation at the coulomb central field

21. Capture Impact parameter treatment Assume: 1. electron exchange may be neglected. 2. effects of the identity of the nuclei may be neglected 3. the relative motion of the nuclei takes place at such velocities v, that the scattering is confined to negligibly small angles. 4. the corresponding trajectory for the incident nucleus may be uniquely distinguished by an impact parameter and a velocity.

22. X Velocity : n e impact parameter: r r2 R r1 n r Z A (target) O (mid-poit) R B(ion) r2=r-R/2 r1=r+R/2 Y

23. Omit nuclear interaction to get a rectilinear orbits from the equation of motion for the nuclei For the atom electron:

24. Defining initial unperturbed eigen function of the electron on A To make an expansion of y(r,t)in the state f(s) of A

25. After reaction: To make an expansion of y(r,t)in the state f(s)of B

26. As it is the cross section describing the capture of an electron from state i of A to state jof B is given by The initial conditions being Finally:

27. Using the Fourier transform w :The difference between the binding energies of capture electron in the initial and final state So the radial part of the exchange amplitude for the n0l0m0-n1l1m1 transition has the form

28. Function F for the initial and final states are defined by the radial integrals The H-like wave functions of an optical electron in the initial and final states: PnlHis the radial wave function of a hydrogen atom and Coulomb interaction potential has the form :

29. Scattering amplitude • Effective charge of target(He): Ejection electron energy: • Projectile velocity: n • Minimum momentum transfer: qmin=（Ip+e）/n • Ip is binding energy of the projectile electron, e is energy of the ejected electron, • For the initial state(nlm) of ionized electron, the Schrodinger equation at multi-electrons system : , • The final state: to solve radial equation in coulomb field

30. Capture cross section Impact parameter treatment • Assumption: • 1. electron exchange may be neglected. • 2. the relative motion of the nuclei takes place at such velocities v, that the scattering is confined to negligibly small angles. • 3. the corresponding trajectory for the incident nucleus may be uniquely distinguished by an impact parameter and a velocity.

31. Ioni. Proj. Ion Targ. atom Aq+ A(q-1)+