Target and projectile K x-ray production by 100, 160, and 200 MeV Nb collisions with thick solid targets

(1)

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Submitted on 1 Jan 1990

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Target and projectile K x-ray production by 100, 160,

and 200 MeV Nb collisions with thick solid targets

E. Liarokapis, T.J.M. Zouros

To cite this version:

(2)

Target

and

_projectile

K

_x-ray

_{production by}

100, 160,

and

200 MeV Nb collisions with thick solid

_targets

E.

_Liarokapis

_(*)

and T. J. M. Zouros

_(**)

Wright

Nuclear Structure

Laboratory,

Yale U., New Haven CT 06520 U.S.A.

(Reçu

le 13 novembre 1989,

accepté

le 8

janvier

1990)

Résumé. 2014 On donne les valeurs des sections efficaces de

production

de rayons-x K dans des collisions par des

projectiles

de Nb sur une série de cibles

_(Z

= 6 à

68)

à des

énergies

de 100, 160 et 200 MeV. On teste différentes théories de

_production

de trous K dans ce

_large

intervalle

d’énergie, parmi lesquelles

la

_promotion

d’électron avec _partagede trous

_{(modèle moléculaire),}

l’excitation directe

_{(théorie ECPSSR),}

_{l’approximation}

de chocs binaires modifiée

_(BEA),

ainsi que certains modèles

semi-empiriques.

On trouve _{que le mécanisme dominant pour la}

_production

des trous K à la fois dans le

_projectile

et _{la cible est, pour la}

_plupart

des

_systèmes

étudiés, le modèle moléculaire. Pour des collisions très

_{asymétriques,}

les calculs de la théorie ECPSSR rendent _comptedes données à un facteur 2

_près

_{pour les cibles}

légères

(V, Al),

mais ne

conviennent pas pour les cibles les

plus

lourdes. Abstract. 2014

Target

and

_projectile

K _{x-ray cross-sections}

_produced

in

_collisions

of Nb

_projectiles

with a series of _targets

_(Zt

= 6 -

68)

are

_reported

for

_energies

of _100,160 and 200 MeV. Various

K-vacancy production

theories were tested over _{this broad range}

_including

electron

_promotion

with vacancy

sharing

(molecular model),

direct excitation

_{(ECPSSR theory),}

modified

binary

encounter

_{approximation (BEA),}

as well as some

_{semi-empirical recipes.}

For most of the collision

systems

investigated

the molecular model is found to be the dominant mechanism for

K-vacancy

production

in both

_projectile

and _target. For

_highly

_asymmetric

collisions, the ECPSSR calculations are found to be within a factor of two of the data for the

_lightest

targets

(C, Al),

but fail for the heaviest _targets.

Classification

Physics

Abstracts 34.50

1. Introduction.

The

_study

_{of inner shell vacancy}

_production

in ion-atom collisions has received considerable attention since the

_early

seventies. In

_particular,

K-shell ionization has been studied

extensively

for

_light

_[1]

and

_heavy

_projectiles

_[2],

at both low

_[3]

and relativistic velocities

_[4].

However,

even

_today,

a

_{complete theory}

that can

_{predict K-vacancy production}

cross-sections

for all collision

systems,

based on first

_principles,

is still

_lacking

[5].

For the case of very

asymmetric

collision

systems

_(ZP/Zt

1/2 )

and moderate

_projectile

velocities

_{(Vp/V2K : 1),}

where

_{v2 K}

is the

_velocity

of the K-electron and the indices p, t refer to the

_projectile

or

_target

(*)

Permanent address :

_Dept.

of

_Physics,

National Technical

_University,

Athens 157 73, Greece.

(**)

Present address :

_Dept.

of

_{Physics, University}

of Crete and Research Center of Crete, Iraklion,

Greece.

(3)

atoms

_{respectively,}

both direct excitation mechanism and electron

capture

[6]

are the

dominant ways of

producing

a K vacancy in the

_lighter

collision

_partner.

At rather low

projectile

velocities

_{(vp «}

_v2K)

and

_{nearly symmetric}

collision

_systems

_{(Zp -}

_{Zt ),}

the molecular model

[3, 7-9]

gives

a

good description

of K _vacancy

production

via the

_promotion

of electrons from the K-shell to

_higher

orbitals. In the case of direct Coulomb

excitation,

the

ECPSSR

_theory

that includes corrections for the Coulomb

_trajectory,

the relativistic

effects,

and

_projectile

energy loss in the

target

[10],

seems to

_reproduce

the measured cross-sections

quite

well for many collision

systems

[1].

However,

this

_theory

is in serious

_disagreement

with data from

_{near-symmetric}

collision

_systems

_[11].

For these

collisions,

the relative amount of

projectile

and

_target

K x-rays can be

_{predicted by}

_{the vacancy}

_sharing

model of

_Meyerhof

[12],

while the absolute cross-sections can be calculated within the modified

_binary

encounter

approximation

model

_(BEA,

Ref.

_[13]),

which

_incorporates

the effect of the molecular orbitals formed in the collision

_{by introducing,}

in a

_{semiempirical}

_{way, the united}atom

binding

energy in the BEA model.

To date a lot of data have been accumulated for

light

projectiles

(Zp

10,

Ref.

[1]),

while

data for heavier collision

systems

is rather limited

_[2].

In this

_{investigation}

we test

_generally

accepted

theories of K _vacancy

_production

for collision

_systems

_involving

heavier ions. This work evolved out of our _{interest in molecular-orbital x-rays}

_produced

in

_heavy

ion-atom collisions and the need to _{know K x-ray cross-sections for various}

_symmetric

and

_slightly

asymmetric

collision

_systems

_involving

Nb

_projectiles

_[14].

The Nb +

_Z,

collision

_systems

were studied

_using

a series of solid

_targets

(Zt

= 6 -

68 ).

K _x-ray

production

cross-sections

for both

_projectile

and

_target

K x-rays were measured for three

_projectile

_energies

so that

their energy

dependence

could be studied. The data was

_compared

with the

_predictions

of the

modified BEA and the ECPSSR

_theory.

The ECPSSR

_{theory approximates,}

within a factor

of two the measured cross-sections for the Nb + C and Nb + Al collision

_systems,

it underestimates the

_K-vacancy

cross-sections for all other collision

_systems

studied,

even for the

_{quite asymmetric}

_system

_{(Nb + Sm ),}

where direct excitation should be the dominant mechanism for K _x-ray

_production

_[6].

An

_improvement

in the theoretical

_predictions

for the Nb + C and Nb + Al collision

_systems

is obtained

_{using semi-empirical}

correction factors

_[15]

which as in the case of the ECPSSR

_theory

also account for Coulomb

deflection,

binding

energy, and relativistic effects. The relative ratio of the

K-vacancy

cross-sections of the two

collision partners

is shown to _{follow the vacancy}

_sharing

formula

_[12],

while the absolute cross-sections are found to _agree

_quite

well with the

_predictions

of the modified BEA

_[13],

even for

_{quite asymmetric}

collision

_systems

_{(ZLight/ZHeavy = 0.6).}

In the

_following,

the

_{experimental procedure}

is described and the results for the three different

_{projectile energies}

are

_presented.

Theoretical calculations based on the direct

excitation mechanism and the molecular model are

_compared

with the measured K x-ray

cross-sections.

2.

Experiment

and

apparatus.

Low

_intensity

_9’Nb+’l

_(q

=

9-16)

ion beams were obtained from a

_negative

ion

_sputtering

source and accelerated to

_projectile

_energies

_{of 100,160,}

and 200 MeV

_using

the tandem Van-de-Graaff accelerator of the

_Wright

Nuclear Structure

_Laboratory

at Yale

_University.

A series of

_targets

from

_Zt

= 6 to

Zt

= 68 _were

placed

inside an aluminum

_scattering

chamber

on a ladder with

_eight

_target

_positions

_and

inclined at 45° with

_respect

to the beam direction

(Fig. 1).

Most of the

targets

were

_{prepared by evaporating}

the

monoisotopic

material on

30

_f.Lg/cm2

carbon

_backing.

The thickness of the

_targets,

shown in table

I,

was determined

_by

(4)

Fig.

1.

_{- Experimental}

_setup

_{showing scattering}

chamber, x-ray detectors,

particle

detectors and beam

line.

Table I . - Table

of

K _x-raycross sections

(in barns),

_target

thickness

(in

ug/cm2)

and the

exponent a

_(see

_Eq.

₍₈₎₎

_for

the Nb

_projectile

and the various

_targets

at the three collisions

energies

used. The relative error

_for

the cross sections is 18 %

_{for Zt >}

32 and 25 %

_for

Zt >

32.

(5)

Two different

_{hyperpure germanium}

detectors

_(HpGe)

were

_used,

one with a 10 mm

diameter and an _{energy resolution of 177 eV}at 6

_keV,

_{predominantly}

used for the K x-rays of the

_lighter

atom, and the other with a 1 000

mm2

active detection area and an _energy

resolution of 560 eV at 6 keV used to _{detect the K x-rays of the heavier}

_partner.

The two

detectors were located

_{symmetrically}

at ± 90° with

_respect

to the beam line in front of the 3.8 cm diameter windows on the side of the

_cylindrical

chamber

_{(Fig. 1).}

The windows were

covered

_by

25 um

mylar,

which was thick

_enough

to

_prevent

electrons from

_reaching

_{the x-ray}

detectors,

When necessary, absorbers were used to attenuate _{L x-rays}as well as the K _x-rays

of the

_lighter

atom. The total efficiencies

_{(including absorbers)}

of the

_HpGe

detectors were

measured as a function of

_photon

_energy

_using

calibrated x-ray sources

_placed

at the

_position

of the beam

_spot

on the

targets.

The formulation outlined in Ref.

_[16]

was used to

_interpolate

efficiencies at other

_energies

and to account for the

_large

detection

_angle

_[17]

within an

accuracy of - 10 %.

Two surface barrier

_particle

detectors were used to count the scattered ions

_{(Fig. 1)}

anchored to the

_top

cover of the

_chamber,

and

_carefully

_positioned

at ± 30° with

_respect

to the beam line at a distance of 5.5 cm from the

_target

holder. On the front face of each

detector,

a

collimator 4 mm x 6 mm wide and

_magnets

(-

500

_{G )}

were

_used,

to

_prevent

detectors

_(left-L30

and

_right-R30),

_any

_wandering

of the beam on the

_target

could be inferred from differences in the L30 and R30 counters

(defined

as L-R

_anisotropy).

Because of the close

_geometry

utilised,

small

_changes

in the

position

of the beam

_spot

on the

_target

_(-

1

_mm),

could lead to a 20 % difference in the

counting

rates of the two

_particle

detectors. Since three

_{projectile energies}

were

used,

the

beam was collimated at the center of the

_target

at the

_beginning

of each run.

Never-the-less,

the L-R

_anisotropy

was found to be in a few cases as

_large

as 40

%,

implying

that the beam

spot

was 2 mm off-center.

The different inclination of the

_target

relative to the

_particle

detectors also introduced a

serious effect. The

_target

thickness that the scattered ion

_{passed through}

before

_reaching

the L30

_particle

detector was about four times that of the R30

detector,

introducing

a

_{large spread}

in the energy of the scattered

projectile

from the recoil or the C

_backing

_{(Fig. 2).}

_Thus,

_only

the total counts

_(target

+

_projectile)

in the L30 detector could be used for the correction of the small variations of the beam

_spot

on

_target

_(from

the L-R

_anisotropy).

Electronics and data

_acquisition

_system

dead-time was measured with a live-time

_pulse

generator

and found to be

_negligible

_{( 1 % ).}

3. Data

_analysis

and results.

The counts _{in each K x-ray}

_peak

were

_{integrated, using}

a Gaussian line

_shape

fit on a

quadratic

background

and corrected for the total

_efficiency.

Nucleus-nucleus

_{bremmstrahlung}

[18]

and MO _x-rays

_[14]

which contribute a rather structureless continuum in the

_region

of

high

x-ray

energies,

were considered as

_part

of the

_{quadratic background}

to _{the K x-ray}

peaks.

The

_peaks

in the

_particle

detector

_spectra

were identified and

_integrated.

In those cases where the recoil

peak

could not be resolved from the

_projectile

_peak,

the total

_intensity

of both

_peaks

was considered. This was

_particularly

true for the L30

_particle

detector

_(see

Fig.

2),

where the

_integration

of each

_peak

was rather uncertain and therefore the total counts

(6)

Fig.

2. -

Spectra

of the two

_(left

and

_right)

_particle

detectors for collisions of 200 MeV Nb with Sn.

anisotropy

to an

_uncertainty

of 10 %

_depending

on the collision

_system

and the

_target

thickness used. The L-R

_anisotropy

was used in the correction of the solid

_angle

subtended

_by

the R30

_particle

detector. It _{should be noted that any}absolute error in the solid

_angle

(-

20

_{% )}

results in an overall normalization

_uncertainty

and will not affect the relative values of the K x-rays cross-sections. The

efficiency

of each

_particle

detector was considered to be

independent

of the

_particle

_energy.

Most of the

_targets

were made

_by

_evaporating

the

_target

material onto a 30

_f.Lglcm2

carbon

backing

and therefore contributions to the Nb K _{x-rays from carbon had}to be subtracted. The relative thickness of the

_backing

to the thickness of the

_target

_{(known approximately)}

was

deduced from the

_{integrated peak}

areas in the

_particle

detector

spectra

due to the carbon

backing

and the

_target

atoms. _{From this ratio the Nb K x-ray contribution of the carbon}

backing

was calculated and found to be rather small

_{( 5}

% of all Nb K

_x-rays),

for all collision

_systems.

_Finally,

the

_absorption

of the emitted K _x-rays

_by

the

_target

and the

_backing

was estimated and found to be

_negligible

in all cases.

The K x-ray cross-sections for Nb and the

target

atoms u (K)

were deduced from the

Rutherford cross-section of the scattered Nb

_{ions uNb(OR)’}

_using

the formula

where

_{Y(K), Y(Nb)}

are the

_target

K x-ray and Nb ion

yields respectively ;

eR30

and e ’are the total

_efficiency

_(detection

solid

_{angle plus}

absorbers,

if

_any)

for the

_particle

and the x-ray detectors

respectively.

It should be noted that the Rutherford cross-sections have been calculated

_using

_{the average energy of the}

_projectile

as it traversed the

target

and at the deflection

_{angle OR}

₍₌

30° ±

_8(J)

which was consistent with the L-R

_anisotropy

of the two

particle

detectors. In this way, any

wandering

of the beam on the

target

was taken

_fully

into

consideration. It bears

_emphasis,

that

_{by normalizing}

to the Rutherford

cross-section,

any

uncertainty

in the value of the

_target

thickness could

_only

affect the evaluation of the average

projectile

energy inside the

target

and introduces a

_negligible

error in the K vacancy

(7)

Fig.

3. -

Projectile (e)

and _target

₍₀₎

K _x-raycross section

_{(in barns)}

as a function of the _targetatomic number

_Z,

for

100, 160,

and 200 MeV collisions. Error bars are of the order of the size of the data

_points.

Continuous line : ECPSSR

_theory

_[10].

Dashed line : Anholt and

Meyerhof

[15].

The measured cross-sections of both

_projectile

and

_target

K _{x-rays for the three}

_energies

of

100, 160,

and 200 MeV are showh in table 1 and are also

_plotted

in

_figure

3. These

cross-sections include a relative error of 10 % due to the total

_efficiency

of the x-ray detectors

(in

the case of

_targets

of

_Zt

32 the error was - 20

_%),

a maximum error of 10 % from the

integration

of the

_peaks

_(both

_{K x-rays and}

_particle

_spectra)

and an overall normalization error of 20 % due to the

_particle

detector

_efficiency

and solid

_angle.

Cross-sections were

evaluated under the

_assumption

of

_isotropy,

_{since K x-rays}are known to be

_{quite isotropic}

[19]

in the emitter frame of

_reference,

and the error introduced from the transformation to the

laboratory

frame of reference is very small

( 1 %) .

Any dependence

of these cross-sections on the initial

_charge

state of the

_impinging

ion was

neglected.

For the

_charge

states used in our collision

_systems,

the innermost shells

responsible

for the K-shell ionization were

_{fully occupied.}

Therefore,

the effect of the initial

projectile

charge

state on the fluorescence

_yield

_(wq)

should be 10 %

[11, 14, 20].

The thick

targets

used in these measurements can

_give

rise to effects such as _{energy loss of}

the

_projectile,

increased ionization of the

_projectile,

and contributions from

_target

recoils. The average energy loss of the

projectile

was taken into consideration

_{by correcting}

the measured K x-ray cross-sections in accordance with their

projectile

energy

dependence

(Eq. (8)

see

below)

and

_{by evaluating}

the Rutherford cross-sections at _{this average}

_projectile

energy. Since the fluorescence

yield

of the

_projectile

is

_{fairly large}

_{(w Nb}

=

0.747,

Ref.

[21]),

the effect of the increased ionization should be small even for

_light

collision

systems

(Zt

28).

The

_dependence

_{of the K x-ray cross-sections}on the thickness of the

target

has been

_previously

observed

_for

_{many collision}

_systems,

all of them

_{utilising relatively light}

projectiles

[22, 23].

For Ni and Nb

_{projectiles impinging}

on

_{Ni, Nb,}

and Sn

targets,

no such

target

thickness

_dependence

was observed

_{[17, 24].}

Therefore,

it is

_expected

that at least for

Zt >

28,

such effects should be small for both

_projectile

and

_target

K x-ray cross-sections. 4. Discussion.

In

_figure

3 we

_present

the measured K _x-raycross-sections both for the

projectile

and

target

as a function of

Zt. Following

Meyerhof et

al.

[3, 9],

this data can be

tentatively

divided into

three

_regions.

The bell

_shaped

central

_region

_{(22 -- Zt ,- 62)}

_having

a near

_exponential

dependence

on

_Z1’

and the

_{regions with Zt «}

_ZP

= 41 or

_{Zt >}

_ZP

=

41,

for

which,

with the

exception

of Erbium

_{(Zt = 68),}

the measured cross-sections vary rather

smoothly

with

(8)

The theoretical

_predictions

of the ECPSSR

_theory

_[10]

are also shown in

_figure

3 as

continuous lines. It is seen that

_only

for the Nb + C

(Zt

=

6)

and Nb + Al

_(Zt

=

13 )

collision

systems,

the measured cross-sections are

_reproduced

within a factor of two. For the rest of the

targets,

the theoretical

_predictions

deviate from the data

_by

one to four orders of

_magnitude

with the

_{theory consistently}

_{underestimating}

the data. Within the formulation of direct Coulomb

excitation,

some

_{semi-empirical}

corrections have been

_proposed

that account for energy

loss,

relativistic

effects,

and the deflection of the

incoming

ion

[15].

The

predictions

of this

_theory

_(shown

in

_{Fig. 3 by}

dashed

_lines)

are similar to those of the ECPSSR

_theory,

showing only slightly

better

_agreement

in absolute value with the measured cross-sections. For

_symmetric

or

_{slightly asymmetric}

collision

_systems,

it has been shown

_[9]

that the main

K-vacancy

production

mechanism in both collision

_partners

is the creation of a _{2 pu}

molecular orbital

_(MO)

_{vacancy which is}

_subsequently

shared between the K-shells of the two atoms.

_According

to

_{Meyerhof et}

al.

_{[3] :}

since

_always

o.- _{1 ,}

_{« U 2}

pu and w

1/2,

and

where 0- L, OH

are the

_K-vacancy

cross-section for the

_light

and

_heavy

collision

_partners

respectively, u, is

the cross-section for the creation of a _{vacancy in the i-th molecular-orbital}

(i

= 1 _so-,

2pu),

uK-L(K)

is the

K-vacancy

cross-section of the

lighter

_atomdue _toK-L

matching

[25]

and w is the vacancy

sharing

factor

_[12].

For o- K-L (K ) « 0’2 p,

(i. e.

only slightly asymmetric

systems),

and thus

where x is defined

_by

IH

and

_{IL being}

the K-shell

_{binding energies}

of the

_heavy

and

_light

atoms and v the

_projectile

velocity respectively.

Under the

_assumption

that

w >

0’ 1 so- ,

we can

_directly

_{compare the calculated}

ratio,

1 - w

_(T2pu

w

,

to the measured ratio of the cross-sections

_{(u HI u d}

as functions of the

_target

1 -w

atomic number. This is shown in

_figure

4. The

_K-vacancy

cross-sections used to evaluate the ratio of

_(OH/O’L)

were _{deduced from the measured K x-ray cross-sections}

_{(Tab. 1),}

_using

neutral atom fluorescence

_yields

_[21].

The ionization state of the

_projectile

is

_expected

to

influence the value of its fluorescence

_yield,

while the

_degree

of ionization will vary with

target

thickness and

_projectile

_{energy. The}error introduced

_{by using}

neutral atom

fluorescence

_yields

is estimated to be - 10 %

_{[11, 14].}

(9)

Fig.

4. -

Experimental

ratio of

_UH/O’L

_{(data points)}

with theoretical values of the

sharing

ratio

w

versus _targetatomic number

_Zt

for the three different

_{projectile energies.}

Continuous line : 1-w

Calculations based on _{the vacancy}

_{sharing probability w}

formula

_{(Eqs. (6)}

and

₍₇₎₎

without the inclusion of the term

_{U IsO" / U 2pO".}

Dashed line : includes the

_{term U IsO" / U 2pO".}

·

which the

_sharing

ratio

_{(w - 0.0003 )}

_{is very small. At}

_higher

_projectile

_energies,

small deviations are observed

increasing

in size with

increasing projectile

_energy

(Fig. 4).

A

difference of a factor of four between data and

_theory

for 200 MeV Nb + Ti

_(Zt

=

22 )

is too

large

to be accounted for

_by

variations in the fluorescence

_yield

of the Nb

_projectile

alone.

Furthermore,

contributions from direct excitation and radiative electron

_capture

_(Fig.

_3,

continuous

_lines)

are - 30 % of the total cross-section for Ti and therefore are also not

_large

enough

to account for this

_discrepancy.

We

expect

the K-L

_matching

mechanism

_[25]

to

become

_{increasingly important}

in these collision

_systems,

since the 3

_do-MO,

correlated to the

3p-level

of the

_projectile,

will be

_{progressively}

excited with

_{increasing projectile energies.}

Therefore the

_{previous assumption}

_{of o, K-L (K) « U2 p,}

will not _{be valid any}

_longer

and contributions from the increased ionization of the K-shell due to K-L

_matching

must be considered. Since the L-shell ionization cross-section of the heavier atom was not

_measured,

the evaluation of these contributions cannot be carried out.

In the

_region

of

_{Zt > Zp,}

_{ignoring U l 50" / U 2 pO"}

in

_{équation (6),}

leads to rather

_good

agreement

(see Fig. 4)

between the theorical

_{(e- 2 x,}

_{Eq. (6))}

_{and experimental}

_(uH/uL)

sharing

ratio for all

_targets

_{used up}to Barium.

_However,

for

_{Zt >}

_56,

a consistent deviation

occurs,

increasing

with

decreasing

projectile

energy. Such a

_projectile

_energy

_dependence

is

not consistent with the direct Coulomb excitation mechanism

_[6].

So,

by correcting

the

sharing

ratio

_{1 w}

for the contribution from the

_{ratio 0-1,,,,IU2p,,}

_[26],

_using

the measured 1 - w

ratio of

_{u2pO" =}

_o-H+ _{0» L,}

(Eqs. (4), (5))

and the estimated value of uIsO"

[15],

the

_agreement

between

_theory

_{(Eq. (6))}

and data

_(uH/uL’

_{Fig. 4)}

is

_improved

to 40 % at 200 MeV.

However,

it is still off

_by

a factor of 4 at 100 MeV

_(dashed

line in

_{Fig. 4).}

A similar

disagreement increasing

with

_decreasing

_projectile

_{energy is}obtained

_using

the values from the ECRSSR

_theory

_{for the o-isr value}

_{(Fig. 3}

continuous

_line).

On the other

hand,

any contribution from K-L level

_matching

should further reduce the

_sharing

ratios

_{(Eqs. (2-3, 6)).}

Increasing

the

_projectile

_velocity,

should also increase the relative contribution of K-L

matching

[25],

in

_disagreement

with our data

_{(Fig. 4).}

_Strong

relativistic corrections

_applied

to heavier collision

_systems

_[27],

_might

also be

_important

in this case,

though

Z =

(10)

systems

(Z >

137,

Ref.

_[28]),

underestimates the measured cross-sections

by

many orders of

magnitude.

Since the

_sharing

ratio formula

_[12]

has been verified for _{many collision}

_systems,

the

_origin

of this

_discrepancy

is still not clear.

In the case of Erbium

(Er),

the K vacancy cross-section is

larger

than the cross-section of Samarium

_(Sm)

_though

_Zsm

= 62

ZE,

= 68

(Fig. 3).

This is due to

background

contributions

to Er from K-shell internal conversion

_decay.

Since Er has a

_strongly

deformed

nucleus,

this

effect will make a

_large

contribution to K _x-ray

_production,

while for the other

_targets

such an

effect will not be

_appreciable.

The contribution from the direct nuclear Coulomb excitation followed

_by

internal conversion

_decay

has been estimated

_using

the internal conversion factors from reference

_[29]

and theoretical values for the direct nuclear Coulomb excitation

[30]

and found to account for most of the Er K x-rays. In the case of the Sm

_target,

the relative

contribution was found to be less than 10 %. Due to this contribution from internal

conversion,

the value of the Er K x-ray cross-section due to atomic effects alone is

_quite

uncertain.

Fig.

5. -

Total 2 pu MO vacancy

production

cross sections for

_{Zt >}

22, scaled as discussed in text. Continuous line : modified BEA

_[13].

Dashed line : Lennard et al.

_[31].

In

_figure

5 the

_{2 pcr}

_vacancy

_production

cross-sections are scaled

_by

the factor

Iip(U)/zz

and

_plotted

versus the

_scaling

_parameter

_{1 2 p (U) =}

_{(El/Ml)/[I2p(U)/me]}

for

Zt

> 22. The cross-sections shown were calculated from the sum of the

_target

and

_projectile

K

x-ray cross-sections corrected for the neutral atom fluorescence

_yield

_[21].

Z is the effective

charge

(2

Z2 =

_Z2

+

Z22 ),

while

_I2p(U)

is the united atom

_binding

_{energy. The}

_predictions

of the modified BEA

_[13]

are shown in

_figure

5 as a continuous line. Within the limitations of this model

_{(ZLight/ZHeavy}

_0.6)

_agreement

between data and

_theory

is

_{quite good,}

for all

targets

in the

_region

24

_Zt

62. It should be noted

_that,

based on

_lighter

collision

_systems,

a modified function _{for the scaled cross-sections had been}

_proposed

_[31].

_{Thèse results}

are

(11)

The K x-ray cross-sections

_(projectile

and

_target)

_dependence

on the

_projectile

energy can

be fitted to an

_exponential

of the form :

as

_already

shown

_[3].

The

_dependence

of the

_exponent

a on

_Zt

is shown in table 1 for both

projectile

and

_target

_{K x-rays. With}a few

_exceptions,

« is a

_{slowly varying}

function of the

target

atomic

number,

going through

a minimum value for

_symmetric

collisions. Its value increases for more

asymmetric

_systems,

in close

_agreement

with

_{previously reported}

results

[3].

This

_dependence

of the cross-sections on

_projectile

_energywas used to

_interpolate

our

reported

K x-ray cross-sections

_(see

_Fig.

₃₎

at _{the average}

_projectile

_{energy inside the}

_target.

This

resulted in small corrections

_(:

10

_%)

to _{the measured K x-ray cross-sections.}

5. Conclusion.

Target

and

_projectile

K ionization cross-sections were determined in

_100,

160 and 200 MeV

collisions of

_4,Nb

with various

targets

(Zt

= 6 -

68 ).

In the

region

of 24

Zt

62,

the ratio of

_projectile

to

_target

_{cross-sections agree}

_quite

well with the

_predictions

of the molecular model and the

_{K-vacancy sharing}

model

_[12].

Predictions of the direct excitation model

(ECPSSR theory)

valid for

_asymmetric

collisions,

agree within a factor of two for the

_lightest

targets

used

_(C

and

_Al),

but

_{disagree by}

a factor of four or more with the measured

cross-sections for Ti and the heaviest

_target

Sm. A

_slightly

better

_agreement

is obtained if one uses a

semi-empirical

model of direct excitation

_[15].

The sum of both

_target

and

_projectile

K vacancy cross-sections was found to be in fair

agreement

with the modified

_binary

encounter

_{approximation}

_[13].

However,

some

semi-empirical

corrections to this

_{theory proposed,}

based on

_lighter

collision

_systems

[31],

were

found to be in serious

_disagreement

with our data.

The ratio of the K vacancy cross-sections for the

heavy

and

_light

collision

_partners

( (T HI (T L)

was found to be in excellent

_agreement

_{with the results of the vacancy}

_sharing

formula

_[12].

However,

increasing disagreement

was found between the measured and theoretical values of the

_sharing

ratio as the

_projectile

_energywas increased. This

_signals

the breakdown of the molecular model at the

_{higher projectile energies}

utilised.

In

_conclusion,

we have

_compared

the results of various

_existing

models for K _x-ray

production

in

_heavy

ion collisions. For the

_{fairly heavy}

_systems

studied here

_{semi-empirical}

or

semi-classical

_{approaches yielded}

the best

_{agreement. However,}

even these theories could not

predict

the cross-sections for all collision

_systems

studied and further corrections were

_usually

required.

More data and a more

_complete

_theory

_{of K vacancy}

_production

in ion-atom collisions is

_required

to

_clarify

the situation.

Acknowledgments.

We would like to thank

_prof.

J. S.

_Greenberg

and Dr. J. J. O’Brien for their contributions to

(12)

References

[1]

PAUL H. and MUHR J.,

1669.

[15]

ANHOLT R. and MEYERHOF W. E.,

Phys.

Rev. A 16

(1977)

190 ;

_{(Academic Press)}

1968.