J. Phys. B: At. Mol. Opt. Phys.32 (1999) 2343–2349. Printed in the UK PII: S0953-4075(99)96545-8

Angular distribution of L β x-rays from decay of L3 subshellvacancies in uranium and thorium following photoionization

J K Sharma and K L AllawadhiNuclear Science Laboratory, Department of Physics, Punjabi University, Patiala-147002, Punjab,India

Received 5 August 1998

Abstract. The anisotropy of Lβ x-rays from the decay of L3 subshell vacancies in uranium andthorium following photoionization is investigated by measuring the angular distribution of photoninduced L3 x-rays (Ll , Lα and Lβ ) in these elements. To enhance the chance of anisotropic emissionof these x-rays, the measurements are made using selective photoionization of the L3 subshell inthese elements. In contrast to the findings of earlier experiments in which Lβ was observed to beisotropic, the present experiment gives clear-cut evidence of the anisotropic emission of this groupand thus, strengthens the view of Fluggeet al (1972Phys. Rev. Lett.29 7) that the vacancies afterphotoionization of states withJ > 1

2 are aligned. The possible reasons explaining the observationof earlier workers that Lβ emission is isotropic are also discussed.

1. Introduction

The decay of the L3 subshell state following ion–atom collision has been well investigatedboth theoretically and experimentally. It is now well established that vacancies created byion–atom collision in states withJ > 1

2 are aligned and the x-ray emission following thedecay of these states is anisotropic and polarized. The existing theories in the case of decay ofvacancies following photoionization do not exactly fall in line with the predictions in the caseof ion–atom collisions. In the case of photoionization, while one theory by Cooper and Zare(1969) predicts that the vacancy states produced after photoionization of states withJ > 1

2are unaligned, the other theory by Fluggeet al (1972) contradicts the above view. The onlypreliminary experiments reported in this direction so far, are the measurements of the angulardistribution and polarization of different L x-ray groups (Ll , Lα, Lβ and Lγ ) in some highZelements by Kahlonet al (1990, 1991) from these laboratories and by Ertugrulet al (1995).The results of both these experiments support the later view that the vacancy states withJ > 1

2,produced after photoionization are aligned. This conclusion is based on the observation thatthe x-ray groups Ll and Lα, which originate from the L3 state withJ = 3

2 are found tobe anisotropic and polarized while the Lγ x-ray group which originates from the L1 and L2

subshells both withJ = 12, is found to be isotropic and unpolarized. A close look at both of

these experiments, which were performed with a gap of nearly five years, reveals that eventhough a part of the Lβ x-ray group originates from the L3 state withJ = 3

2, no anisotropywas observed in the emitted Lβ x-rays in these experiments.

The work reported in this paper was designed so as to observe anisotropy, if any, inthe emitted Lβ x-rays originating from transitions to the L3 subshell, which was found to beabsent in both of the earlier experiments. The investigations were made by measuring angular

0953-4075/99/102343+07$19.50 © 1999 IOP Publishing Ltd 2343

2344 J K Sharma and K L Allawadhi

Figure 1. Schematic diagram of the experimental set-up: R, radiation source Am241 (annular); P,primary target; S, secondary target; D, detector [Si(Li)].

distribution of L3 x-rays (Ll , Lα and Lβ) in Th and U emitted as a result of the vacanciescaused by photoionization. To enhance the chances for the anticipated observation in the caseof Lβ , the method used in the earlier experiment by Khalonet al (1990) was modified and themeasurements made using selective photoionization of the L3 subshell of these elements. Thedetails of the method of measurement, the experimental set-up and the results are discussed inthe following sections. The possible reasons why Lβ emission in the earlier experiments wasobserved to be isotropic, are also discussed.

2. Method, experimental set-up and measurements

The angular distribution of different L3 x-ray groups in Th and U have been investigated bymeasuring the differential x-ray group production cross section for Ll , Lα and Lβ groups of x-rays at emission angles of 60◦, 70◦, 80◦ and 90◦ by selective photoionization of the L3 subshellsin these elements. For selective photoionization of Th and U, Nb and Mo K conversion x-rayswere used. It can be seen that all the K x-ray lines (Strom and Isreal 1970) of Nb and Mo canonly photoionize the L3 and higher subshell electrons in Th and U respectively and the L2,L1 subshells and K shell of these elements are not ionized. The Nb and Mo K x-rays for thispurpose were obtained by irradiating the targets of these elements by 59.57 keVγ -rays froman Am241 source.

The experimental set-up used for these measurements is shown in figure 1. In thisarrangement, 59.57 keVγ -rays from a≈1 Ci Am241 annular source were collimated to fall onself-supporting primary targets of Nb and Mo in the form of circular discs of 4 cm diameterand the K conversion x-rays emitted from the primary targets were, in turn, collimated to fallon secondary targets of Th and U again in the form of circular discs of diameter 4 cm eachand thickness 0.0517 and 0.3399 gm cm−2, respectively. The annular Am241 source with abuilt-in filter to almost completely absorb all the Np L x-rays and 26 keVγ -rays was purchasedfrom Amersham International Incorporated, UK. The metallic targets of Mo, Th and U werepurchased from Reactor Experiments Inorporated, USA. Because of the non-availability of theNb target in the metallic foil form, the target was prepared from Nb powder using a methoddescribed earlier (Singhet al 1983). The L3 subshell fluorescent x-rays emitted from the Th

Angular distribution ofLβ x-rays 2345

Table 1. Experimental values of differential L x-ray production cross sections at angles 60◦, 70◦,80◦ and 90◦ in Th, at Nb K x-ray energy.

Cross sectionsAngle

Serial no (deg) dσLl /d� dσLα /d� dσLβ /d�

1 60 53± 4 908± 54 217± 192 70 44± 3 603± 36 166± 173 80 36± 3 533± 32 157± 164 90 35± 3 546± 33 154± 15

Table 2. Experimental values of differential L x-ray production cross sections at angles 60◦, 70◦,80◦ and 90◦ in U at Mo K x-ray energy.

Cross sectionsAngle

Serial no (deg) dσLl /d� dσLα /d� dσLβ /d�

1 60 50± 4 952± 57 298± 302 70 43± 3 715± 43 262± 263 80 36± 3 595± 36 217± 224 90 34± 3 571± 34 209± 21

and U targets as a result of photoionization of their L3 subshell were counted and analysedwith a Si(Li) detector of active diameter 10 mm, sensitive depth 4.66 mm with a Be windowof thickness 0.0254 mm and coupled to the computer based EG&G ORTEC MultichannelAnalyser System. The resolution of the Si(Li) x-ray spectrometer was 170 eV at 5.9 keV.

For these measurements, the angle of incidence (for Nb or Mo K x-rays) and angle ofemergence (for Th or U L x-rays) with the normal to the surface of the secondary targets(Th or U) were kept equal in all the measurements. The measurements were made at fourdifferent angles 60◦, 70◦, 80◦ and 90◦ as mentioned above. The angular spread in the presentgeometrical set-up was estimated to be around±2.5◦. In the present experiment the limit onthe lower angle of 60◦ was imposed by the dimensions of the detector and source collimatorsand their distances from the secondary target. The correction for the unwanted contribution ofL x-rays produced by scattered 59.57 keVγ -rays and also due to the natural radioactivity ofTh and U was applied to L x-rays counted in the detector by using an equivalent aluminiumtarget in place of the primary target, as discussed in detail in an earlier paper (Mannet al1990). Typical spectra of radiation emitted from Th target when irradiated with radiation fromNb and equivalent Al targets respectively using the above experimental set-up are shown infigure 2(a) as spectra A and B. The difference spectrum C of the two spectra A and B (i.e.C = A − B) is also shown in figure 2(b). In this spectrum Ll , Lα and Lβ x-ray groups of Thare seen to be well resolved from each other. The differential Ll , Lα and Lβ x-ray productioncross sections(dσθ (Li )/d�) at different emission angles(θ) were determined by comparingintensity of the different L x-ray groups of the secondary target element(Iθ (Li )) with that ofthe incident primary target element K x-rays(I (x)) using the following relation.

dσθ (Li )/d� = Iθ (Li )

I (x) · t · ρ · βθ(x, Li ) · εθ (Li ) (i = l, α, β).

Wheret is the target thickness,ρ is the atomic density of the target element,βθ(x, Li ) is thecorrection factor which takes into account the self absorption of incident primary x-rays andthe emitted Li x-rays in the material of the secondary target andεθ (Li ) is the detector efficiency

2346 J K Sharma and K L Allawadhi

Figure 2. (a) Typical spectra of the radiation from the Th target recorded with a Si(Li) spectrometer.A, Nb primary target and Th secondary target; B, equivalent Al primary target and Th secondarytarget. (b) Net Th L x-ray spectrum (C= A − B).

Angular distribution ofLβ x-rays 2347

of the Si(Li) detector. The other details of the experiment were similar to the ones reported inearlier papers (Kaholanet al 1990, 1991).

3. Results and discussion

The measured values of Ll , Lα and Lβ differential x-ray production cross sections in Th andU at 16.896 and 17.781 keV at emission angles 60◦, 70◦, 80◦ and 90◦ are listed in tables 1and 2, respectively. The overall uncertainties in the measured values of Lα and Lβ x-rayproduction cross sections were estimated to be 6%, while for Ll , x-ray production cross sectionsthe estimated uncertainties were 8%. The higher uncertainties in the values of the Ll crosssections were due to the poor counting statistics in case of these x-rays. Since no otherexperimental or theoretical values of the differential Ll , Lα and Lβ x-ray production crosssections at present energies and elements are available in the literature, the present resultscould neither be compared with theory nor with any experiment. From the results of themeasurements it is evident that, in the present case, all the three Ll , Lα and Lβ differential x-rayproduction cross sections depend on the emission angle and thus, the emission is anisotropic.It may be mentioned that the only measurements of the differential Ll , Lα, Lβ and Lγ x-rayproduction cross sections available in the literature are by Kahlonet al (1990, 1991) andErtugrulet al (1995) in some highZ elements at 59.57 keVγ -rays. As the energy of incidentphotons in both of these experiments was above the L1 subshell energy, all three L subshellswere photoionized and thus the emission of different L x-ray groups was from all the threeL subshells. In these experiments, while the Ll and Lα x-ray emission was observed to beanisotropic, the Lβ emission was found to be isotropic. The Lβ x-ray production cross sectionsmeasured by Kahlonet al and Ertugrulet al at 59.57 keV in element Pb are shown in figure 3along with the present results for both the elements Th and U (the element Pb was chosen as theexperimental values for this element are available in the case of both the earlier experiments).From figure 3, it is evident that while no anisotropy in the emitted Lβ x-rays was observed inthe earlier experiments, the present experiment gives clear-cut evidence of anisotropy in theLβ x-ray emission.

The possible reason for the observation of the isotropic emission of Lβ x-rays by the earlierworkers (Kaholanet al 1990, 1991) and (Ertugrulet al 1995) are as follows:

(1) In the earlier experiments the Lβ emission was from all the three L subshells i.e. L1, L2

and L3. The relative intensities (Strom and Isreal 1970) of different x-ray lines in the Lβ

group of Th and U are given in table 3. It is clear from the table that the relative intensitiesof x-ray lines resulting from the transitions to the L3 subshell and contributing to Lβ isnearly 12% only that of the transition to all the three subshells. Thus, the major part of theLβ group in the earlier experiments, originated from transition to L1 and L2 subshells withJ = 1

2. In the present experiment as the L3 subshell in elements Th and U are selectivelyionized, the entire Lβ group originates from transitions to the L3 subshell withJ = 3

2.(2) In the earlier experiments the vacancies in the L3 subshell were not only caused by the direct

photoionization of the L3 subshell but also by the Coster–Kronig transfer of vacancies fromthe L1 and L2 subshells to the L3 subshell. The ratio of the L3 subshell photoionizationvacancies to the total (photoionization + CK transfer) vacancies as estimated for elementsPb and U at 59.57 keV, as derived from the relation:

NL3

NL3 + f12NL2 + (f12f13 + f23)NL1

is found to be 0.7662 and 0.7613, respectively. (In this relationNLi are fractional Lisubshell vacancies andfij are CK transition probabilities.) However, in this experiment,

2348 J K Sharma and K L Allawadhi

Figure 3. The differential x-ray production cross sections at different angles for Pb at 59.57 keVreported by Kaholanet al (1990) and Ertugrulet al (1995) are shown along with the present resultsfor Th and U at Nb and Mo K x-ray energies. (4) our values (for U at 17.781 keV); (�) ourvalues (for Th at 16.896 keV); (×) Kaholanet al (for Pb at 59.57 keV); (♦) Ertugrulet al (for Pbat 59.57 keV).

Table 3. Lβ x-ray intensities of Th and U.

Lβ x-ray intensities Lβ x-ray intensitiesSerial no Transitions of Th of U

1 L1–M2 = β4 34.6 35.52 L1–M3 = β3 31.6 30.53 L1–M4 = β10 1.54 1.664 L1–M5 = β9/1 2.29 2.245 L1–N4 = β9/3 0.257 0.2826 L2–M3 = β17/1 0.189 0.1957 L2–M4 = β1 135 1368 L2–N3 = β17/4 0.0551 0.05929 L3–N1 = β6 1.71 1.7810 L3–N4 = β15 0.0551 0.059211 L3–N = β2 20.7 20.912 L3–O1 = β7 0.421 0.48813 L3–O4,5 = β5 4.16 4.41

as the L1 and L2 subshells are not ionized, there is no transfer of unaligned vacancies inthe L1 and L2 subshells to the L3 subshell and all the vacancies in the L3 subshell arephotoionization vacancies.

Angular distribution ofLβ x-rays 2349

Thus, the extent of anisotropy in the emitted Lβ x-rays is expected to be small and thereforecould not be observed, perhaps due to the quantum of uncertainties in these measurements,which are reported to be 6%. The observation of anisotropic emission of Lβ x-rays resultingfrom transitions to the L3 subshell withJ = 3

2 further confirm the view of Flugeeet al (1972)that states withJ > 1

2 are aligned.

Acknowledgment

Financial assistance from the Council of Scientific and Industrial research, India, under projectNo 03 (0797)/96 EMR-II is gratefully acknowledged.

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2733——1991Phys. Rev.A 431455Mann K S, Singh N, Mittal R, Allawadhi K L and Sood B S 1990J. Phys. B: At. Mol. Opt. Phys.233521Singh N, Mittal R, Allawadhi K L and Sood B S 1983PhysicaC 123115Strom E and Isreal I 1970Nucl. Data TablesA 7 565