THE EFFECT OF MO FORMATION IN LIGHT ION INDUCED K-SHELL IONIZATION

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THE EFFECT OF MO FORMATION IN LIGHT ION INDUCED K-SHELL IONIZATION

O. Benka, M. Geretschläger, H. Paul

To cite this version:

O. Benka, M. Geretschläger, H. Paul. THE EFFECT OF MO FORMATION IN LIGHT ION IN- DUCED K-SHELL IONIZATION. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-251-C9-254.

�10.1051/jphyscol:1987942�. �jpa-00227360�

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Colloque C9, suppl6ment au n012, Tome 48, d6cembre 1987

THE EFFECT OF MO.FORMATION IN LIGHT ION INDUCED K-SHELL IONIZATION

0. BENKA, M. GERETSCHLAGER and H. PAUL

Institut fiir Experimentalphysik, Universitdt Linz, A-4040 Linz-Auhof, Austria

In a recent experiment Ti K-shell ionization cross sections were measured for low energy 0-ion impact. Large deviations were found when the experimental results were compared with the ECPSSR theory.

A modification of the ECPSSR theory is now proposed, which considers the effect of MO formation. The modified MECPSSR theory is then in muc.h better agreement with the experimental data.

The understanding of the direct Coulomb K-shell ionization process for light projectiles would appear to be fairly complete at present time. Among the easily calculable theories the ECPSSR [l]

gives the best overall agreement [2], except at low velocities, where it overestimates the cross section the more the higher the target atomic number Z2. The ECPSSR theory is based on the plane-wave Born approximation (PWBA) and includes various improvements based on plausible physical considerations. The presence of a projectile near the K-electron perturbs its stationary state (PSS). This leads to polarization of the wave function at high

5 , and to increased binding at low 5 . Here t=(2/8)(vi/v2) is the

scaled projectile velocity, viand v2 are the projectil and K-shell electron velocities and 8 describes the outer screening [l]. Both effects are treated by a factor

C

that multiplies 8 (and hence, changes the binding energy). The deceleration and deflection of the projectile by the target nucleus is treated by a Coulomb factor (C).

The relativistic correction (R) takes care of the fact that the standard PWBA uses non-relativistic electron wave functions. It is important for large Z, and small 1 . The energy loss correction (E) finally takes care of the projectile's energy loss during the collision.

Recently K-shell ionization cross sections were measured for some elements between Ti and Cu for low energy oxygen ion impact[3], the experimental results normalized to the ECPSSR theory are shown

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987942

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C9-252 JOURNAL DE PHYSIQUE

in Fig. 1. Deviations (s#l) increase when collisions are getting more symmetric, and it was proved in ref. 3 that electron capture, electron promotion between quasimolecular orbits or excitation by recoiled target atoms is most probably not the reason for these deviations. We propose now that the effect of MO formation for low velocity projectiles is the reason for the deviations. We considere then this effect by changing not only the binding energy, but also the velocity of the K-electrons. Neglecting the Coulomb deflection, for very low C we use an united atom (UA) model, whereas at high C we have the separated atom (SA) model normally used for ECPSSR. We introduce a function a(e) (where Osasl) so that a=O corresponds to the SA case (large

e)

and a = l to the UA case (C=O). Considering first the case of a straight trajectory, we assume for convenience the functional form

which has the desired limiting properties. Here $,=CMCM and a=CACM, the parameters C M , CA were adjusted to give best agreement with our oxygen data [3] (CM=O. 8 and CA=O. 3) and CM=(ZzK+Zl)ZI/ZzK where 2 Z2K=Z2-0.3, and Z i and Z 2 are the projectile and target atomic numbers,resp. The C dependence on (Zl/Z2) is for the fact that high Zi projectile will more probably cause MOs than low Zl.

Fig. 1. Experimental ionization cross sections normalized to ECPSSR cross sections for oxygen ion impact as a function of

C.

4.0

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0 ^{2 . 5 1} 01 0

CI ( ,

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a

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v T t W F IRON

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1. E-1 1. €0

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rad<2d, where radis the adiabatic radius and 2d the distance of closest approach for a head on collision. For projectiles with normalized impact parameter C=r,,/aaK (aaK is the K-shell radius of the target atom Z,), the normalized distance of closest approach on a hyperbolic orbit is increased from

C

to

hence the normaliced distance of highest ionization probability will be closer to

CD

than to C. We therefore evaluate as at CD, not at

C.

If C approaches zero, d and hence

CD

increase. But slow ions should ionize only high momentum electrons, which move closer to the target nucleus and are therefore more SA-like. To describe this reduction of MO-character, we introduce an additional factor

The parameter a is therefore given by

The ECPSSR theory is now modified by the following steps:

i. ZaK is replaced by ZaK=ZaK+aZ1. In the velocity-independent a factor of the PWBA cross section, written in [l] as

a a a

UoK=8naaK(Zl/ZaK)

,

the area of the K-shell, "aaK, is left unchanged, however.

ii. The modification of 8 is more complicated. For a=l, we should

a U A a

have 8 =8

,

for a=O, 8 =8. This is done by defining an a

a a

depending ionization energy IK and 8 a = ~ ~ / ( ~ a K + a Z l ) Ry.

iii. The binding/polarization correction factor

C

is replaced by

where the functions g and h are defined in [l].

For a=O, the replacements i to iii do not change the ECPSSR theory. For a=l, we have a united atom ECPSSR theory: Coulomb deflection for a nuclear charge Z a , wave function and binding energy for a nuclear charge ZaK+Z1, but no binding correction (tall). For Z l = l or 2 and Z2>20,

C,

is very small. Because of Coulomb deflection, we then always have C,>C, and a-0, hence there is almost no MO effect. Only for larger Z l and for low

C

(as, e.g., for our measurements [3]), MO effects become significant and can increase the

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C9-254 JOURNAL DE PHYSIQUE

ECPSSR theory by as much as a factor 3. This change is largest for t*0.25. For lower C , the Coulomb deflection reduces the MO effect.

Fig.2. Like Fig 1, but normalized to the new modified ECPSSR theory.

-- -

1.5 0

(U C C3

H

m

\ 1.0-

n X

(U

C3

I+

m

0.5

0.0

In Fig. 2 the same experimental results are shown as in Fig. 1, but now normalized to the modified ECPSSR thoery (MECPSSR). In this MECPSSR calculation also a modified relativistic correction is used to consider the effect of Coulomb deflection on the relativistic correction. This relativistic modification is here not of importance, it is only significant for high Z, targets. As can be seen in Fig. 2, agreement to the new MECPSSR theory is now much better. We therefore conclude that the deviations in Fig.l are an indication of MO formation. The low enhancement for the Cu cross section is because of the increasing importance of the Coulomb deflection on the MO formation. In the new proposed MECPSSR theory these effects are now considered and good agreement to the experimental data is now found.

. . . .

T TITANIUM

-

V VANADIUM R c m n I u n

-

^{F IRON}

-

N NICKEL

-

T C COPPER

C SILVER

-

C N N E

- -

[l] Brandt, W., Lapicke, G., Phys. Rev.

A23

(1981) 1717 [2] Paul, EI., Muhr, J., Phys. Reports 135 (1986) 4 7

[3] Geretschlager, M., Benka, O., Phys. Rev.

A34

(1986) 866

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