This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Akimune, H.

Berg, G.P.A.

Chang, S.

Davis, B.

Fujiwara, M.

Harakeh, M.N.

Jänecke, J.

Liu, J.

Pham, K.

Roberts, D.A.

Stephenson, E.J.

English

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ATOMIC CHARGE EXCHANGE 
BETWEEN FAST SINGLY- AND DOUBLY-IONIZED HELIUM IONS 
IN TARGETS FROM CARBON TO BISMUTH AT P = 0.36 
H. Akimune 
Kyoto  University, Kyo to  606, Japan 
G.P.A. Berg, S. Chang, J. Liu, and E.J. Stephenson 
Indiana University Cyclotron Facility, Bloomington, Indiana 47408 
B. Davis 
University of Notre Dame,  Notre Dame ,  Indiana 46556 
M. Fujiwara 
Research Center  for Nuclear Physics, Osaka University, Osaka 567, Japan 
M.N. Harakeh 
Kernfysisch Versneller Inst i tuut ,  974 7AA Groningen, T h e  Netherlands 
J.  Janecke, K. Pham, and D.A. Roberts 
T h e  University of Michigan, Ann Arbor, Michigan 48109 
Atomic charge exchange between singly- and doubly-ionized helium atoms in atomic 
collisions depends on the speed of the helium atoms and the atomic charge of the target 
foils. Atomic stripping (ionization) and capture cross sections contribute to this phe- 
nomenon, and both of these cross sections can in principle be determined individually. 
However, in targets of thickness greater than typically 50 pg/cm2 an equilibrium charge- 
state distribution is established. Only equilibrium charge-state distributions were deter- 
mined in this work. 
While neutral atoms must in principle be included in the equilibrium charge-state 
distribution, their contributions can be neglected at the ion speeds considered in the present 
experiment. Therefore, in equilibrium we have 
and hence 
N ( H ~ + ) / N ( H ~ + + )  = ocap/ostrip 
The present experiment was performed with a beam of fully ionized 3He++ ions of 
energy E(3He) = 200 MeV and speed P = 0.36 impinging on targets of 28Si, 56Ni, 
' O Z ~ ,  * ~ n  (A = 112, 114, 116, 117, 118, 119, 122, 124), 165Ho, l 8 l ~ a ,  2 0 9 ~ i ,  .e. for 
Z = 6, 14, 28, 40, 50, 67, 73, and 83. The number of singly-ionized 3He+ ions of energy 
200 MeV was measured by detecting them individually in the focal plane of the K600 
magnetic spectrometer (together with tritons from the (3He,t) reaction), and the number 
of fully ionized 3He++ particles was measured by recording the charge collected in a beam 
stop located at the inner surface of the first dipole magnet of the K600 spectrometer. 
The ratio N ( ~ H ~ + ) / N ( ~ H ~ + + )  was found to vary from about 3 x lo-' for Z = 6 to 
2 x for Z = 83. The results are shown as data points in Fig. 1. The statistical errors 
1 os . I I I I I I I I 
total 
Figure 1. Experiment a1 ratios N(3 He+)/N(3 He++) and calculated ratios of atomic strip- 
ping and capture cross sections (solid lines) as functions of the atomic number Z of the 
target atoms. The calculated cross sections are decomposed into the contributions for 
capture from the atomic shells K + N. 
are smaller than the data points, but systematic errors of about 4110% must be assumed. 
As expected, no differences within error bars were observed for the different isotopes with 
2=50. 
A complete theoretical interpret ation of the data was carried out using calculated 
stripping1 and capture2 cross sections. The equations and procedures used are similar to 
those employed earlier for lower-energy data by Kat ayama, e t  aL3 
Three expressions for the stripping cross sections have been reported1 for low-Z, 
medium-Z, and high-Z targets. However, it was found, in agreement with earlier  result^,^ 
that the equation 
for medium-2 targets agrees quite well with all data except for the lowest values of 2. Here, 
a0 is the Bohr radius, Zp and Zt are the charges of the projectile and target, respectively, 
and Vl is the velocity of the projectile in atomic units, i.e., the ratio with respect to the 
Bohr velocity. An adopted stripping cross section was used in the present work equal 
to that of Eq. (3) except for the range Z = 6 to 14 which was interpolated between the 
expressions for low-Z and medium-Z. 
Fig. 2 displays experimental and theoretical atomic capture cross sections. The exper- 
imental values were obtained from the measured ratios N(3He+)/N(3He++) multiplied by 
the adopted stripping cross sections. Theoretical predictions from the first- and second- 
order Oppenheimer-Brinkman-Kramer (OBK) approximations based on asymptotic ex- 
pressions are displayed in the figure as dotted curves. The agreement with the data is very 
poor. However, the theoretical predictions based on the equations reported by Nikolaev3 
give very good agreement. These equations represent a generalization of the OBK method 
including arbitrary external and internal screening corrections. One-electron hydrogen- 
like wave functions are employed. The atomic binding energies were taken from a recent 
t a b ~ l a t i o n , ~  and the screening corrections and effective charges were calculated using the 
Slater rules. Fig. 2 also shows the decomposition of the contributions from the various 
atomic orbits of the target nuclei. It is quite apparent that the cross section is dominated 
by capture from the K orbit only for atoms up to about Z = 25. For the heaviest atoms 
contributions up to principal quantum numbers n = 4 and even 5 (N and 0 orbits) must 
be included. The maxima for the contributions for capture from the K and L orbits occur 
when the speed of the projectile is close to the speed of the electrons in the respective orbit 
of the atom with the given Z. Corresponding experimental ratios N(3 He+)/N(3 He++) and 
calculated ratios o ~ ~ ~ / o ~ ~ ~ ~ ~  are shown in Fig. 1. They display similar characteristics. 
1 o-" I I I . I I I I I 
' ,  
total 
Figure 2. Atomic electron-capture cross sections for transitions He++ + He+ at P = 0.36 
as function of the atomic number Z of the target atoms. The calculated cross sections 
(solid lines) are decomposed into the contributions for capture from the atomic shells 
K + 0 .  Predictions from the first- and second-order OBK approximations are shown 
as dotted curves, and predictions for capture from the K-orbits based on a relativistic 
equation are shown as a dashed curve. The data points are from the measured ratios 
N(3 He+)/N(3 He++) multiplied by the adopted atomic stripping cross sections. 
Recently, Anholt and ~ i c h l e r ~  have calculated the cross sections for electron capture 
by relativistic projectiles in the eikond approximation. In this formalism they were able 
to evaluate the cross section for electron capture into the K shell of a projectile from the K 
and L shells of the target atoms by a numerical integration of a two-dimensional integral. 
However, in the case where the target and projectile charges are small, i.e. aZt  and aZp 
are much less than unity (a is the fine structure constant), the integral can be expanded to 
first order in a Z  to yield an approximate formula [Eq. (4) in Ref. 51 for the isll2 +lsl12 
(K+K) cross section. By neglecting the phase distortion of the final-state wave function 
of the transferred electron it could be shown that this formula reduces to the relativistic 
OBK approximation. 
We have used this formula to evaluate the K+K cross sections (only) for 3He projec- 
tiles from various nuclei at bombarding energies of 200 and 450 MeV. In this calculation, 
we have again used the experimental binding energies for the 1s electron in the target 
n ~ c l e i , ~  and we used effective charges Z* = Zt - AZ. The value AZ = 0.3 was assumed 
for the lsl/2 orbital to account for the partial shielding by inner-shell electrons. The re- 
sults are included in Fig. 2 as a dash-dotted line. The agreement with the results based 
on the Nikolaev equations2 is very good but starts to deviate for larger Zt where the ap- 
proximation aZt  << 1 is not valid anymore. The use of calculated binding energies4 and 
the relativistic OBK approximation give unsatisfactory results. 
Calculations for E(3 He) = 68, 99, 130, and 450 MeV were also performed based on 
the equations of Nik~laev .~  The agreement with the data of Katayama e t  aL3 at the lower 
energies is very good and requires again the inclusion of atomic orbits in the target nucleus 
up to principal quantum number n=4 (N orbits). Data for E = 450 MeV will become 
available soon. 
1. N. Bohr, K. Danske Vidensk. Selsk., Mat.-Fys. Meddr. 18, No. 8 (1948). 
2. V.S. Nikolaev, Zh. Eksp. Teor. Fiz. 51, 1263 (1966) [JETP 24, 847 (1967)l. 
3. I. Katayama e t  al., Phys. Lett. 92A, 385 (1982); Phys. Rev. A 27, 2738 (1983); J.  
Phys. B: At. Mol. Phys. 17, L23 (1984). 
4. C.M. Lederer and V.S. Shirley, Table of Isotopes, 1989, Appendix. 
5. R. Anholt and J.  Eichler, Phys. Rev. A 31, 3505 (1985). 


Atomic Charge Exchange Between Fast Singly- and Doubly-Ionized Helium Ions in Targets from Carbon to Bismuth at β = 0.36

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Atomic Charge Exchange Between Fast Singly- and Doubly-Ionized Helium Ions in Targets from Carbon to Bismuth at β = 0.36

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