NONCHARACTERISTIC X-RAYS FROM HEAVY-ION COLLISIONS

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NONCHARACTERISTIC X-RAYS FROM HEAVY-ION COLLISIONS

W. Meyerhof, R. Anholt

To cite this version:

W. Meyerhof, R. Anholt. NONCHARACTERISTIC X-RAYS FROM HEAVY-ION COLLISIONS.

Journal de Physique Colloques, 1987, 48 (C9), pp.C9-169-C9-176. �10.1051/jphyscol:1987926�. �jpa-

00227344�

JOURNAL DE PHYSIQUE

Colloque C9, supplément au n°12. Tome 48, décembre 1987 C9-169

NONCHARACTERISTIC X-RAYS FROM HEAVY-ION COLLISIONS

W.E. MEYERHOF and R. ANHOLT(x'

Department of Physics, Stanford University, Stanford, CR 94305, U.S.A.

Abstract

On discute l a formation des rayons x quaisimoleculaires dans une collision lente, presque symmètrique, entre un ion et un atom, et la formation des rayons x dans la capture radiative d'un électron dans une collision rapide d'un ion avec un atom.

We discuss the formation of molecular-orbital x-rays in slow, near symmetric ion-atom collisions and of r a d i a t i v e - e l e c t r o n - c a p t u r e x-rays in f a s t ion-atom c o l - l i s i o n s .

I . Introduction

The organizers of t h i s conference thought i t would be i n t e r e s t i n g t o give an overview of processes in which noncharacteristic x-rays are produced, since, typi- c a l l y , t h i s conference has dealt with various topics involving c h a r a c t e r i s t i c x- rays. To keep t h e topic within bounds, we l i m i t t h i s review t o t r a n s i t i o n s in which the i n i t i a l and f i n a l electronic s t a t e s a r e bound.

Noncharacteristic x-rays are produced in ion-atom c o l l i s i o n s . If these c o l l i - sions are slow compared t o the Bohr velocities of the active e l e c t r o n s , molecular o r b i t a l s (MO) a r e formed as the collision p a r t n e r s approach each other. Radiative electronic t r a n s i t i o n s can then take place between a higher and a lower lying MO, if a vacancy e x i s t s in t h e l a t t e r . Hence, the production of "MO x-rays" i s i n t i - mately r e l a t e d t o MO vacancy production, a topic i n t o which we cannot go here, though. The l i n e shape of MO x-rays r e f l e c t s the variation of t h e energy differ- ence between t h e i n i t i a l and final "MO1 s during the c o l l i s i o n , as well as the dyn- amics of t h e c o l l i s i o n . If t h e ion-atom collisions a r e f a s t compared t o the Bohr velocities of the active e l e c t r o n s , MO's do not form, but e l e c t r o n i c t r a n s i t i o n s can occur from bound t a r g e t s t a t e s t o vacant p r o j e c t i l e s t a t e s . The l i n e shape of these "radiative e l e c t r o n capture (REC) x-rays" r e f l e c t s the e l e c t r o n momentum distribution in t h e t a r g e t .

MO and REC x-ray production and properties have been reviewed in two recent a r t i c l e s .112 Hence our discussion will be r e l a t i v e l y cursory. All relevant r e f e r - ences can be found in these a r t i c l e s and a r e not cited s e p a r a t e l y here.

I I . Molecular-Orbital (HO) X-Rays 1. Line shape (and backgrounds)

A typical MO spectrum i s shown in Fig. 1. I t i s a r e l a t i v e l y f e a t u r e l e s s continuum extending approximately t o t h e united-atom (UA) x-ray l i m i t , which can be understood from the MO c o r r e l a t i o n diagram (Fig. 2) where the relevant t r a n s i - tions a r e indicated. There a r e , in f a c t , two main continua, one due t o t r a n s i t i o n s ending up i n the 1so MO, the other, in the 2po MO. We concentrate on the former.

Important backgrounds can appear due t o room and beam induced radiations and due t o nucleus-nucleus bremsstrahlung.

In a q u a s i s t a t i c model, one assumes that a t every i n t e r n u c l e a r separation R an x-ray can be emitted with energy Mw(R) corresponding t o the MO energy d i f f e r - ence at R. The shape of the d i f f e r e n t i a l spectrum do/dio i s then proportional t o the volume element 4irR2dR for t h a t distance R and the radiative t r a n s i t i o n proba- b i l i t y AX(R):

* 'Present address : Solid-state Electronics Laboratory, Stanford University. Stanford. CA 94305, U.S.A.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987926

JOURNAL DE PHYSIQUE

Although Ax

-

a w 2 , w decreases s o rapidly with increasing R t h a t dox/dw decreases approximately exponentially with w.

I n a f u l l quantum mechanical treatment, t h e radiation p a t t e r n is determined by t h e Fourier transform d(w,b) of t h e dipole momentum matrix element

between i n i t i a l and f i n a l MO wave functions ~ ( g , ; )

(i!

⁼ e l e c t r o n coordinate, b =

impact parameter). Since t h e wavefunctions

x

a r e expressed i n a non-inertial, r o t a t i n g reference frame, one has t o t a k e i n t o account Coriolis coupling. For t h e s m a l l values of b relevant t o MO x-ray production, t h i s coupling is s o strong t h a t i n t h e lab. frame t h e electronic wavefunctions e s s e n t i a l l y keep t h e i r incident ori- entation throughout t h e collision independent of the motion of the nuclei ('Iperfect e l e c t r o n s l i p modelI1). Hence one can visualize a 2 p a + 1 so and 2 p r + 1 so transi- tion i n terms of e f f e c t i v e components of

6

along (D,) and perpendicular (DL) t o t h e incident velocity direction (Fig. 3). The differential intensity of t h e MO x- ray spectrum f o r emission of the photon i n t o t h e s o l i d angle d.Q a t an angle 0 with respect t o t h e incident beam direction can be expressed i n terms of averages I, of

161

and I, of ID,1 over impact parameter:

The anisotropy parameter 11 is given by

which f o r I, = 0, '/,Io, 2/,1,, and I, takes on t h e values -0.5, 0, 1.5, and

-,

res- pectively.

2. Angular d i s t r i b u t i o n

Equation (3) gives a good account of the MO s p e c t r a l shape if t h e relevant o

+ 1so and n + l s o t r a n s i t i o n s from n = 2 and higher s h e l l s a r e taken i n t o account, The antsotropy coefficient r) is appreciably d i f f e r e n t from zero only i f t h e i n i t i a l a and ^IT o r b i t s a r e unequally populated. Such a population difference is indeed expected, because e l e c t r o n ionization from t h e MO1s increases rapidly with decre- asing binding energy. Hence, one expects the i n i t i a l o o r b i t a l s t o be more s t r o n g l y populated than a o r b i t a l s (see Fig. 2), making I, l a r g e r than t h e o t h e r intensUy components, and producing positive values of ^q. This

is

indeed found (Fig. 4).

.

Interestingly, ^r) peaks near t h e united-atom (UA) K,,B energy, a f a c t t h a t has been used f o r a kind of spectroscopy of UA binding energies.

I n t h e system of t h e e m i t t e r t h e radiation p a t t e r n is symmetric about 90°.

This f a c t has been used t o show t h a t t h e velocity of t h e emitting system is t h e c.m. v e l o c i t y of t h e nuclear quasimolecule found i n t h e collision and confirms t h e MO n a t u r e of these x-rays.

3.

Impact p a r a m e t e r dependence

Interference e f f e c t s between t h e radiation amplitude on t h e incoming and out- going branches of t h e collisions a t a given impact parameter have been detected (Fig. 51. These e f f e c t s wash out i f

an

average over impact parameters is taken.

I n summary, t h e properties of MO x-rays confirm t h e f a c t t h a t i n slow c o l l i - sions MO's a r e indeed formed and t h a t radiative t r a n s i t i o n s can occur between them.

111. R a d i a t i v e E l e c t r o n C a p t u r e (REC) X-Rays 1. Kinematics -.---

AS t h e velocity of the p r o j e c t i l e increases toward t h e Bohr velocity of the a c t i v e electron, o r exceeds it, t h e formation of MO's is l e s s l i k e l y and a new f e a t u r e appears: d i r e c t radiative t r a h s i t i o n s of

an

e l e c t r o n from t h e t a r g e t t o vacant p r o j e c t i l e s t a t e s (Fig.

6).

I f t h e e l e c t r o n were a t r e s t i n t h e t a r g e t , then, with respect t o t h e pro- j e c t i l e , it would undergo an energy change upon capture i n t o a p r o j e c t i l e s h e l l i (predominantly t h e K s h e l l , i f it is vacant) is given by:

where mc2(y-I) is the kinetic energy of the e l e c t r o n with respect t o t h e projec- t i l e and Ei is t h e binding energy of s h e l l i. I n t h e lab. frame, t h e e n e r g of t h e photon emitted a t the l a b . angle 9' with respect t o t h e incident velocity g is

For r e l a t i v i s t i c p r o j e c t i l e beams, t h i s r e l a t i o n can be used t o c a l i b r a t e t h e beam energy (Fig. 7).

2. Line shape (and backgrounds)

Equation (5) assumes+that t h e e l e c t r o n is a t r e s t i n t h e t a r g e t . For t a r g e t electrons with momentum p t , t h e REC peak r e f l e c t s the momentum distribution i n th$ +target which has a width, f o r a p a r t i c u l a r t a r g e t s h e l l t, of the order of Ycg-pt. Unfortunately, with r e l a t i v i s t i c beams, t h e width of t h e REC peak is sme- ared o u t by t h e f i r s t order Doppler s h i f t variation over t h e photon detector open- ing. Hence, even though t h e REC peak is well i s o l a t e d from t h e c h a r a c t e r i s t i c x- rays, t h e l i n e shape cannot be used t o determine t h e momentum distribution with r e l a t i v i s t i c p r o j e c t i l e s without using d e t e c t o r s with very narrow openings (Fig.

8a). Considerable success has been obtained f o r l i g h t t a r g e t atoms with lower velocity p r o j e c t i l e s , though (Fig. 9). Another disappointment is t h a t with heavy t a r g e t s , f o r which low-energy beams do not give an REC peak w e l l separated from t h e c h a r a c t e r i s t i c l i n e s , r e l a t i v i s t i c beams induce t o o much secondary e l e c t r o n bremsstrahlung (SEB) t o make a REC peak analysis possible (Fig. 8b). SEB is due t o bremsstrahlung of t a r g e t electrons, released by t h e projectile, which s c a t t e r on o t h e r t a r g e t atoms o r t h e chamber w a l l s .

Target e l e c t r o n . can a l s o s c a t t e r on t h e projectile, i n which case t h e radia- tion is c a l l e d primary bremsstrahlung (PB). I n t h e frame of t h e p r o j e c t i l e t h e s e electrons approach t h e t a r g e t with a kinetic energy mc2 (Y-I) [Eq. (5) with Ei =

01, smeared by t h e momentum distribution i n t h e target. The PB continuum is indi- cated i n Fig. 8. It has not yet been possible t o give a complete t h e o r e t i c a l account of t h e i n t e n s i t y of PB.

3. Angular distribution

From a theoretical point of view, REC can be considered a s an inverse photoe- l e c t r i c e f f e c t of t h e electron capture by t h e p r o j e c t i l e (except f o r e f f e c t s caused by t a r g e t - e l e c t r o n binding). I n p a r t i c u l a r , t h e photon-electron angular c o r r e l a t i o n s i n t h e p r o j e c t i l e frame a r e identical:

where 13 is the angle between t h e e l e c t r o n and t h e photon. I f one transforms REC t o t h e lab. frame, one finds t h a t t h e Lorentz transformation

e

⁺ 0' and dS2 -* dQ' gives approximately

a curious f a c t which has been demonstrated experimentally. A t r e l a t i v i s t i c pro- j e c t i l e velocities, the e f f e c t is very dramatic (Fig. 10). Actually, t h e r e a r e s m a l l deviations from sin2e', indicated i n Fig. 10, which a r e expected i f Dirac o r Sauter calculations of t h e photo-electric angular distribution a r e used.

Summary

I n t h i s brief review, we have t r i e d t o present some of the properties of non- c h a r a c t e r i s t i c x-rays which can be generated i n slow and f a s t ion-atom collisions.

MO x-rays r e f l e c t the MO s t r u c t u r e and t h e c o l l i s i o n dynamics, where REC x-rays r e f l e c t mainly t h e target-electron momentum distribution. I n t e r e s t i n g inf0rtIIatiOn

C9-172 JOURNAL DE PHYSIQUE

can be obtained from t h e angular distribution of these x-rays with respect t o t h e incident projectile. Several types of continuum radiation, which a r e worthy of study i n t h e i r own r i g h t , form backgrounds under t h e MO and REC spectra.

This work was supported i n p a r t by t h e U.S. National Science Foundation grants PHY-86-14650 and INT-84-14671.

References 1. R. Anholt, Rev. Mod. Phys. 57, 995 (1985).

2. R. Anholt and H. Gould, ~ d v y ~ t . Mol. Phys.

22,

31 5 (1986).

1 0 6 ^{I I}

75!3 MeV Nb

+

Nb COLLISIONS

105

- -

- - -

-

TOTAL BACKGROUND CNNB + BIB

y)104

-

^TNNB

I-

5103 ^-

0

"102-

10

-

_{I ! I .}

\:.

.\..

^-

I!

^{I I I}

40 80 120

PHOTON ENERGY

(

keV

Fig. 1. MO x-ray spectrum a t 90° f r a n 75-MeV Nb+Nb collisions. AB and (T)BIB a r e room and beam induced backgrounds. (C,T)NNB is nucleus-nucleus bremsstrahlung i n t h e C backing and t h e t a r g e t . (P. Vincent, Ph.D. thesis, Yale Univ., 1977.)

0.5 1.0

Internuclear Distance Lo.u.)

Fig. 2. Simplified o n e e l e c t r o n c o r r e l a t i o n diagram f o r Kr+Xe. Some MO transi- tions i n t o Iso and 2po vacancies a r e indicated by s o l i d and dashed v e r t i c a l lines.

[Based on J. Eichler and U. Wille, Phys. Rev. Ax,1973 (197511.

Fig.

3.

Sketch of components D, and D, of t h e dipole velocity matrix element par- allel

t o

and perpendicular t o t h e incident velocity.

0.6

-

-

0.1

12.6 MeV 0.6

0.2 -

*

$'

0.0

-

** N ~ T C = 0.45

-

20 30 LO 50

Fig. 4. MO x-ray aniatropy coefficient I-, a s a function of x-ray energy f o r v?rio'-'s N i + N i collisions. [P. Vincent, Ph.D. t h e s i s , Yale Univ., 1977. C a l c u a t e d curves

from R. Anholt, Z. Phys. A22, 257 (197813.

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Fig. 5. Impact parameter dependence of lso MO x-rays i n 5, 10, and 20 MeV C l + A r c o l l i s i o n s [R. Schuch et 61, Z. Phys. A.

320,

185 (198511. Calculated curves are based on t h e e l e c t r o n s l i p model [R. Anholt, 2. Phys. A 2 2 , 257 (1 97811.

l o o

Photon Energy ( k e V )

Fig. 6. Photon s p e c t r a from 16-MeV S + C, A 1 and 90-MeV S+A1 collisions. [H.D.

Betz e t al, Phys. Rev. Lett.

3,

1259 (197511. Eu is the UA energy K, energy. The dashed l i n e is a calculated extrapolation of t h e REC peak [M. Kleber and D.H.

Jakubassa, Nucl. Phys. A 2 2 , 152 (1975)l.

C

.-

t:

loo

w

L a b o r a t o r y angle (degrees)

Fig. 7. (a)

Lab. energy

and (b)

lab. cross section f o r characteristic La

K,

x-rays emitted i n 174-MeVM La+Be collisions

CR.

Anholt

and W.E.

Meyerhof, Phys. Rev.

A a , 1556 (198613.

Fig.

8. Photon spectrum a t -90° from (a) 82-MeV/N Xe+Be and

^(b)

422-MeV/N

U ⁺ U

collisions. Dotted curves, estimated Compton contribution t o

REC.

Extended

dashed curves,

SEB.

Dot-dashed curves, PB.

[A.

Anholt et

al,

Phys. Rev.

A&

2270

(19861.1

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Fig. 9. Comparison between experimental and theoretical REC cross sections f o r 125-MeV Sib+ + C collisions ( I A = impulse approx@ation, SPB = strong potential Born approximation) [D.H. Jakubassa-Amundsen, R. Hoppler and H.-D. Betz, J. Phys.

517, 3943 (198411.

I I I

dm(8)

dm(90°)s~n28LAB -

0.8 - I I t? -

197 MeV/omu

-

No Retard Xe +Be

- -.-

- Sauler ^D~roc

(210 MeV/ornu Sn+Be)

0 45 9 0 135 180

~ L A E

Fig. 10. Lab. angular distribution of K REC x-rays from 197-MeV/N Xe+Be colli- sions. Dashed and dot-dashed lines represent Sauter and Dirac calculations. With- out retardation effects, the solid l i n e would be obtained [R. Anholt e t al, Phy.

Rev. Lett.

53,

234 (1984); see a l s o K. Hino and T. Watanabe, Phys. Rev. A s 581 (198711.