Fast Neutron Cross Sections of 2l*°Pu; Measured Results and a Comparison
with an Evaluated File
À. B. Smith, P. P. Lambropoulos and J. F. Whalen Argonne National Laboratory Argonne, Illinois
Abstract
Fast neutron total cross sections and elastic- and inelaetic-scatter- ing cross sections of 2**°Pu are reported. The total cross sections are measured from neutron energies of 0.1 to 1.5 MeV in increments of *»* 25 keV.
The elastic-scattering cross sections are measured at ^ 50 keV intervals from incident neutron energies of 0.3 to 1.5 MeV. The inelastic neutron excitation cross sections of states at 4 2 + 5 , 140 + 10, 300 + 2 0 , 600 + 20 and 900 + 50 keV are measured. The experimental results are discussed in the context of the optical, compound-nucleus and direct-reaction nuclear models including the effects of resonance width fluctuations and the fission process. The measured results are critically compared with the corresponding quantities in the evaluated nuclear data file ENDF/2.
I. INTRODUCTORY REMARK
The isotope 2t*°Pu is a major constituent of many fast-breeding reactors wherein the plutonium fuel may consist of £ 20 percent 2lf0Pu.^
Therefore fast neutron interactions with this isotope are a considera tion in the neutronic design of these systems. Despite this applied importance the experimental microscopic fast neutron cross sections of
2*°Pu are relatively unknown and a number of requests for measured in- 2 ' formation are outstanding. Major reliance continues to be placed upon evaluated data sets based largely on nuclear-model estimates. The fission neutron cross section of 2tfl*Pu has been reasonably well 3 4 5 measured. * * It is large with a relatively low energy threshold. At
low energies the fission cross section is of interest in the context of g fission theory due to its sub-threshold characteristics. Experimental
total cross sections and elastic- and inelastic-scattering cross sections
of 21*°Pu above * 100 keV are experimentally essentially unknown. This
ignorance is, in part, due to the limited availability of suitable samples
and to experimental problems associated with the high spontaneous fission
rate of the material.^ The present work was undertaken in an effort to generally improve experimental understanding of the fast neutron cross sec
tions of 2**°Pu by direct measurement of total and of scattering cross sec
tions to 1.5 MeV and to specifically satisfy requests for fast neutron
2<*°Pu data. It was also the objective to*, provide a reasonable experimen
tal foundation for the nuclear models employed in the interpolation and ex
trapolation of measured quantities, and to obtain additional insight into
nuclear structure and fission properties in the trans-uranlum region*
II. EXPERIMENTAL METHODS
The experimental measurements were made possible through the avail
ability of a 54 gm sample of plutonium ^ 100% enriched in the isotope
2**°Pu. The material was a metal foil 98.7 weight-percent plutonium and
1.3 weight-percent aluminum. It was formed into a cylindrical sample 2.0
cm in diameter by pressing the foil into a 0.013 cm thick stainless steel
can. The uniformity of the sample density was governed by the pressing
procedure* The sample was, in itself, an appreciable fast neutron source
due to spontaneous fission.
Total neutron cross sections were deduced from the observed trans
mission of essentially mono-energetic neutrons through the 2**°Pu sample assuming a uniform sample density« The measurements were made at ^ 5 keV intervale with 'v 5 keV resolution from incident neutron energies of 0.1 to 1.5 MeV. Sample transmissions were ^ 75%. The statistical precision of the measured cross sections was 1%. Small corrections were made for
"in-scattering" and background contributions and the fidelity of the apparatus verified by determination of the well known total neutron cross 3 8 sections of carbon. *
The neutron scattering cross sections were measured using the pulsed- beam fast time-of-flight technique. The apparatus consisted of collimated detectors which concurrently measured neutrons scattered at eight labora tory angles. The 7Li(p,n)7Be neutron source was so arranged as to provide an incident neutron resolution at the scattering sample of ^ 20 keV. The scattered neutron velocity resolution was generally ^ 1.5 nsec/M. All
scattering cross sections were determined relative to the known differ- 9 ential elastic scattering cross sections of carbon and corrected for multiple-scattering and other experimental perturbations.
The specific details of the total and scattering apparatuses and
methods are described elsewhere.
III. EXPERIMENTAL RESULTS®
A. Total-Neutron Cross Sections
The measured total cross sections displayed considerable energy-
dependent structure which was well correlated with known prominent reso nances in the total cross section of aluminum. The primary results were
corrected for the 1.3 weight-percent aluminum content of the sample using
£ A numerical tabulation of all measured values is given in the Appendix and all experimental results have been transmitted to the National Neutron Cross Section Center, Brookhaven National Laboratory. aluminum total cross sections measured at this Laboratory and smoothed by averaging the corrected values over 25 keV intervals. The final cor rected and averaged results are shown in Fig. 1. The remaining structure near 530 keV is believed a residual artifact due to uncertain corrections for the effects of the large aluminum resonance in this region and to have no physical significance. The errors associated with the results were largely of a systematic nature and, particularly, are due to the uncertain transmission-deneity of the sample. The combined total-cross-section error was conservatively estimated at five percent and the mean deviation of the measured values for a smooth curve was generally appreciably less.
No previously reported total cross sections of 2**°Pu in the energy range of the present experiments were found in the literature. The meas ured partial elastic- and inelastic-scattering cross sections (see below) 3 were confined with the reported fission cross section for comparison with the directly measured total cross sections. As shown in Fig. 1, the agreement was good with no discrepancy greater than ъ 300 mb. This con sistency indicates that both total and partial cross sections have been reasonably determined.
B. Biastic-Neutron-Scattering Cross Sections
The differential elastic-scattering cross sections were deduced from the measured time-of-flight (TOF) spectra with careful attention to back ground effects. Each TOF distribution was corrected for non-saraple associ ated backgrounds inclusive of contributions due to the sample container using direct experimental measurements. After this correction there re mained an appreciable fission-neutron background, time-uncorrelated from
2-°Pu spontaneous fission and time-correlated from neutron-induced fission.
Both fission-neutron backgrounds were estimated using a least-square fitting procedure. Time intervale were selected from each TOF distribution in such a manner that elastic- and/or inelastic-scattered neutrons were either physically inadmiesable (for example» at times before detection of the elastic event) or were judged to make no significant contribution to the selected Interval. The measured data in these selected time intervals was fitted with a low-order power series in time (usually quartic) Which rea sonably Interpolated the fission-neutron background over the entire TOF distribution. The fission-neutron contribution determined from the fitting procedure was subtracted from the measured TOF spectra.
The 2 At backward scattering angles (y 155 deg.) and, particularly, at higher energies the two elastic components were well separated due to the differ ent energy transfer to the recoiling nucleus. In these instances consid erable attention was given to the correct evaluation of the aluminum elas tic contribution in the presence of inelastic neutrons resulting from the excitation of the 42 and 140 keV states in 2<*°Pu. The combined 2tf0Pu and aluminum differential elastic scattering cross sections were determined from incident energies of 0.3 to 1.5 MeV in incre ments of 50 keV and at eight scattering angles between 25 and *v* 155 degrees. The measurement angles varied slightly from distribution to dis tribution but were typically 28, 38, 53, 68, 84, 114, 128 and 154 degrees. The resulting differential cross sections were least-square fitted with the expression dû “ 4тГ (1 + wipi> where a (angle-integrated cross section) and coefficients were deter mined from the fitting procedure and P^ are Legendre polynomials expressed 451 in the laboratory system. The differential elastic-scattering croes eec- tione» expressed in the form of Eq. (1)» were corrected for the aluminum contamination using the aluminum elastic-scattering cross sections of Ref. 13. The scattered neutron resolution was not generally sufficient at incident energies of £ 1.0 MeV to differentiate the elastic neutron group from inelastic neutrons resulting from the excitation of the 42 keV state in 2 'ъ 1,3 MeV. Assuming an isotropic inelastic neutron distribution and inter polating and extrapolating measured inelastic values with theoretical guid ance (see below)» the measured elastic cross sections were corrected for inelastic neutron contributions above ^ 1.0 MeV. This correction was small at forward scattering angles but appreciable at large scattering angles. However» uncertainties in the inelastic correction procedure did not sig- niflcantly contribute to errors in the angle-integrated elastic scattering cross section values. The fully corrected results were well described by Eq. (1) throughout the measured angular interval. However, extrapolation of the measurements beyond chis interval» particularly to backward angles» may not be reliable and may even lead to illicit cross sections. Uncertain behavior of Eq. (1) beyond the measured interval did not appreciably effect the deduced angle- integrated cross sections nor were they significantly influenced by alter nate termination of the series of Eq. (1) at i « 4 or 5. Representative differential elastic-neutron-scattering angular dis tributions are shown in Figs. 2A and 2B. Due to the complexities of the correction procedures» outlined above» the uncertainties associated with the measured differential cross sections were based on subjective judge ments. It was estimated that the error in the measured differential values varied from 5-10% at forward angles to as much as 30-50% at extreme back- ward scactering angles. These uncertainty estimates included errors associ ated with the carbon reference standard. The behavior o£ the elastic scat tering results over the entire measured energy range is summarized in Fig. 3 in the format of Eq. (1 ). The uncertainties associated with the angle-inte grated elastic crose sections were estimated to be 8-10% and the illustrated uncertainties in the omega coefficients are indicative of the quality of the fit of Eq. (1) to the measured data. Elastic-scattering cross sections of 2 C. Inelastic-Neutron-Scatterinft Cross Sections The differential inelastic-neutron-scattering cross sections were determined from the respective neutron groups observed in the TOF spectra. The background and other experimental-correction procedures were generally carried out as outlined above in the context of elastic scattering. In elastic measurements were made concurrently with elastic-scattering deter minations. However» at some incident energies and scattering angles the experimental results associated with the excitation of low energy excited states were rejected because of undue contributions from neutrons elastically scattered from the aluminum contaminant of the 2 Where reasonably defined the observed inelastic angular distributions were essentially Isotropic. Thus the angle-integrated inelastic neutron excita tion croes sections were obtained from a simple average of the measured differential values multiplied by 4it. Throughout the work the experimental emphasis was on inelastic cross section magnitudes for applied use rather than on nuclear structure information often better obtained by other means. Inelastic-neutron-excitation cross sections corresponding to states at 42 + 5, 140 + 10 , 300 + 20 , 600 + 20 and 900 + 50 keV were observed. Further, neutrons corresponding to the excitation of states at energies £ 1.0 MeV were qualitatively observed but subject to large background effects which made quantitative interpretation unreliable and therefore the respective cross sections are not reported here. The excitation energies were determined from the neutron flight-tiines and verified by observation of well known inelastic-neutron processes (for example, sc 14 &bFe Q « -850 keV). The energy uncertainties associated with the various neutron groups reflect estimates of experimental accuracy and the apparent contribution to some of the inelastic groups of several compo nents. The observed structure is summarized and correlated with more de- 7 tailed information reported in the literature in Fig. 4. The above excitation cross sections associated with the above neutron groups are outlined in Fig. 4. The indicated uncertainties are based upon estimates inclusive of experimental errors and those associated with the carbon reference standard. Ho comparable microscopic cross sec tions have, apparently, been previously reported. However, the magnitudes of the measured inelastic cross sections are consistent with the total and elastic-scattering cross section results described above. The interpretation of the experimental results was primarily based upon optical- and statistical-nuclear models.The point of departure was an optical potential of the form V(r) « - Vf(r) - iWg(r) - V h(r) £*0 , (2) so — — where f(r) was of the Saxon form, g(r) a guassian surface form, and h(r) a Thomas form.Over the energy range of the present experiments the potential parameters were assumed energy-independent. Compound-nucleus processes were calculated using the Hauser-Feshbach^ formula with fluctua tion corrections _ 2 T ,T о t - тгХ — -—~ • F , (3) cc* г T cc* ¿ c " c '1 where T are conventional transmission coefficients and F , the resonance- c cc 17 width-fluctuation correction. Fission was considered but radiative cap ture was assumed small and ignored. 21*°Pu is known to be appreciably de formed and thus the basic spherical potential of Eq. (2) was extended to 18•19 20 include the effects of collective deformation. * * The fission cross section of 21+0Pu rises from low sub-threshold values, through a threshold at 600 - 800 keV to large values of 1.5 b at ^ 1.0 3 MeV and above. Compound-nucleus decay through fission will be prominent over much of the energy range of the present experiments. The initial ob jective was the determination of a neutron model descriptive of total neutron cross sections throughout the measured interval and of partial reaction cross sections below ^ 600 keV where fission contributions were small. Using this neutron model attention was given to partial reaction cross sections, including fission, at incident energies above * 600 keV. Param eters suitable for the description of fast neutron processes in the similar nucleus 238U were taken as the starting point with adjustments to achieve 455 a "good" description of measured values. The selected spherical poten tial parameters are summarized in Table 1. Deformation was introduced for values of the parameter 0 j< 0.3 using the spherical potential in a rota tional coupled-channel model.^ Calculated total-neutron cross sections are compared with the corres ponding measured values in Fig. 1. The spherical (3 » 0.0) results agree with or are slightly smaller (*v 250 mb) than the measured values. The cal culated values increase with 0, becoming as much as 600 mb larger than the experimental values for 0 » 0.3. The 3 of 240Pu reported from studies of 18 other nuclear processes is in the range 0.2 to 0.3 and generally resulted in calculated total cross sections appreciably larger than the experimental values. Calculated and measured differential elastic-scattering angular dis tributions at 400 keV are compared in Fig. 2A. Both spherical and deformed calculated results are inclusive of compound-nucleus contributions with fluctuation and overlap corrections. The latter were determined using Moldauer's transmission coefficients, G^» with overlap parameter Q * 0.5 as defined in Eq. (4).*^ 9 “ T + ~ Cl - (1 - Q T Л2 (4) o a Q a a a Where T^ is the transmission coefficient of Eq. (3). The results were not strongly dependent on the choice of Q and its selection was primarily governed by fission considerations (see below). The calculated and measured distributions of Fig. 2A are in qualitative agreement, with discrepancies of the same magnitude as those resulting from changes of A3 by ^ 0 .1 . These comparisons tended to Indicate a 6 of * 0.2 . Measured and calculated inelastic excitations of the 42 keV (2+) state below ^ 600 keV were in qualitative agreement as illustrated in 456 Fig. 4» At these lower energies the calculated cross section Increased with deformation primarily due to larger calculated reaction cross sec tions with little contribution (< 100 mb) from direct processes. Concur rently, large deformation generally led to calculated total cross sections appreciably larger than the experimental values as is evident in Fig* 1. The omission of the fluctuation and overlap effects led to calculated values rather higher than indicated by experiment. Calculated I * 0 strength functions determined with both spherical (g « 0.0) and deformed ($ 19 0.1» 0.3) potentials are outlined in Table 1. 22 23 Comparable values deduced from resonance measurements and systematics ’ are reported in the range * 1-2 x 10~\ again indicating В 'v 0 .2 . It was concluded that the above neutron model, summarized in Table 1, was a suitable basis for subsequent calculations at higher energies where the fission process is pronounced. Fission was introduced by means of transmission coefficients (see Eq. (3)) and the respective cross sections calculated using the computer 19 program NEARREX. The fission transmission coefficients, , were assumed to rise to a value close to unity above the fission threshold and the over lap parameter Q was adjusted to obtain agreement between calculated and 3 measured fission cross sections. Concurrently, agreement with the observed inelastic excitation of the 42 keV (2+) state was sought. The latter ob jective was restrictive as choices of T^ and Q describing fission often led to smaller excitations of the 42 keV state than observed experimentally. Generally, the best low-energy ('S 700 keV) agreement with experiment was obtained assuming fission was prédominently in the J * 1/2+ channel. How ever, even when saturated, this channel did not account for the large fis sion- cross sections above threshold. Thus additional J * 1/2- and 3/2- flesion channels were Introduced at an incident energy of 600 keV. With these additional fission channels calculated fission cross sections were > similar to the experimental values. Interestingly, the measured 2l*0Pu fission cross section shows structure near 600 keV, the energy where the model Introduces additional fission channels. The selection of fission transmission coefficients was sensitive to the choice of the overlap param eter, Q» with Q * 0.5 giving the best overall agreement with experiment. The fission model outlined above Is not inconsistent with either the double barrier concept of fission** or the results of experimental studies of reso- 25 nance structure in sub-threshold fission both of which suggest a J « 1/2+ fission channel at low energies. Calculated Inelastic excitation cross sections corrected for fission, fluctuation and overlap effects, were in reasonable agreement with the meas ured values as illustrated in Fig. 4. The excitation of the 42 keV state calculated using the spherical potential was marginally lower than the ex perimental values over the entire energy range. The deformed potential with channel-coupling and ß * 0.2 or 0.3 gave results very similar to the experimental values. At higher energies (£ 1.0 MeV) the direct process makes a significant contribution to the inelastic cross section (*v 200 mb) with resulting cross sections higher than those obtained without deforma tion. The somewhat better agreement between measured and calculated in elastic excitations of the 42 keV state obtained with larger ß*s was not without detrimental consequences in the area of total cross sections (see Fig. 1). The excitation of energy states above 42 keV inclusive of states to 'v 1.5 MeV was calculated only with the spherical potential using spin and parity assignments of Ref. 7 as shown in Fig. 4. In these cases the agreement with experiment was good particularly in view of the available experimental resolution and of uncertainties in the excited structure that has been reported for 2lf0Pu or as can be deduced from the present measure ments. There was no experimental evidence for the state reported at ^ 740 keV» This was not surprising as» with the reported spin of this state» the calculated cross sections were small. Calculated and measured angle- int eg ra ted elastic-scattering cross sections were similar (see Flg. 1) with discrepancies within the range of reasonable uncertainties in 3, and experimental values. Calculated elas tic-scattering angular distributions at energies above ^ 1.0 MeV were less satisfactory as Illustrated ln Flg. 2B. The difference between calcula tion and experiment was particularly evident in the Legendre format of Eq. (1) (see Fig. 3 ). The discrepancies are larger at backward scattering angles and for small deformations. At energies £ 1.0 MeV the calculated distributions consist essentially of shape-elastic scattering. For small 3 values the shape-elastic distribution has low minimla not experimentally observed. For larger ß (y 0.2-0.3) the calculated results at backward angles were more similar to the experimental quantities but the forward angle values tended to be too large. A compromise choice of 0 * 0.2 seemed most desirable in the context of the elastic-angular distributions. The calculations assumed a constant overlap parameter» Q» for all chan nels. Perhaps more desirable would be a large Q in the fission channels with smaller values in neutron channels. The option of variable Q was not available in the computational framework. Very likely improved agreement with experiment could be obtained by detailed adjustments of the potential parameters using a specifically selected $ value. Generally it was felt that the Q uncertainty, experimental uncertainties, possible alternative 3 values and uncertainties In fission-transmission coefficients were such that a more detailed potential parameter adjustment to possibly achieve a better description of the experimental results was not warranted. The above procedures, while having physical merit, are costly and complex and involve the selection of a number of uncertain parameters. From a pragmatic point of view a simpler statistical adjustment of partial reaction cross sections to account for known fission cross sections, as described in Ref. 21, can give essentially the same numerical results as obtained above. The simpler calculation may be more convenient for pro viding numerical values for applied purposes. V. COMPARISON WITH THE ENDF/B EVALUATED FILE The results of the above experiments are quantitatively compared 25 with the relevant contents of the ENDF/B evaluated file. The measured and evaluated total-neutron cross sections are in rea sonable agreement over the entire experimental energy range as illustrated in Fig. 5. The discrepancies near 500 keV are not judged significant as they could be attributed to experimental errors as discussed in Sec. Ill, above. At energies above 1,0 MeV the evaluated results tend to be sys tematically larger than the measured values but the difference is small, less than 300 mb. Measured and evaluated elastic-scattering cross sections differ from one another in both shape and magnitude as shown in Fig. 5. The evaluated quantities are slightly larger than the measured values near 500 keV and pronouncedly lower at 1.0 MeV and above. At the higher energies the dis crepancies are a full bam. Evaluated cross sections are given for the excitation of states at 43, 142, 296, 599, 863, 903 and 945 keV. These energies are very similar to those measured in the present experiments with the latter three being experimentally observed as a composite state with an average excitation energy of 900 keV. The evaluated and measured inelastic-excitation cross sections are compared in Fig. 6. Below 500 keV the evaluated results for the excitation of the 42 keV state are in agreement with experimental ob servation. However, at higher energies the evaluated results are much 460 larger than either the corresponding experimental values or those deduced from the model discussed in Sec. IV, above. Moreover, the energy depen dent shape of the evaluated cross section is not consistent with measure ment or microscopic calculation. This is puzzling. As discussed In Sec. IV, the competition from fission will appreciably reduce this cross sec tion above the fission threshold and lead to a characteristic shape of the excitation function near the fission threshold. The shape is qualitatively evident from even simple-model considerations. The evaluated and measured cross, sections for the excitation of the 140 fceV state are similar. The agreement ,1s not so good for the excitation of the 300 keV state but the cross sections are small and as a consequence experimentally uncertain and of minor importance In the context of applied use. The agreement be tween measured and evaluated cross sections for the excitation of the 600 keV state Is fairly good with the evaluated result tending to be somewhat lower. The combined evaluated cross sections for the excitation of the 863, 903 and 945 keV should be compared with the single observed composite state at an average energy of 900 keV. These combined results are about twice as large as the experimental values. This is difficult to explain unless the spin and parity assignments used in deducing the evaluated quantities differed appreciably from those used here and defined In Fig. 4 or the measured values are In appreciable error. Alternate choices of spin and parity can be questioned in the context of other experimental evidence. Generally, it is concluded that the evaluated file is reasonably de$crlptive of the measured total-neutron cross sections. In the areas of elastic- and inelastic-scattering cross sections there are appreciable discrepancies between the measured and evaluated results. These w ill, of course, be reflected in discrepancies in associated quantities such as the non-elastic cross section as internal consistency of the file is manditory. 461 It is suggested that the observed discrepancies may be due to inappropriate consideration of the fission process in the calculations from which the file was largely deduced. VI. CONCLUSION The experimental results reasonably defined total and elastic- and inelastic-scattering neutron cross sections of 2**°Pu over a region of previous uncertainty. The experimental results directly pertained to re quests for nuclear data and suggested some revision in widely used evalu ated cross sections particularly in the area of neutron scattering. A neutron-optical model was proposed based largely upon measured total-neu tron cross sections and partial-neutron cross sections below the fission threshold energy of *v* 600 keV. The model was Inclusive of fluctuation and overlap corrections and of nuclear deformation. The model was extended to include major contributions from the fission process near and above the threshold. Comparison of calculated and measured fission cross sections and inelastic excitations of the 42 keV (2+) state suggest that fission near and below threshold is predominently in the J « 1/2+ channel with additional fisslon-channels opening as the incident neutron energy passes across the fission threshold. When inclusive of fission processes the model was reasonably descriptive of total and angle-integrated elasticrr and inelastic-scattering experimental cross sections throughout the meas ured energy range and provided a suitable framework for interpolation and extrapolation. The model was less successful in the area of differential elastic cross sections at energies £ 1.0 HeV. ACKNOWLEDGEMENTS The authors are indebted to Dr. H. Motz and other members of the Loe Alamos Scientific Laboratory Staff for making available the unique sample of 2 TABLE Is OPTICAL MODEL POTENTIAL PARAMETERS V (real depth), MeV 41*5 Rj (real radius), F 8.20 a (real diffuseness), F 0.47 W (imaginary depth), MeV 6.14 &2 (imaginary radius), F 8.20 b (imaginary width), F 1.00 V ^ (spln-orbit depth), MeV 7.5 Q (overlap parameter) 0.5 a £ (deformation parameter) case a, (spherical) 0.0 case b, 0.1 case c, 0.3 (£ « 0 strength function) x 104* case a, (spherical) 0.73 case b, 0.91 case c, 2.37 direct well assumed equal to real well. Measured total (crosses) and elastic-scattering (boxes) neutron cross sections of 2**°Ри. Solid curve Indicates the total-scat tering cross section deduced from the present measurements. Dashed curves show results of model calculation as discussed in Sec. IV of the text. Fig. 2 Measured and calculated differential elastic scattering cross sections of ztiQ?u at 400 (a ) and 1200 (B) keV. Curves indicate calculated results as described in Sec. IV of the text. Data points are measured at or near the stated neutron energies. Fig. 3 Differential elastic scattering cross sections of 2tf®Pu expressed In the format of Eq. (1 ). Crosses are results deduced from meas ured values. Curves are derived from calculations (see Sec. IV of the text). Fig. 4 Inelastic neutron excitation cross sections of 2,*°Pu. Crosses indicate measured cross sections and associated errors for the Individual excited states. Curves result from calculation as described in Sec. IV of the text. The insert correlates the re** ported excited structure of 2**°Pu with that observed in the present measurements (boxes). The energy dimensions of the boxes indicate the effective experimental resolutions and the brackets associate the experimental results with reported structure. Fig. 5 A comparison of measured total- (crosses) and elastic-scat- terlng (boxes) cross sections with comparable quantities from 25 the ENDF evaluated file (curves). Fig. 6 A comparison of measured inelastic neutron excitation cross sections (crosses) with the respective quantities of the ENDF 25 file (curves) REFERENCES 1. See for example. Reactor Development Program Progress Report, Argonne National Laboratory Report ANL-7742, (1971), et* seq. 2. See RENDA Compilation nf EANDC Requests for Neutron Data Measure ments, EANDC-85(U), O .E .C .D ., (1970). 3. J. R. Stehn et a l ., Nuclear Cross Sections, BNL-325, Vol. Il l , 2nd ed., Supplement No. 2 (1965) Brookhaven National Laboratory. 4. N. 6 . Nesterov and G. N. Smirenkin, Atomnaya Energiya B, 139 (1960). 5. P. Ruddick and P. H. White, J. Nuclear Energy 18, 561 (1964). 6. J. E. Lynn, Proceedings of Helsinki Conference on Nuclear Data for Reactors, 249, IAEA press, 1970, Vienna* 7. Nuclear Data Sheets, B4, 661 (1970). 8. S* Cierjacks et a l., High Resolution Total Neutron Cross Sections between 0.5 - 30.0 MeV, KFK-1000, Gesselschaft für Kernforschung M .B .H ., Karlsruhe, 1968. 9. A. Langsdorf et a l., Neutron Scattering Angular Distributions, Argonne National Laboratory keport, ANL-5567 (Rev.) (1960). 10. J. Whalen et al., Nucl. Instr. Methods 39» 185 (1966). 11. A. Smith, Nuclear Research with Low Energy Accelerators, ed. J . Marion and D. Van Patter, New York, Academic Press (1967). 12. A. Smith, private communication. 13. J . Chien and A. Smith, Nucl. Sei. Eng. 26, 500 (1966). 14. E. Barnard et al., Nucl. Phys. Al18, 321 (1968). 15. P. Hodgson, The Optical Model of Elastic Scattering, Oxford Press, 1963, London. 16. H. Feshbach et a l ., Phys. Rev. 96>, 44B (1954). 17. P. A. Moldauer, Rev. Mod. Phys. 36, 1970 (1964); see also Phys. 18. P. Stelson and L. Grodzins, Nucl. Data 1A. 21 (1965). 19. Spherical model calculations employed the computer code ABACUS-2, E. Auerbach» BNL-6562, Brookhaven National Laboratory. Compound- nucleus calculations were carried out with, "NEARREX, Computer Code fot Nuclear Reaction Calculations," P. Moldauer et al*, Argonne National Laboratory Report ANL-6978. 20. Deformed potential calculations employed the computer code, "2-PLUS, A Non-Spherical Optical Model for Fast Neutron Cross Sections," Atomic International Report NAA-SR-11706 (1966). C. L. Dunford 21. P. Lambropoulos, private communication, to be published. 22. K. Seth, Nucl. Data 2A, 299 (1966). 23. M. A. Preston, Physics of the Nucleus, Addison-Wesley Publ. Co., Reading, Mass. (1963). 24. E. Migneco and J . Theobald, Nucl. Phys. A112, 603 (1968). 25. Evaluated Nuclear Data Flle-B (ENDF/B) National Neutron Cross Section Center, Brookhaven National Laboratory. 1.3 TOTAL SCAT. TOTAL / ELASTIC . . .X. - 1.0 -TOTAL + -TOTAL En. MeV En. 0.7 0.4 0.1 9 3 6 IE О О b’ JO Figure Figure 1. 467 г L ß*0.\ ------______T J 400 keV 400 90 Pu, ® Iob» 240 1 . 0 02 ■° 0 .1 cs ? Figure 2- A. 2- Figure 468 Figure 2-B. dcr/dñ, b/sr 9 e d - b o l « 2 I Г Н I.... I i Г " Т J О 2 I I I I I 1 О *111111111 2 г т т I I I I ... I1 ...Г 1 -1 — 1 I О I I I I I___I I I I 2 ТТТ I...Г...I ... II I "Г I О I I I J__ I__ I__ I__ I__ I__ I__ L 12 ГГТ 1 I I I I I I I Г 8 Э’ 0.3- 4 О 0.8 1.1 En, MeV Figure . M«V Q J ьк ф 0.5 2.0 0.5 1.5 1.0 0 0 iue 4. Figure I 1.6 ______I ______1 1.3 ______1 TOTAL. ______I 1.0 ______J t~~PTT t~~PTT ч > 1 t i * ■( < > i ч г -» ♦ n г i « ; >■ т e r En, En, MeV Figure Figure 5. 472 С PU-240 CROSS SECTIONS PU-240 С BATb 7/71 PU.240 Ç ÜAÎA—«ARB0NNÊ NATIONAL LABORATORY PU-240 Ç AÚTÜORS— A. SMITH ANDJ . WHALEN* ТВ BE PUBLISHED PU-240 Ç SAMPLE ESSfcNTJALLY IS0T0PICALLY ENRICHED T0 100 PERCENT IN PU-240 PU-240 С S a HPl.6 WNTAlNèl) ABOUT'1,3"HT,-PERCENT ALUMINUM* ALL DATA HAS PU-240 С CORRECTED THIS CHEMICAL IMPURITY PU-240 5 PU*240 Ç ¿»TAL CROSS SECTION BLOCK PU-240 С ЮНМАТ(4Е12,бГ " PU-240 Ç " 1. ÈNêHôY IN KbV PU-240 С 2» X-S6C IN 8A&NS PU-240 6 3, UNCERTAINTY IN X-SEC IN BARNS PU-240 £ 4, ENERGY RtseLUTI0N <♦-> IN KEV Py-240 С METHOD —‘WÍNO-ENERGETJC SOURCE PU-240 Ç CORRECTED FOR IN-SCATTERING PU-240 Ç 6800 GEOMETRY ‘ PU-240 Ç * PU-240 . lit?9921: 03 .11195IE 02 ,335852E 00 .125000E 02 PU-240 .1$1140E 03 ,10/6426 02 .322927E 00 »125000E 02 PU-240 ,16jte26E 03 , Ю 8831Б 02 ,326494E 00 .125000E 02 PU-240 ,l9W»2fc 03 . 10 J305fc 02 .310516b 00 « 1250006 02 PU-240 ,216344Ё 03 .104962Ê 02 .314886E 00 .125000E 02 PU-240 •2JX389E 03 ,100408b 02 .3012236 00 .1250006 02 PU-240 ,2664286 03 .962943E 01 ,2888836 00 ,125000E 02 PU-240 ,ií9üfc62b 03 .9*338*6 OÍ .2830156 00 .125000E 02 PU-24Q ,3158286 03 ,940248b 01 .282074É 00 .125000E 02 PU-240 .44J445E 03 ,9189336 OÍ .2756806 00 .12500PE 02 PU-240 ,3$8u29E 03 «9U4649& 01 ,271395E 00 .125000E 02 PU-240 ,3VV$VH 03 ,888260b 01 ,266470b 00 .125000E 02 PU-240 »416445E 03 .892359È 01 .26?708E 00 .1250Q0E 02 PU-240 .44Ш9Е 03 ,882545b 01 .264764E 00 .125000E 02 PU-240 .46¿4$¿E 03 ,8430436 01 .252913E 00 .12500PE 02 PU-240 ,4VX788b 03 ,771467b 01 ,231440b 00 .125000E 02 PU-240 .5U53&È 03 ,7»37¿6fc Ql .22Í118É 00 .125000E 02 PU-240 , »42193b 03 .738906E O Í .2215526 00 .125000E 02 PU-240 ,5660766 03 ,7/51096 01 .232533E 00 .125000E 02 PU-240 ,5 9 |$ ÿ 5ê 03 ,740656b Oi ,2221976 00 .1¿5000E 02 PU-240 ,6166Í3b 03 ,746919b 01 .224076È 00 .125000E 02 PU-240 •64U/20È 03 ,741123b 01 .222337E 00 .125000E 02 PU-240 ,6§6ó4/£ 03 .7/6313E 01 .232954E 00 .125000E 02 PU-240 ,6?*16$b 03 ,7$3130b OÍ ,22»939b 00 .125000E 02 PU-240 •7161786 03 ,7U4969fc 01 .2114916 00 .1250006 02 PU-240 .7U694E 03 ,740736b oí .2246216 00 ,1250006 02 PU-240 .7672096 03 ,767075b 01 .230123E 00 .125000E 02 PU-240 ,/91225t 03 ,744127b OÍ ,2232386 00 .125C00E 02 PU-240 ,816737E 03 ,¿94584g 01 .206375E 00 .125000E 02 PU-240 .84225ÍÉ 03 «708674&Q l ,2126Q2E 00 .125000E 02 Рц-240 .8651926 03 ,7173246 01 .215197E 00 .125000E 02 PU-240 ,b?¿//4t 03 ,721043b OÍ ,216313b 00 .125000E 02 PU-240 ,9172t)6É 03 ,722770b 01 ,216831b 00 ,1250006 02 PU-240 ,9409¿2K 03 «734482E 01 .220345É 00 ,1250006 02 PU-240. ,96¿8Q9E 03 ,71)524*6 O l .2U873É 00 .125000E 02 PU-240 ,VV232ib 03 ,73/24Ób 01.22Ц 72Е 00 .125000E 02 PU-240 .101703b 04 ,720687b 01 ,2162066 00 ,125000g 02 PU-240 .1Ü41Ö4E 04 ,701115t 01 .2103356 00 .125000E 02 Рц-240 .1U6/J&S 04 ,¿9¿132fe 0 1 ,2073406 00 .125000E 02 PU-240 .lU?l87b 04 .691»06Ь01 ,2074S2b 00 .125000E 02 Pu-240 •liltOttb 04 .6У$1в2Ь01 »20975SE 00 .1290006 02 PU-240 .1Í4089E 04 .604O79E01 .208224E 00 .125000E 02 PU-240 ,116640g 04 .6У1»38ЕOl ,2074616 00 .125000g 02 PU-240 .livigib 04 ,680778b Qi .206633b 00 .125000E 02 PU-240 .1*164»* 04 ,7oS236Ê01 .21Ó971Í 00 .125000E 02 PU-240 .1242716 04 ,6?3600b01 .202080E 00 .1250006 02 Pu-240 94 .67Ф711Е 01 ,2039136 00 .125000E 02 PU-240 , i m g 3 b 04 ,6$Ов9$Ь01 ,207260b 00 .125000E 02 PU-?*0 ,13164»E 04 ,69?792E 01 .209338E 00 .125000E 02 PU-240 ,134046t 04 «693722b 01 .208Ц6Е 00 .125000E 02 PU-240 »136S97E 04 «6/»»26E 01 .202658E 00 .125000E 02 PU-240 .l3vi3Ôfc 04 ,669360k Oi ,200808b 00 .12»OOOE 02 PU-240 ,141»»0b 04 ,66?8Ï7b 01 ,200345b 00 «12500QE 02 PU-240 , 1 ; 4 1 0 1 E 04 ,680669bQl .204201E 00 .125000E 02 PU-240 ,1466»lfc 04 ,676078b 01 ,2034?4E 00 .125000E 02 PU-240 S PU-240 С bN|) T0TAL CR0SS SECTI0N BLOCK PU-240 С PU-240 Ç PU-240 Ç PU-240 Ç bUSTIC SCATTERING CR0SS SECTMN BL0CK PU-240 Ç F0ftHAT'(6X,214#»il5.J4>> PU-240 c i, Energy in kev p u -240 В 2, X-S6Ç*100 IN BARNS PU-240 С 3, 0ME8Â-1 PU-240 C 4. UNCÉftTAINTY IN 0HEGA-1 РЦ-240 Ç 9 0MEGÂ-2 ' PU-240 С «— PU-240 Ç — PU-240 Ç ECT,, THROUGH 0HEGA-5 PU-240 С NHfcRfc«— *> PU-240 Ç ’ X-S6C IS IN LbG&NDRE EXPANSION IN CAB, SYSTEM 0Г THE F0RH PU-240 Ç D«X-SEC/SR.»(X-SEC/4*Pl>* 197 O.1400E 00 00-♦14Ô0E .40 00 >.l400E 00 >.l400E 00 ■•1400E 00 >.14Ú0E sliOOE 00 00 >.1400E 00 ’.1400E 00 >.1460E ».42006-01 -.42006-01 -.42Ô0E-01 -.42006-01 -.42006-01 •.4200E-01 >.42006-01 >.4200E-01 -.4200E-01 ’.4200E-01 ■.42Ô0E-ÔI •.4200E-01 ‘.42006-01 >.42Ö0E-01 .40 00 ’.1400E enerby 98 54 -.042000 -.042000 Í9 91 77 72 •2.40000 • b P 28148 1228 1197 1240 1129 Í183 20238 1280 Í246 1183 1198 80 Ц lie* o - i e aiu v in 26$ 11* 19? 3 1285 132 10« 63 315 51 1352 93 52 58 54 nev .5000E-02 .5000E-02 .ЬОООЕ-02 .5000E-02 .50006-02 «5000E-02 .50006-02 .50006-02 •1000E- .10006* .5000E-02 .t,0006-02 .5000É-02 .50006-02 ,*0006-02 «90QOE-02 .1000E' .10006* .Í000E* •1000E* .1000E« .10006* 1000E« • .10006- .50006-02 .9000E-02 .10006* .10006* 1360 1378 1149 1132 4396 1473 1»15 1374 1183 20128 1290 128Ô 44231 1444 in nev 7 723 174 278 0 840 308 194 3 587 137 01 01 01 01 01 01 01 01 01 01 01 51 4591 54 58 156 Ql .13506 21E 00 .2418E 00 .6902E 01 .Ю20Е 00 .8864E 01 «10d7E 01 78E 2 .1 01 .1217E 01 «11996 01 .1231E 01 .1309E 01 1278E . 02 00 2072E . 00 .1989E 00 .2386E 00 .6890E 00 .6280E 39E 00 .3297E 00 .3611E 00 .3140E 00 .1978E 41E 00 .4019E 00 »2177E 00 »2763E 31E 00 •3Ô14E 779 721 500 684 830 890 615 96 434 442 353 220 391 293 174 162 9 279 196 94 92 65 248 92 96 17 00 3157E . 00 3735E . .2261E 00 00 .2261E 00 1064E . 11E 00 «1217E 00 .2949E 93 00 1933E . 00 1199E . .72536-01 .72536-01 .78506-01 .31096-01 .3627E-01 .2967E-01 .3977E-01 00 .1400E 00 •2034E 00 .1017E 00 .2022E 00 .18126 00 .1846E 10E 00 .1206E .7222E-01 .34836-01 .55266-01 .45226-01 .45226-01 324 299 0 130 103 311 452 4 229 245 370 383 4 7 0 0 179 241 174 0 90 103 407 944 0 0 0 306 9 0 0 391 272 242 90 59 73 356 00 ,31576 •37356 16E 00 «1064E 00 .1217E 00 .1199E 00 «1846E .29496 22E 00 •2022E 00 .2261E 00 «1812E 00 .1533E 10E 00 «1500E ,31096-01 ,31096-01 .3627E-01 .3977E-01 00 2034E , 10E 00 .1206E .7253E-01 »7222E-01 .78506-01 .3483E-01 .55266-01 .2967E-01 00 .1017E .45226-01 .45226-01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 Pg-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 PU-240 .11>1Ь иг .2000fc*01*. 14006 00 .10006*01 .34756 00 .8687E*0l .8687Е-01 Рц*240 .l2d*Ê Öl .20006-0Í-.14Ó0E 00 .ЮоОб-Ol .3014Е оО .90436*01 .90436001 PU-240. .1*296 01 .20006*01-.14006 00 .10006*01 .49406 00 .12356 OQ .12356 00 PU-240 ,1K8>£ 01 .20006-01-.1400E 00 «10008*01 .46476 00 .11626 00 .11626 00 PU*240 .14001; 01 .20006*01«.14006 00 .10006-01 .26696 00 .80076-01 .80076-01 Рц*24о PÚ¿240" Ф« -.300000 PU-240 ,l2(>!>6 0t .200ÛÉ-Q1-.3000E 00 .20006-01 .95466-01 .28646-01 .28646-01 PU-240 ,lJÿ«6 01 *20006-01"»30006 ОО .20006*01 .18216 00 .54646-01 ,54646-01 PU-240 ,l*ûôk 01 ,20006-01*.3ÔO06 Oo .20006*01 .17586 00 .87926-01 .87926*01 PU-240 .l » m Ô1 »2000Í-Q1«»30006 00 .20006-01 .13826 00 .55266-01 .55266*01 PU-240 PÛ-24Q Qâ -.600000 PU-240 •92tftfi'00 .200ÜÉ-01-.6Û00E 00 .20006-01 .32976 00 .9B91E-01 .98916-01 PU-240 ,9»&ft6 00 .200Ô6-0Î-.6Ô00E 00 .20006-01 .11306 00 .56526-01 .56526-01 PU-240 •lUibe 01 >20006-01-.60006 00 . 20006-01 .25126 00 .10056 00 .10056 00 PU-240 .liüOb 01 .200dE-0i-.60006 00 .20006-01 .30776 00 .15396 00 .15396 00 Pu-240 *1Í¿0Í Ô1 .2000|-01-.60б06 00 .20006-01 .2638E 00 .79136-01 .79136-01 PU-240 •12ÖSE Ô1 .20006-01-,60006 00 .2000E-01 .31406 00 .4710E-01 .47106*01 Pu-240 .lü¿áE 01 .20006-01-.60006 00 .2000E-01 .20606 00 .41206-01 ,41206-01 PU-240 ,l2bSfe 01 .20006*01*.6ÓOOE 00 .20006>0l .21356 00 .53386-01 .53386-01 Pÿ-240 .12У06 Ô1 .20006-01«.60Ô0E 00 .20006-01 .30146 00 .60296*01 ,60296*01 PU-240 •1ÀÔ06 01 .20006-01*.60006 00 .20006-01 .23246 00 .10466 00 .10466 00 Py-240 .1Í4UE 01 .200V6-01-.6000E 00 .20006*01 .22456 00 .4490E-01 .44906-01 PU-240 ,l350fc 01 .200Ófc-0Í*.6ÓQ06 00 .2000E-01 .27886 00 .55776-01 .55776*01 Pu*240 61 .ÎOOÔê-Ol-.ÂOÔOE 00 .2OO0E-OI .29836 00 .89496*01 .89496-01 Pu-240 ,1**06 01 «20006*01-.60006 00 .2000E-01 .25626 00 .76876-01 .76876-01 Py-240 •144Ú6 01 .20006^01*.60Ô06 00 .2000E-01 *28136 00 .9847g*0l .9&47g*01 PU-240 ,l?45fc Ql ,20006*01*.6Ó00E 00 .20006*01 .19476 00 .38946*01 .38946*01 Pu*240 PÙ-240' 0« -.900000 PU-240 ,1JV06 01 .2000Ë-01*«9Ó00E 00 .50006-01 .2386E 00 .11936 00 .11936 00 Pu-240 .13906 01 .20006-01*.90006 00 .50006-01 .25546 00 .76626*01 .76626*01 PU*240 ,1440b 01 .20OÔt-OÎ-.9ÔOOE 00 .>0006*01 .21106 00 .63306*01 .63306*01 PU*240 ,14406 01 .200Ôi*OÎ*.90Ô06 00 .50006-01 .26856 00 .80546*01 .8O54E-01 PU-240 ,1*Ъб 01 .20006-01*.90006 00 .50006-01 .16876 00 .50606-01 .50606*01 PU-240 .1*4*6 01 .20006-01«.90Ô06 00 .50006*01 .15546 00 .46636-01 .46636-01 PU-240 ,14456 01 .20QÓfc-0¿*.9Ó0Q6 00 .¡>0006*01 .16156 00 .48456*01 .4845E*0l Pu-240 .l5<№fc 61 .¿006i-0i-.90006 00 .éOOOE-pl .35426 00 .10636 00 .Ю63Е 00 PU*?40 .1&Ö06 01 .20006*01«.90006 00 .50006*01 .17276 00 .51816*01 .51816*01 Pu-240 ,1»ÔV6 01 .20006*01*.90006 00 ,50006-01 .Ц626 00 .34856*01 .34856*01 PU-240 ii . . . Pu-240 С PU-240 6 6N0 гг 1NEUASTJC вивск Pu*240 e pu -240 С •••••••••• tNO 9F PU-240 SET * * * • * • ♦ • • • PU-240 С PU-240 b PU-240