Ernst, A.

Froehner, F.H.

Kompe, D.

Froehner, F. H.

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Februar 1970Institut für Angewandte KernphysikNeutron Capture Cross Sertions of Cprillrn ,mn Tl1,111ill1Tlin the keV RegionD. Kampe, A. Ernst, F. H. FrähnerKFK 1165GUUlSCHAn HiR K"UI~OR5C~HJNGM. ß.~.KARLSRUHEI 2.A.l I Nuclear Physics A141 (1970) 602-608; © Nortl/-Holland Pubfishing Co., AmsterdamNot to be reproduced by photoprint or microfilm without written permission from the publisherNEUTRON CAPTURE CROSS SECTIONS OF CERIUM AND THALLIUMIN THE keV REGIOND. KOMPE,t A. ERNST and F. H. FRÖHNERInstitut jiir Angewandte Kernphysik, Kel'lljorschungszentl'llm Karlsl'llhe ttReceived 14 November 1969Abstract: The neutron capture cross sections ofnatura1 cerium and thallium were measured between10 and 200 keV. The time-of-flight method was used, with a pu1sed Van de Graaff acce1eratorproviding the neutron source and with a 1arge liquid scintillator detector. The measured crosssections are extreme1y low owing to the near-magic nuc1eon numbers of Ce and Tl. They wereaveraged over Maxwellian velocity distributions with kT values between 10 and 100 keV so asto be useful for ca1culations of nucleosynthesis in stars.E NUCLEAR REACTIONS Ce, Tl(n, y), E = 10-200 keV; measured a(E); deducedaverages over Maxwellian velocity distributions. Time-of-flight method.1. IntroductionIn the last decade fast-neutron capture cross seetions of many elements were mea-sured, often to obtain data for calculations for fast breeder reactors, particularly onelements with large capture cross sections. However, capture data on elements withmagie or near-magie nucleon numbers are still scarce. These elements have very smallcapture cross sections 1) which are not easy to measure with present-day neutronsourees. Just because of their "magie" properties, however, they are of special in-terest in nuclear physics 2) and perhaps even more so in astrophysics.According to modern concepts of element formation 3) a large fraction of theexisting elements heavier than iron was formed by relatively slow successive neutroncapture in the interior of stars. The temperatures for this "s-process" 3) are thoughtto correspond to roughly 20 to 50 keV. Attempts are being made to reproduce theobserved solar abundances in detailed calculations using the s-process concept. Inputdata are the seed abundances and capture cross seetions averaged over Maxwellianspeed distributions for the assumed stellar temperatures 4). Unknown cross sectionsare usually estimated by means of the rule that the product of observed abundanceand averaged capture cross seetion varies only slightly from element to element [fordetails see ref. 4)]. At present, however, it is still difficult to say how good such esti-mates are, especially since solar abundances are known only with large uncertainties.t Present address: Philips Electrologica, 5904 Eiserfeld, West Germany.tt Work performed within the association in the field of fast reactors between the European AtomicEnergy Community and Gesellschaft für Kernforschung m.b.H., Karlsruhe.602NEUTRON CAPTURE CROSS SECTIONS 603For nueleosynthesis calculations two key elements are Ce (two main isotopes with82 and 82+2 neutrons) and Tl (two main isotopes with 82-1 protons and 126-2 resp.126-4 neutrons) [ref. 5)]. Both elements have insufficiently known cross sections.Moreover, cerium is one of the more abundant fission products and therefore its fast-neutron capture cross section has also a certain technological importance. In thepresent paper we present neutron capture cross sections for these elements between10 and 200 keV neutron energy. In addition we list Maxwellian averages for kTvaluesbetween 10 and 100 keV calculated with the measured data.2. Experimental procedureThe apparatus and the experimental procedure employed have been reported ear-lier 6), therefore we shall give only a short description here. The measurements wereperformed by the time-of-flight method at a pulsed 3 MV Van de Graaff accelerator,with 10 ns pulses and a 1.5 m flight path. Neutron capture events were detected in an800 I liquid scintillator surrounding the sampie in 4% geometry. The capture crosssections were measured relative to gold.The sampies were metallic discs of 8.6 cm diameter containing 163 g of naturalcerium (1.207 . 10- 2 nuelei/b) with a purity of 99.9 %and 128 g of natural thallium(0.650' 10- 2 nuelei/b) with a purity of 99.999 %. Bach of these sampies was inter-changed at short time intervals with a gold sampie which provided the standard andwith a graphite scatterer which served to determine the time-dependent backgroundcaused by neutrons scattered by the sampie and subsequently captured in the struc-tural materials ofthe detector. The thickness ofthe graphite scatterer in terms ofmeanfree paths was chosen as elose as possible to that of the sampie under study. With thevery low capture cross sections investigated here this background determination wascrucial.3. Results3.1. MEASURED DATA AND ERROR ESTIMATESThe results of our capture measurements are shown in figs. 1 and 2. Above 20 keVthe spacing of successive data points corresponds roughly to the experimental reso-lution. Below 20 keV channels were grouped in the time-of-flight spectra in order toimprove the statistical accuracy. Although we did not attempt to resolve resonancesit can be seen that our resolution was good enough to reveal pronounced resonancestructure for both elements, especially at low energies. The contributions to the ex-perimental uncertainties are estimated as follows.(i) Dur reference cross section is the (n, 1') cross section of gold as measured byKompe against lOBen, ay) and 6Li(n, a) [cf. refs. 6,7)], normalized to the absolutevalue 596 mb at 30 keV recommended by Poenitz 8). Linac measurements recentlypublished by Fricke and Lopez 9) and areanalysis of shell transmission data by Sem-ler 10) indicate that our reference cross section may be too low. The uncertaintiesCl\o"""o~;g~~100 keV 200.50-E20\0° 0010. 1020501005001000mb0yt 200100 keV 20050~E2052110102050100mb0yfFig. 1. Ceriwn capture cross-section data. The open cireIes are theresuIt of this work, the triangles are the data of Gibbons et aT. 16). Theline connecting the experimental points is only a guide for the eye, thesmooth curve is a X2fit to our data with So = 0.9 . 10-4 (fixed parame-ter), Si = (0.79±2.1) . 10-4, S2 = (0.16±0.25) . 10-4, Sy = (0.17±0.07) . 10-4 (adjusted parameters). All data correspond to the samegold standard cross section.Fig. 2. Thalliwn capture cross sections. The open cireIes are the resnltofthis work, the triangles are the data ofGibbons etaT. 16), the solid cir-eIes are data reported by Konks and Shapiro 17) for natural thalliwn.The solid squares are data calculated by Konks and Shapiro 17) from cap-ture datameasured with thin enriched sampies of203TI and 2osTI. The lineconnecting the data points is a mere eye-guide, the smooth curve is a X2fitto the data with So = 1.2· 10-4, Si = 1.3 . 10-4 (fixed parameters),S2 = (0.18±0.11) . 10-4 , Sy = (0.94±0.06) . 10-4 (adjusted param-eters). All data correspond to the same gold standard cross section.NEUTRON CAPTURE CROSS SECTIONS 605given in ref. 8),3 %near the calibration point at 30 keV, increasing to 8 %at 200 keV,were therefore raised here to 8 % and 13 %, respectively.(ii) The uncertainty in the probability for interaction of at least one photon out ofa capture y-ray cascade in the scintillator is estimated as 3 % [see ref. 6)].(iii) The uncertainty in the probability that a detector signal from a capture eventexceeds the discriminator threshold (the uncertainty in the spectrum fraction) is esti-mated as 6 %.(iv) Corrections for self-shielding and multiple scattering were calculated by themethod proposed by Macklin 11) based on work by Dresner 12). This method is sup-posed to be adequate if each data point represents an average over many resonances.This is obviously not the case here, but since a rigorous calculation requires an iterativeresonance analysis and since the corrections were never larger than about 10 % weconsidered the Macklin formulae as applicable, with an estimated error of 3 %.(v) The statistical error in the corrected data (ratios of background-correctedcounting rates) is listed for three representative energies in table 1.TABLE 1Energy(keV)Statistical uncertaintyfor each data point (%)Ce TlTotal uncertaintyfor each data point (%)Ce Tl20501001175854161314141213(1)From these contributions one obtains the total uncertainty estimates listed in table1, and indicated by error bars in figs; 1 and 2.3.2. MAXWELLIAN AVERAGESA large fraction of the existing heavy elements is thought to stem from neutroncapture in stars which have burnt most of their hydrogen 3). The interior of thesestars is assumed to contain mainly helium (density >::::: 104 gjcm3) and an extremelysmall amount of heavy nuclei at a temperature of about 3' 108 °K. Under theseconditions neutrons originating in charged-particle reactions will be thermalized be-fore being captured by the heavy nuclei. This means that the probability for the speedof a neutron relative to. the capturing nucleus is given by the Maxwell-Boltzmanndistributionp(v, T)dv = ~ (~)2 exp [_ (~)2J dV,..}1O VT VT VTwhere VT is the most probable relative speed (1-mvi: = kT, 111 is the reduced mass, andkT the temperature in energy units). The capture rate per unit volume for a given606 D. KOMPE el al.seed nucleide with capture cross section ay isNn(vay) == N(nv)(ay)T' (2)where N and n are the densities of seed nuclei and neutrons, respective1y, ( ... )denotes an average over the Maxwell-Boltzmann distribution (1), and (ay)T is theMaxwellian average mentioned above. Since nv is the relative flux, (aY)T is an averageover the flux distribution,(a )T = (vay) =y (v)I)') dvp(v, T)vay{v)t<XJ dvp(v, T)v(3)(4)In order to ca1cu1ate (aY)T one has to know ay over a rather wide range of energies.Our measurement covered the range between 10 and 200 keV which gives the maincontribution to (ay)T at the stellar temperatures considered here. The contributionsfrom beyond this region were estimated as follöws: statistica1 theory yie1ds for theaverage capture cross section, i.e. for the average over many unreso1ved, non-over-1apping resonances with spins J, parities (-1)', spin factors gJ [see :t:efs. 6,13)]- _ 2 h2" BYS1V1.J(E/1 eV)Syf(J)ay - n 11. L. gJ 1'1' •1,1 L BJ S" V" .J(E/l eV)+Syf(J)I'TABLE 2MaxweIIian averages n)kT <ay>T b)(keV) Ce (mb) Tl10 41 ±10 185±4015 31 ± 6 135±3020 26 ± 5 11l±2025 22 ± 3 94±1l30 19.9± 3.2 83± 935 18.1± 3.0 74± 840 16.6± 2.5 68± 745 15.5± 2.0 63± 650 14.5± 1.6 59± 660 13.1± 1.5 53± 570 11.9± 1.4 48± 580 11.0± 1.3 44± 490 10.2± 1.2 41± 4100 9.6± 1.2 38± 4n) It should be noted that the quantity <vay>/vr introduced by Macklin and Gibbons 18) exceeds theaverage <a",>T Iisted here by a factor 2/yn ~ 1.13.b) See eq. (3). The uncertainties quoted are due to cross section uncertainties (compare table 1) andextrapolation uncertainties (taken as one third the contribution from the extrapolation).NEUTRON CAPTURE CROSS SECTIONS 607We used here conventional notation: J(1) ~ (2J+ l)e -JÜ+ 1)/2(12 describes theenergy dependence of the level density according to DJ = D/J(J), and Sy == Ty/Dwith T y taken as independent of 1and J. Inelastic scattering does not occur below200 keV for the elements investigated here.A least-squares fit of (4) to the data was made by adjusting the strength functionsS1' S2' Sy for cerium, and S2' Sy for thallium. Partial waves with 1> 2 were neglected.The values of So were taken from Seth's compilation 14), S1 for Tl from ref. 15). Thebest fits obtained in this way are shown in figs. 1 and 2 as solid lines. They were usedto extrapolate iiy into the regions below and above the range of our measurement.The strength functions fitting our data are given in the captions of figs. 1 and 2. Theyshould not be taken too seriously, however. Although perfectly adequate for the cal-culation of the Maxwellian average «(Jy)T (contributions from outside the range ofour measurement are smaller than 5 %except at the lowest temperatures) the strengthfunctions found in the fit have large uncertainties.The calculated Maxwellian averages and their estimated uncertainties are listed intable 2.4. DiscussionThe only available data on neutron capture by natural cerium and thallium in thekeV region are the cerium and thallium cross seetions at 30 and 65 keV reported byGibbons et al. 16) and the thallium cross seetions published by Konks and Shapiro[ref. 17)]. The former data were obtained relative to indium, with reference values of763 mb at 30 keV and 448 mb at 65 keV. Using the same standard cross seetion theauthors measured a gold capture cross section of 515 mb at 30 keV and 332 mb at65 keV. Renormalizing their data to the gold cross seetion adopted here (596 mb at30 keV) one obtains the values shown in figs. 1 and 2 as solid triangles. For thalliumthere is agreement with our data within the error bars. The cerium values, however,differ significantly, the 30 keV cross seetion exceeding our data by almost a factar oftwo, and the 65 keV value being much lower. An indication that the Oak Ridgevalues may have larger errors than estimated by the authors could be seen in the factthat they are not compatible with the l/E behaviour of (Jy which one expects quali-tatively in the keV region [cf. ref. 6)1.The Russian values were measured with the slowing-down-time spectrometer (leadpile) relative to low-energy resonances in Br, Ta and Au. They are lower than ourdata. Two sampies were used, and a consistent discrepancy exists between the tworesulting sets of data. The thicker sampie yielded smaller cross sections which may bean indication that resonance self-shielding was underestimated. This hypothesis ap-pears to be confirmed by the fact that values which Konks and Shapiro calculatedfrom data taken with very thin enriched sampies of 203Tl and 205Tl [also plotted inref. 17)] agree much better with our data.Our Maxwellian averages for kT = 30 keV can be compared to the values used byAmiet and Zeh in their s-process calculations. These authors estimate (VCJy)/VT as608 D. KOMPE ef al.12 mb for 140Ce and 200 mb for 142Ce, which corresponds to <lTY>T = 29 mb fornatural cerium (see footnote to table 2). This is considerably larger than our value<lTY>T = (20±2) mb. For Tl there is no big discrepancy. The values 140 mb for 203T1and 50 mb for 2osT1 correspond to <lTY>T = 68 mb for natural thallium. Our value of(83 ±10) mb agrees reasonably weIl with this estimate.5. ConclusionThe very low neutron-capture cross seetions of the near magie elements cerium andthallium were measured between 10 and 200 keV. They show considerable resonancestructure. The steep decrease of the cerium cross seetion reported in ref. 16) could notbe confirmed. Our Maxwellian average at kT = 30 keV for cerium is only two thirdsof the value estimated in ref. 4) on tlle basis of the rule "abundance times capturecross section is a smooth function of mass number". If this rule is valid one must con-clude that the solar abundance of cerium should be 50 %higher than the presentlyknown value.The thallium data are in reasonable agreement with the few previously measuredvalues and with the estimates used in nucleosynthesis calculations.We thank Dr. H. D. Zeh for stimulating discussions. The help of Dr. Miessner andthe Van de Graaff crew is gratefully acknowledged.References1) R. L. Maeklin, J. H. Gibbons and T. Inada, Phys. Rev. 129 (1963) 26952) J. E. Lynn, Neutron resonance reactions (Oxford, 1968) eh. VII3) E. M. Burbidge, G. R. Burbidge, W. A. Fowler and F. Hoyle, Rev. Mod. Phys. 29 (1957) 5474) J. P. Amiet and H. D. Zeh, Z. Phys. 127 (1968) 4855) H. D. Zeh, private eommunication6) D. Kompe, Nuel. Phys. A133 (1969) 5137) W. P. Poenitz, D. Kompe and H. O. Menlove, J. Nuel. Energy 22 (1969) 5058) P. Poenitz, Nuel. Instr. 58 (1968) 399) M. P. Frieke and W. M. Lopez, Phys. Lett. 29B (1969) 39310) T. T. Semler, Trans. Am. Nucl. Soe. 11 (1968) 16211) R. L. Maeklin, Nucl. Instr. 26 (1964) 21312) L. Dresner, Nuel. Instr. 16 (1962) 17613) Yu. P. Popov and Yu. I. Fenin, ZhETF (USSR) 43 (1962) 2000, JETP (Sov. Phys. )19 (1964) 5914) K. K. Seth, Nucl. Data A2/3 (1966)15) M. Divadeenam, BuH. Am. Phys. Soe. 12 (1967) 106; AED-Conf. 1967, 035-05416) R. L. Maeklin, J. H. Gibbons, P. D. Miller and J. H. NeUer, Phys. Rev. 122 (1961) 18217) V. A. Konks and F.L. Shapiro, ZhETF 47 (1964) 795, JETP (Sov. Phys.) 20 (1965) 53118) R. L. Macklin and J. H. Gibbons, Rev. Mod. Phys. 37 (1965) 166; Astrophys. J. 149 (1967) 577;150 (1967) 721

Neutrons Capture Cross Sections of Cerium and Thallium in the keV Region

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Neutrons Capture Cross Sections of Cerium and Thallium in the keV Region

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