RELATIVE INITIAL POPULATIONS OF HYDROGEN-LIKE IONS AFTER FOIL EXCITATION

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RELATIVE INITIAL POPULATIONS OF

HYDROGEN-LIKE IONS AFTER FOIL EXCITATION

W. Nitsche, E. Träbert, P. Heckmann

To cite this version:

W. Nitsche, E. Träbert, P. Heckmann. RELATIVE INITIAL POPULATIONS OF HYDROGEN-

LIKE IONS AFTER FOIL EXCITATION. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-266-

C1-268. �10.1051/jphyscol:1979157�. �jpa-00218437�

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Colloque C1, suppl4ment au n " 2, Tome 40, fgvrier 1979, page C1-266

RELATIVE INITIAL POPULATIONS OF HYDROGEN-LIKE IONS AFTER FOIL EXCITATION W. Nitsche, E. Trabert, P.H. Heckmann

Experimentalphysik 111, Ruhr-Universitat, 11-4630 Bochum 'I

~esurne: Les ions de He, B, C, N et 0 sont excitgs par passage d travers des feuilles minces de carbone. LV&nergie du faisceau est choisie de facon ii produire des 6tats hydrogeniques (entre 1 et 18 MeV). Les courbes de durge de vie sont mesurges en prenant en consid6ration la fonction de fengtre spatiale du monochro- mateur ii incidence rasante (2,2 m). La procgdure d'gvaluation permet d'extraire

les populations initiales relatives N $ ~ des &tats n = 3 et 4 pour plusieurs 1.

Les chiffres font apparaitre es tendances suivantes: N ; ~ / N ~ ~ a z ~ * ~ ~ , N $ ~ / N ~ ~ a 2 0 ~ 7 N ~ ~ / N P = ~ 0 . ~ . Pour les ions legers les rapports sont presque ggaux. Une tenaance vers la distribution statistique des populations initiales est observee quand Z aupente. Les intensites relatives des transitions de Lyman de ~ e + sont en accord avec la loi en n-3 pour les &tats np (2rnr5).

Abstract: Ion beams of He, B, C, N and 0 are excited by passing through thin carbon foils. The beam energies are chosen to produce hydrogen-like states (1 to

18 MeV, resp.). Lifetime curves are measured taking into consideration the spatial window function of the 2.2 m grazing-incidence morrachromator used. The evaluation procedure allows to extract relative initial populations ~ $ 1 of states n = 3 and 4 for various values of 1. The data show the following trends: N? /N = 20-5G1 N $ ~ / N ~ ~ a z O - ~ , N P ~ / N $ ~ = 20s8. For the light ions the ratios N$/itJ9 are of the order of one but show a trend towards the statistical distribution wlth increasing Z. The relative intensities of the Lyman transitions of ~ e + (up to n = 5) are in agreement with a n-3 scaling law for the np states.

1. INTRODUCTION

Foil excitation has become a valuable tool for the study of atomic levels and lifetimes. There is, however, at present no adequate theory for the excitation mecha- nism [ I], even in the case of ionic species with very few electrons.

Experimental studies of beam-foil populations are discussed by Veje [I] in terms of his independent-electron model, and by other authors (e.g. [2]). There axe argu- ments leading to the conclusion that cap- ture in the last monolayer of the foil is responsible for most of the observed population. Hydrogen-like ions constitute the simplest case. For a proton it is very improbable to bind an electron while traver- sing a carbon foil. However, for a nucleus with higher X , there should be a certain probability (increasing with 2 ) that an electron is kept in a bound state even within the foil. Thus one should expect a Z dependence of the relative initial populations of the excited states. The present work was undertaken to study this dependence in H-like ions, using projectiles of

helium, boron, carbon, nitrogen and oxygen.

2 . EXPERIMENT AND EVALUATION

An ion beam of He, B, C, N and 0, resp., supplied by the Bochum Tandem accelerator, is passed through a thin carbon foil

(about 10 ug/cm 2 ) . The beam energy (from 1 MeV for He to 18 MeV for 0) is chosen to produce hydrogen-like states. Typical beam currents are of the order of 1-2 uA. The foil is moved relative to the optical axis of a 2.2 m grazing-incidence monochromator

(grant of the Deutsche Forschungsgemein- schaft) by a step motor via a precision screw, A 600 limn gold coated blazed gra- ting serves as the dispersing element, single photons are detected behind the movable exit slit with a channeltron.

The spectra are normalized either to the beam charge or to the integral light in- tensity emitted immediately behind the foiL The results obtained are found to be independent of the kind of normalization.

The measured decay curves are convolu- tions of the detection window function (ty-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979157

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pica1 width 5 60 ps) and the decay exponen- t i a l ~ . For details of the evaluation procedure, see [3] (note, however, that the window function meanwhile has been improved).

A typical decay curve is shown in fig. I .

Fig. 1 Decay curve showing fit and window function

Due to the degeneracy of hydrogenic levels, a curve corresponding to the transition

(n=3) + (n=2) is composed of contributions from transitions 2p-3d, 2p-3s, and 2s-3p, plus cascades from higher levels. The main cascade contribution in this case arises from 3d-4f.

Adjustable parameters in the fit procedure are the lifetimes T~~ and initial populations NE1 of the hydrogenic levels (relative to the detection efficiency of the set-up of about

,

and the detection window data [31. Up to 3 exponentials plus

constant background are used in the fit. As the T~~ are known from theory, they are kept constant in the fit which thus yields the relative initial population numbers.

The detection window data as given by the fit can be checked from geometry and from internal consistency of the various measurements.

In the case of He

+ ,

the 3+2 transition (X=164 nm) is beyond the range of the monochromator. Here the Lyman-a-like transition (Is-2p) has been measured. AS the 2p level is repopulated from 3s and 3d, this yields information about the initial population ratio N:~/N:~. The analogous transition has been studied in the boron case confirming the results of the 3+2 transition. Other transitions investigated are 4+2 for B4+-07+

and 3+l for He

+ .

Within our experimental accuracy (which is about 10 % for N ~ ~ / N ~ , ) measurements

using different entrance slit-widths (50- 200 um) yielded the same relative initial populations.

For B4+ to 07+, the 3p lifetimes are short compared to the window width. Thus, the 3p contribution acts like a 6-function reproducing essentially the window function and is neglected. The error caused to N ~ ~ / N ; ~ by this neglect is estimated to be

less than 3 % . In all of the Ha-like transitions, for times ~ > > T ~an additional ~ , T ~ ~ cascade tail shows up which cannot be fit- ted with a single exponential. This tail appears as a straight lPne in a log/log display (fig. 2)

.

4.2 4.6 5.0 5.4 5.8 6.2

In ( t I p s )

Fig. 2 Log/log display of decreasing part of a decay curve

We have included an inverse power law

=(t-to) -a into the fit function. This im- proves the fit convergence but the N:~/N;, results are not altered significantly.

From the log/log plots, the coefficients a of the inverse%power law are obtained as follows :

Ion IOB

I2c

I4N 6~

a 1 -56f0.1 1.6'0.1 1.57t0.1 1.59'0.1 A value of a near 1.5 has been found ear- lier in other transitions [4] and has been explained theoretically (e.g. by cascades along the yrast line) [ 51

.

In the H6-like 4+2 transitions r is 4 P long enough so that an information about the relative initial population of the 4p level can be deduced. Here no nonexponen- tial cascading has been observed, as there is no yrast cascade.

In a spectral scan of the ~ e + Lyman series up to n=5, relative intensities of the pertinent lines have been obtained.

These lines are located in the wavelength

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Cl-268 JOURNAL DE PHYSIQUE interval 23.7 to 30.4 nm. If it is assumed

that the detection efficiency does not vary significantly in this interval, the line

-

³

intensities are in agreement with a n scaling law for the initial popilation numbers of the np states.

3. RESULTS AND DISCUSSION

From log/log plots like Fig. 3 one ob- taines the following Z dependences of initial population ratios:

Fig. 3 Z-dependence of N;~/N;,

For the light ions the ratios are near unity instead of showing a statistical distribution [=(21+1)

1.

For larger Z, a trend towards the statistical expectation is apparent.

The velocity of the boron projectiles has been varied from 9 to 15 mm/ns. No dependence of N:~/N:~ on the projectile velocity has been observed. This is in accor- dance with other experimental observations

(e.g., [6]) and the Veje model [I].

In the Veje model [I] it is assumed that excited Rydberg states are formed by electron pick-up from the back surface of the foil, and that the probability of this pro- cess is influenced by the form of the elec- tronic wave function in the vicinity of the projectile nucleus. To put this quantita- tively, one can assume that the pickup probability is proportional to

6rz

S l r 2 dr, where Rnl is the radial wave function of the hydrogenic system and rZ is some cutoff radius which itself may be Z dependent.

Nothing is known about the Z dependence of rZ. If one assumes r ⁼^3.

z-o.

75

z

(in atomic

units) it is possible to reproduce the measured Z dependence of the initial population ratios within the experimental error.

Hence, at the present status of theoretical understanding, our experimental results are not in contradiction to the pickup model of Veje, although they should not be conside- red a stringent test. Nevertheless, we feel that as Z increases, an increasing contribution to the initial population of a hydrogenic state comes from processes in the bulk of the foil material, as the mean radius of the electron cloud shrinks with increasing nuclear charge.

The authors wish to thank Prof. von Buttlar for his support, the Bochum accelerator crew of K. Brand, and H.H. Horn for his assistance during the beam-time.

The financial support by the Deutsche For- schungsgemeinschaft is gratefully acknow- ledged.

REFERENCES

[I] E. Veje, Phys. Rev.

e,

2077(1976) [2] J.D. Garcia, Nuclear Instrum. Meth.

110, 245(1973)

Y

[3] E. Trabert, H. Winter, P.H. Heckmann, H. v. Buttlar, Nucl. Instrum. lleth.

135, 353(1976)

-

[4] P. Richard, Phys. Letters

s,

^13(1973);

W.J. Braithwaite, D.L. Matthews, C.P.

Moore, Phys. Rev.

All,

465(1975) [5] R.M. Schectman, Phys. Rev. F_12, 1717

(1975); F. Hopkins, P. v. Brentano, J. Phys.

2,

775(1976)

[6] R. Tielert, H.H. B u k ~ w , P.H. Heckmann, R. Woodruff, H. v. Buttlar, Z. Physik 264, 129(1973)