Electron capture from the krypton M-shell by MeV protons

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Electron capture from the krypton M-shell by MeV protons

S. Andriamonje, J.F. Chemin, J. Roturier, B. Saboya, J.N. Scheurer, Dž.

Belkić, R. Gayet, A. Salin, H. Laurent, J.P. Schapira

To cite this version:

S. Andriamonje, J.F. Chemin, J. Roturier, B. Saboya, J.N. Scheurer, et al.. Electron cap- ture from the krypton M-shell by MeV protons. Journal de Physique, 1985, 46 (3), pp.349-353.

�10.1051/jphys:01985004603034900�. �jpa-00209974�

Electron capture ^{from the} krypton ^M-shell by ^MeV protons

S. Andriamonje (*), ^{J. F. Chemin} (*), J. Roturier (*), ^B. Saboya (*), ^{J. N. Scheurer} (*),

D017E. Belki0107 (**), ^R. Gayet (***), ^{A. Salin} (***), H. Laurent (~) ^{and J. P.} Schapira (~) (*) Institut National de Physique Nucléaire ^{et de} Physique ^des Particules,

Centre d’Etudes Nucléaires de Bordeaux-Gradignan, ^Le Haut-Vigneau, ³³¹⁷⁰ Gradignan, ^France (**) Institute of Physics, ^{P.O. Box 57, 11001} Belgrade, Yugoslavia

(***) Laboratoire des Collisions Atomiques (ER ^{260 du} CNRS), 40, ^rue Lamartine, ³³⁴⁰⁰ Talence, France

(t) Institut National de Physique ^{Nucléaire et de} Physique ^des Particules, Institut de Physique Nucléaire, 91406 Orsay, ^France

(Reçu ^le 12 juin 1984, accepté le 1 G novembre 1984 )

Résumé.

La capture électronique ^{dans un} jet ^{gazeux de} krypton par des protons de 2 à 3 MeV est étudiée expéri-

mentalement et théoriquement. ^La comparaison des données expérimentales ^avec la théorie CDW (« ^Continuum

Distorted Waves » ou

Ondes Continues Déformées ») révèle que la capture ^{a lieu} préférentiellement depuis ^la

sous-couche 3d du krypton. ^Une analyse ^est faite du rôle joué par le ^moment orbital électronique initial dans le processus de capture électronique.

Abstract.

An experimental ^and theoretical study of electron capture by protons ^{from a} krypton gas jet target in the energy range 2-3 MeV is performed. ^A comparison ^of experimental data with the Continuum Distorted Wave

theory reveals that electrons are captured predominantly from the 3d subshell of krypton. The role of the initial electronic angular ^momentum in electron capture is discussed.

Classification

Physics ^Abstracts

34.70

Introduction.

A number of measurements of total cross sections for electron capture ^from gaseous targets by protons ^has been carried out (for ^{a review, see Tawara and Russek} [1]). These data do not relate to any particular ^inner

shell of targets. ^{It was} only recently, that Macdonald

et al. [2] ^{have been able to} experimentally ^determine

cross sections for electron capture from the K-shell of _argon by protons. ^This measurement was sub-

sequently ^{extended to other} gas targets by ^Cocke

et al. [3], Rodbro et ^al. [4] ^{and for} capture ^{from the L} and M subshells by Pedersen and Larsen [5]. ^These experiments ^show that, ^{for a} given energy, ^one specific

shell contributes predominantly and, ^{for the} highest velocities, ^K-shell capture dominates. On the other

hand, ^{for lower} velocities, ^{the outermost} shells of the target determine the total electron capture ^cross sections. From the theoretical point ^{of view, cal-}

culations for the outer shells of heavy targets ^at high

velocities had been based on the Oppenheimer-

Brinkman-Kramers approximation [6] (hereafter ^refer-

red to as OBK), ^{with some} empirical ^{and rather} arbitrary modifications [7]. However, ^no prediction

based on the first-order of the perturbation theory

could conceivably be reliable for high energy electron capture [8]. Therefore, ⁱⁿ considering capture ^from multielectron targets, ^it appears natural to adopt ^a generalization ^{of the most} adequate second order

theory, i.e., the Continuum Distorted Wave (CDW)

method of Cheshire [9]. ^{Such a} generalization ^{has been} proposed ^and applied successfully by Belkic et al. [8]

to electron capture ^from Ar, ^Ne and alkali atoms.

In practice, however, calculations have thus far been limited to only ^{a few} low-lying initial and final bound states. Recently, ^{Belkic et al.} [10] extended the method of obtaining ^{the CDW electron} capture ^{cross section} for transitions between arbitrary subshells of an atom.

Subsequently, this extended CDW approximation

has been used by Andriamonje ^{et al.} [11] ^{in a detailed}

evaluation of the cross section for electron capture from the L-shell to L and M-shells in Siq+-Ar collision,

with the charge state q

^{13 and 14.}

In the present paper, ^we report ^the results of experi-

mental and theoretical studies of electron capture from the krypton ^M-shell by protons ^with energies

between 2 and 3.5 MeV. Calculations of total cross

sections for this _process were carried out by using

the extension of the CDW approximation, ^which

has recently become available from [10]. ^The plan

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004603034900

350

of the _{paper is} as follows. In the first section we

describe the experimental set-up ^{as well} as measure-

ment procedure. The second section summarizes theoretical results. Finally, ⁱⁿ the third section we

compare ^our experimental data with the theoretical results and study ^the contribution of the various subshells to electron capture.

1. Experimental arrangement.

A schematic diagram ^{of the} apparatus ^{for this} expe- riment is shown in figure ^{1. The} proton ^{beam with}

energy between 2 and 3.5 MeV was obtained from the 4 MeV Van de Graaff of the Centre d’Etudes Nucl6aires de Bordeaux. The beam was collimated

by ^two pairs of slits located 4 m and 2 m away from the target. ^This arrangement ^{was effective} enough ^{to both}

reduce the proton ^beam intensity (~ ¹ nA) ^and

remove particles ^scattered by ^{the first} diaphragm

from the beam. To avoid multiple collisions, ^a gas jet target ^was used Details on the _gas jet systems ^are

given by Saboya ^and Denagbe [12] ^for argon gas, and here we will only discuss that of the krypton gas target. ^The Kr gas ^was continuously ^flown through capillary tubes into the scattering chamber and pumped by ^{a nominal 8} 0001/s ^diffusion pump. The _pressures measured during ^the experiments ^were typically

5 x 10-3 torr in the interaction region ^{and 5 x 10-5}

torr in the rest of the chamber.

Fig. 1.

Experimental set-up ^{to measure the total} capture

cross section by protons.

The neutral hydrogen ^{atoms formed} by ^{the one}

electron transfer ^are detected by the surface barrier detector D3 ^{located 1 m away from the target} region

in the beam axis. The active ^area of D3 ^{is defined} by ^a

8 mm diameter circular slit. The residual proton beam,

after passing through ^the interaction region, ^is

deflected by ^an electrostatic analyser, and then subse-

quently collected in a Faraday cup.

For each measurement the mean number of Kr atoms in the interaction region ^{was determined} simultaneously by ^two methods : Rutherford mea- surement and L X-ray measurement

In the Rutherford measurement the particles ^elas- tically ^scattered by ^{the Kr atoms were detected in a}

50 mm’ surface barrier detector (D1) ^{mounted at a}

mean angle ^{of 45° with} respect ^to the beam direction.

By knowing ^{the solid} angle ^defined by ^the diode, ^the integral ^{of the counts in} the elastic peak ^is directly proportional ^{to the mean number of Kr atoms.}

Now, ^the krypton ^L X-rays have been detected in a Si(Li) ^detector (D2) placed ^{at a mean} angle ^{of 90°.}

The number of Kr atoms is still proportional ^{to the} integral ^{of the L} X-ray peak. ^{The Kr L} X-ray ^emission

cross section by protons is known from the work of winters et al. [13]. The detection efficiency ^{of the} Si(Li) ^{diode was measured} by conventional techniques using ^a calibrated ^source of 55Fe and then corrected for photon absorption ^{in the Be} window and gold

metallization using the results given by ^McMaster

et ale [14].

The mean number of Kr atoms in the interaction

region NKr, ^obtained by ^both methods, ^was typically

of the order of 1024 atoms/cm2.

The total cross section _{(J CT} is given by :

where NH+ is the number of the incident projectiles.

e(H) the detection efficiency of the neutral hydro-

gens by the detector D3, has been taken equal ^to unity. ^The differential cross section is strongly peaked

forward and the quasi totality of the neutral H atoms is emitted in an angular range from 00 to 0.10.

Since the angular aperture ^{of the} D3 detector is equal

to 0.2°, ^{we believe} that the assumption E(H)

^{1 is} justified.

NH is the number of neutral hydrogen ^atoms

detected in D3 after subtraction of the background

contribution which is due mainly ^to proton scattering

at small angles by the slits. Consequently, ^{for each}

measurement, ^we made the experiment ^{in the same}

conditions but without _gas in the chamber in order to have a quantitative evaluation of the background.

The ratio of the intensities of neutral atoms detected with and without _gas ^was of the order of 10.

2. Theoretical methods.

Only «second-order methods » (i.e. going beyond

the first-order of perturbation theory), ^are adequate

at high energies. These have usually dealt with simple systems, i.e., ^{one electron} systems ^or systems ^{close to}

one electron systems (e.g. ^K-shell capture). ^The only exception is the CDW approximation ^{which has been} generalized ^to capture ^from complex systems by

Belkic et al. [8]. The collision problem is reduced to a

three-body problem through ^the description ^{of the}

interaction between the active electron in the final state and the target ^core (supposed frozen in its initial

state) by ^an effective Coulomb potential (expression

12.5 of Ref. [8]). ^It is therefore of much interest to test

this hypothesis through comparison ^with experiment

The reaction considered here is :

Details of the method of calculation have been

explained ^{elsewhere [10] and will not be} repeated ^here.

We use the wave function of Clementi and Roetti [15J

to describe the electronic states of krypton.

Let us call a(3 1; mi --> nf If mf) ^the capture ^cross section onto the orbital _nf, lf, mf of the hydrogen ^atom

from _{every 3} li Mi orbital of the M-shell of krypton.

To calculate the total capture ^{cross section} acm ^{from the}

M-shell of krypton, ^{we have to} sum-up Q(3 li mi -.

nf lf mf) ^over all initial orbitals 3 li ^{n; and over all final}

orbitals nf, If, mf. We suppose that the final ^state distribution varies as nf-3 for nf > No [8]. ^{Hence we}

have :

where

3. Comparison ^and discussion of experimental ^and

theoretical results.

In table I, cc ^is given ^for No

^{3 and} No

⁴ together

with unr for n, ^4. The results are nearly independent

of No ^{which shows that the} nf 3 ^{rule is accurate} enough

for the determination of ac

Now it is worth looking ^at contributions to QM coming from various subshells of the M-shell of

krypton. ^{From table I, it is} immediately ^{seen that}

the major contribution to cc ^{is due to the} capture

onto the 1 s state, ^a point which will be discussed later

on. Hence our study is restricted to a(3s - Is), a(3p -+ Is) ^and a(3d --+Is) ^{where :}

Comparisons made in table II and figure ^{2 show}

that the capture process is largely ^dominated by J(3d - ls) ^{at the} velocities under consideration while

the smaller contributions of a(3s-+Is) ^and a(3p-+Is)

are comparable. ^This point ^can be elucidated by ^the following considerations. At _very high velocities, ^the

CDW theory (and all second order theories) ^{show that}

the capture process is dominated by ^{the Thomas} peak

characteristic of a two step process (see section 13

Table I.

Total cross section (Jnr ⁱⁿ cm2 for ^{the capture onto} the level nf of hydrogen (see ^text, Eqs. 4-5)for

various proton impact energies. ^{In columns 6 and} 7, ^{the total cross section} 6cM ^{summed over} all,f inal ^{states is} given.

The summation assumes the validity of ^the nf-3 ^rule beyond either nf

3 in column 6 or nf

^{4 in} column 7 : the

good agreement between both results supports ^our assumption. ^The superscript ^{in columns 2-7} indicates the _power

of ^ten by which the number is to be multiplied.

Table II.

Total cross sections in cm2 for capture ^onto the Is shell of hydrogen from ^{various subshells} of ^the

M-shell of krypton for ^{various energies. The} contributions from the Zeeman levels of every ^{subshell are also indicated.}

The dominance of ^{the m}

^{0 states is visible in each case. The} superscript ⁱⁿ columns 4-11 indicates the _power of

ten by which the number is to be multiplied

352

Fig. ^2.

Experimental ^and theoretical as a total capture

cross section for the collision H+ + Kr in function of the proton energy. A) CDW calculation without the 3d contribution in the Kr M-shell capture by protons; B) ^CDW

calculation including ^{the 3d} contribution in the Kr M-shell capture by protons.

in Ref. [8]). ^The peak is located at « quite large » scattering angles. ^{At moderate} velocities, charge exchange is dominated by ^small angle scattering.

Then it is determined by the initial and final distribu- tions of electronic velocities around both centres.

Such a feature is present in the CDW theory, ^{but it}

cannot be simply exhibited. However, ^it may be

pictured by ^{means of the OBK} theory although ^{it is}

worth noting ^{that it} provides ^us just ^{with a} qualitative explanation of various contributions to aCM. ^{It cannot}

pretend ^to give quantitative ^results because, ⁱⁿ

contrast with the CDW method, ^{it does not allow for}

Coulomb distortions in both channels. Thus the OBK T-matrix element _may be written as :

where

In (7) ^and (8), 8c and n f ^are respectively the electronic energy and the principal quantum number of the final state; q is the momentum transfer and v is the proton velocity ^{in the} laboratory ^frame. Pi and Pf ^{are res-}

pectively the initial and final momentum space ^wave functions that can be obtained by the Fourier trans- forms of Clementi and Roetti’s wave functions [15]

of each of the n

3 subshells of krypton. ^{The eikonal} expression ^of q is given by ^the expression (6.31b) ⁱⁿ

reference [8], ^{with an} opposite sign, ^ie.

were 11 ^{is the} transverse momentum transfer (11. v

0)

and

where 8; ^is the initial orbital _energy. Then the total OBK cross section for capture from the 3f subshell of krypton may be written as (see expression (6.38)

in Ref. [8])

where N31 is the number of electrons in the 3é subshell.

From (7) ^and (9) ^{one has :}

Using the Fourier transforms of the hydrogen ^wave

function [16], ^{it can be} verified that the electron transfer to the Is state of hydrogen ^{dominates the total}

capture ^{cross sections at} present velocities in agree-

ment which the results given ^{in table I. From Clementi}

and Roetti’s tables [15], ^it may be readily verified that present ^values of A: ^{may be neglected with respect to}

p

v2 Y g p

1/2. Also values of r comparable ^with v/2 do contribute to the total capture ^{cross section.} Hence, the behaviour of the matrix elements 1 T1.!ls(r) 12, ^{in the region}

where they contribute significantly ^to Ut.!lS’ ^are

mainly determined by the functions N3d 1 CP3f(q) 12.

Since 1

/£# « § , q; iS in ^{practice :}

Thus, q; runs over a practically ^infinite range, the minimum value of which is v/2 ^with v/2 £r ^{5.0. The}

functions N31’ 1-’(f)3f(q) 12 ^{are displayed on figure 3.}

The striking feature of this figure ^{is the} prominence ^of

the 3d shell over a large interval because v/2 ^{is close}

to the first zero of lP3s ^{while the zero of} 4>3P ^{appears at}

qi

9.0. It explains why QM ^is mainly ^{due to the} capture from the 3d subshell.

From figure ^{3 one} could also predict ^that capture from the M-shell at v/2

9.0, ^{i.e. at} proton impact energies ^{close to 8} MeV, should be still dominated by

the 3d subshell. Because the total cross section is obtained by integration ^{over an interval} [v/2, + oo[,

the 3s subshell contribution should be about five times less than the 3d one. Now it appears that the 3p

contribution should be greater ^{than the 3s one.}

However, ^{at such} velocities, contributions from the

L-shell become significant.

Fig. ^3.

N3,, I Ø3C(Q) 12 ^{as a} function of the electronic momentum q (see text). Also indicated by vertical lines are

the exact minimum values of the momentum transfer for various impact energies.

Finally ^{let us} notice that it is _easy to show in a way similar to that mentioned above (i.e. ^electronic velocity distributions), that contributions from the K, L and N-shells to the total capture ^are negligible ^at

present energies. ^More generally, ^the contribution of a shell is dominant roughly ^{when the} impact velocity

is slightly greater ^{than the mean} quadratic ^electronic velocity of the shell. It would be the case for E > 3.5 MeV for the L-shell and E > 26 MeV for the K-shell. This rough ^rule also shows that the M-shell dominates over the N-shell when E > 0.6 MeV.

4. Conclusion.

The present comparison between CDW theoretical results and experimental data shows that the former is an excellent tool to predict capture ^{cross sections}

quantitatively. Furthermore, ^a simple ^{use of the OBK} approximation ^{allows us to conclude} that, ^as long

as the velocity ^{is small} enough ^to prevent ^{the Thomas} mechanism from showing up, the capture process is

mainly controlled by the electronic velocity ^distribu-

tion in both initial and final orbitals.

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