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Fast neutron capture by vanadium and titanium
Journal of Nuclear Energy. Vol. 23. pp. 443 to 456. Pergamoa Press 1969. Printed in Northern Ireland
FAST NEUTRON N.
CAPTURE BY VANADIUM TITANIUM*
AND
D. DUDEY, R. R. HEINRICH and A. A. MADSON
Argonne National Laboratory,
9700 South Cass Avenue, Argonne, Ill. 60439, U.S.A. (Received 17 April 1969)
Abstract-Fast neutron capture cross sections of 51V and 5oTi have been measured by the activation method as a function of neutron energy between about 150 keV and 1.7 MeV. These cross sections were measured relative to both the zseU(n, f) cross section and the lg7Au(n, y)1“8A~ cross section. Neutrons were produced by the rLi(p, n)‘Be reaction from a Van de Graaff accelerator. The uncertainties on the absolute activation cross sections are rt8.5 per cent for Y and 59.9 per cent for 6oTi and were evaluated with the aid of a computer code which is described. A complete error analysis is given. The data have been compared with calculations based upon the statistical compound nucleus model of nuclear reactions. The significant feature of the measured reactions is the sizeable fluctuations of the cross section about a smooth average which cannot be described by the theoretical calculations. Possible explanations for this observed structure are given. 1. INTRODUCTION
of fast-neutron processes is essential to the design and development of fast-breeder reactors. Accurate measurements and calculations of neutroncapture cross sections for structural and fuel-cladding material are essential to the understanding and description of neutron energy and flux degradation processes occurring in nuclear reactors. Alloys of vanadium and titanium are one of the types of fuel-cladding materials being considered for future fast reactors. At present, only a few measurements have been reported by JOHNSRUD (1959) and STAVISSKII (1962) for fast-neutron capture on vanadium over the energy range of principal interest to fast-reactor design (10 keV-3 MeV). No measurements have been reported for the capture cross sections on titanium between 30 keV and 2.5 MeV. For these reasons we have measured the neutron capture cross sections of 51Vand “Ti as a function of neutron energy between about 150 keV and 1.7 MeV. In addition to the direct practical application to reactor technology, capture cross sections are of considerable importance in evaluating theoretical models which may be used to calculate these and other important nuclear parameters. The statistical model has been widely used with varying degrees of success to predict nuclear properties, including energy-averaged cross sections. The work presented here provides a means for examining the accuracy of the statistical model of nuclear reactions. The 51Vand 60Ti capture cross sections were measured by means of the activation technique. The samples were irradiated in a monoenergetic neutron beam and the radioactive products were identified and counted from their characteristic gamma rays. The results are compared to theoretical values calculated from a self-consistent set of optical model and statistical model parameters. These parameters have been derived from other independent experiments and are expected to describe adequately the reactions reported in this work.
AN UNDERSTANDING
* Work performed under the auspices of the U.S. Atomic Energy Commission. 443
N. D. DUDEY, R. R. HEINRICH and A. A. MADSON
444
2. EXPERIMENTAL
2.1 Irradiations The monoenergetic neutrons were produced by means of the ‘Li (p, n)‘Be reaction using the Argonne 4 MeV Van de Graaff accelerator. The lithium targets were prepared by evaporating metallic lithium onto the inside of a 0.025 cm thick tantalum cup. The target thicknesses were measured by the proton stopping power in lithium at the reaction threshold. During irradiations the targets were rotated at speeds up to 600 rev/min and the tantalum cup was sprayed with a fine mist of cooled alcohol to reduce local heating. This permitted beam current intensities as large as 50 ,uA to be run for up to 6 hr without experiencing any serious deterioration of the lithium. Typical irradiation times for the vanadium and titanium, however, were about 30 min. “‘U
FOIL
ROTATING Ta CAP
t FISSION
FIG. l.--Schematic
COUNTER
drawing of experimental arrangement
for fast neutron irradiations.
The targets were irradiated in the form of a natural metallic disc of 1 cm dia. Thicknesses varied between O-130 cm and O-270 cm for vanadium and 0.250 cm and O-263 cm for titanium. Isotopic abundance of 51Vwas 99.76 per cent and that of 50Ti was 5.34 per cent. The purity of the target materials was examined by thermal neutron activation and high resolution Ge(Li) detectors were utilized to assure that no impurities were present which would interfere with subsequent counting. The targets were usually sandwiched between gold secondary monitor foils of about 0.0013 cm thickness and placed in direct contact with the backing material of a 235Ufission monitor. These packets were irradiated with and without a 0.0165 cm cadmium cover in order to examine the effects of room-scattered low energy neutrons. A schematic diagram of the experimental arrangement is shown in Fig. 1. All targets were irradiated at 0” to the proton beam axis. The size of the proton beam spot was measured for each irradiation and varied between O-151 cm2 and 1.080 cm2. The integrity of the lithium targets was continuously monitored for each proton energy by comparing the number of fissions per PC of protons striking the tantalum cup as a function of time. Neutron source-to-fission counter distances varied between 1.0 cm and 2.5 cm.
Fast neutron capture by vanadium and titanium
2.2 Neutronjlux
445
monitoring
The gold foils sandwiching the targets were intended as secondary monitors and their thicknesses were kept sufficiently small to assure that only a negligible number of neutrons would be removed from the beam. The primary neutron flux monitor was a 235U fission chamber similar in construction to that described by FRIGERIO(1965). This chamber is of lightweight construction to minimize backscatter and is operated as a flow counter with P-10 gas at 2-3 psig. The 235Uwas vacuum evaporated onto a 0.013 cm platinum backing foil which served as one plate of a parallel-plate ionization chamber. Under experimental conditions, fission spectra similar to the pulse-height
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distribution shown in Fig. 2 were obtained. The 235U deposit was sufficiently thin enabling the alpha particle and fission counts to be clearly resolved. By minimizing electronic noise, sufficient fission-fragment resolution was obtained to observe the typical ‘double-humped’ fission fragment distribution. In addition to recording the pulse-height spectra, all fission fragments above -10 MeV energy were integrated and recorded as a function of time. These data enabled corrections to be made for neutron flux variations throughout each individual irradiation. The efficiency of this chamber was estimated to be 98 per cent of 271 geometry and 99 per cent of the fragments measured are above the ~10 MeV cut-off. The 235Ufission foil was 1 cm dia. and weighed 285 ,ug. This amount was determined both by weighing and by alpha pulse analysis. Isotopic composition was 93.34% 235U, 10.35 % 2W, 4.83 % 236Uand 5.15 % 238U, and was determined by mass spectrometry and alpha pulse analysis. The number of 235U atoms on the foil are thought to be known to better than 1 per cent.
446
N.
D. DUDEY, R. R. HEINRICHand A. A. MADSON
2.3 Gamma-ray counting of irradiated targets
The decay scheme characteristics pertinent to the “V (n, y) %V and 50Ti (n, r) SITi reactions are shown in Figs. 3 and 4, respectively. The gamma rays of energy l-434 MeV were counted in the case of 62Vand O-320 MeV for 51Ti. The irradiated samples were counted either on a 2 x 1 in. NaI(T1) detector at about 45 per cent geometry or on a 20 cc Ge(Li) detector at about 25 per cent counting geometry. Both gamma-ray detectors were coupled to a 4096-channel pulse-height analyzer. The samples were
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3.-Level and decay characteristics of ‘IV and 9,
in a multi-spectrum scaling mode such that 16 individual counts of 256 channels each were recorded with a dwell time variance sufficient to provide l-3 per cent counting statistics at the peak of interest. The initial counts were started about O-8min after the end of the irradiation and the activity was followed over a period of at least three half-lives. Detector calibration was accomplished in the following manner. System linearity and relative detector efficiency were determined from the known gamma-ray energies and branching ratios of 152E~-154E~and laoTb. The relative efficiencies were converted to absolute values by normalizing to calibrated standards of s7Co, 13’Cs, lWs, “Mn and Wo. These standards were prepared from absolutely calibrated solutions obtained from Amersham Radiochemical Center and National Bureau of Standards.
counted
447
Fast neutron capture by vanadium and titanium
Duplicate standards of @‘Coand gomYcalibrated in our laboratory by y-y coincidence counting, and 13’Cs calibrated mass spectrometrically were also used to aid integrity to the efficiency curves. Each counting standard was prepared in the form of a pellet having the same diameter, thickness and similar matrix composition as the actual vanadium and titanium target samples. Independent sets of pellet standards were prepared for the NaI(T1) and Ge(Li) detectors because of their different intrinsic efficiencies. e
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FIG. 4.-Level and decay characteristics of 50Tiand 61Ti. 3. RESULTS Experimental cross section calculation considerations
A computer code Nucaps has been written to perform many of the required corrections and to carry out the necessary computations to transform the raw data into capture cross sections. The essential features of Nucaps are described only superficially here. The proton energy incident upon the lithium target is computed from the potentiometer setting of the Van de Graaff energy magnets at the operating condition and the settings at the (p, n) reaction threshold. The proton energy loss or spread in proton energy throughout the lithium target is determined from a range-energy relationship of protons on lithium. The spread in neutron energy and the angle subtended by the
448
N. D. DUDEY,R. R. HEINRICH and A. A. MADSON
sample target and fission foil are computed from several parameters: the proton energy and energy spread, the area of the proton spot, the area of the target, the distance between the neutron source and target, and finally, a kinematic calculation of the neutron energy as a function of proton energy and angle. Average energies of the neutrons incident upon the fission foil, the gold secondary monitor foils, and both the front and back of the sample target are independently calculated and a correction made for the angular distribution of neutrons. The number of neutrons incident upon the 235Umonitor foil is computed from the (n,f) cross section, the total number of observed fissions, the duration of the irradiation, and the weight and isotopic composition of the 235Ufoil. Since the fission foil was only 93.34 per cent 235U, it was necessary to correct for (n,f) contributions resulting from =U, 23sU and 23*U. All fission cross section values were taken from those recommended by HUGHES (1966). The neutron flux incident upon the gold monitor foils and on each sample target was determined by computing the solid angle intercepted by a sample and appropriately relating this value to the solid angle and the neutron flux intercepted by the fission foil. The solid angles were computed from approximate solutions to integral equations determined by JAFFEY(1954) and take into consideration the area and thickness of both the neutron source (lithium target) and the sample targets. The computer code also corrects the gamma-ray counting data for decay during the counting time, fits the data by the least-squares method to the appropriate halflives, and computes the counting rate at the end of the irradiation with the associated error. The number of radioactive atoms produced in the irradiation is computed from the decay rate, half-life, duration of the irradiation, detector efficiency, and decay properties of the nuclide. The capture cross section is then computed from the number of target atoms determined from the weight, isotopic abundance and chemical composition of the sample target, the neutron flux on the target, and the number of product atoms produced in the irradiation. Two additional corrections not yet incorporated into Nucaps were also made. Above neutron energies of -700 keV, a second group of low energy neutrons are produced in the ‘Li(p, n)‘Be reaction. The intensity of this second group relative to the first group is a function of both energy and angle. The calculated cross sections have been corrected for this second neutron group by means of the data reported by BEVINGTON (1961) and A. B. SMITH(Private communication). Corrections were made for variations in neutron intensities during each irradiation and were in general f2 to +4 per cent. No corrections were made for neutron scattering or self-absorption. A worse case calculation of the sample scattering correction factor following the procedure of SCHMITT(1960) indicated less than a 2 per cent correction for the vanadium targets and much less than a 1 per cent correction for the titanium targets. 4. RESULTS 4.1 Capture cross section results The capture cross sections for 51Vand 50Ti are given in Tables 1 and 2, respectively. These data together with the results of previous investigations are shown in Figs. 5 and 6. The error bars indicate the rms standard deviation in the absolute values of the cross sections, the horizontal bars at the bottom of the figures represent the neutron
Fast neutron capture by vanadium and titanium
449
TABLEI.-CAPTURE CROSSSECTIONS OF 9 Neutron energy ocev)
Energy* spread WV)
139 163 170 204 240 272 326 337 377 379 402 444 472 503 511 577 645 727 789 848 898 939 985 1048 1125 1197 1292 1385 1488 1659
79.4 79.9 31.9 51.6 51.6 78.9 80.1 35.3 53.5 84.5 37.0 37.2 45.4 59.4 9@3 93.4 89.4 92.2 53.6 96.5 98.4 99.9 56.9 104 107 109 79.2 86.1 83.5 92.1
Cross? section G-W 11.98 8.68 11.87 5.81 5.09 4.80 4.90 4,66 3.37 3.24 3.87 4.19 2.66 2.47 2.11 2.14 2.23 1.92 2.52 1.69 1.67 1.94 2.38 1.95 1.72 1.77 2.21 1.68 2.01 2.65
f k f zt
0.87 0.65 1.07 0.50 ??0.47 5 0.42 * 040 i 0.38 k 0.29 f 0.27 i 0.28 & 0.38 rt 0.23 rt 0.23 i 0.16 i 0.17 5 0.17 5 0.15 i 0.23 f 0.15 f 0.13 f 0.18 f 0.17 f 0.19 * 0.16 f 0.16 * 0.19 A 0.16 * 0.20 & 0.20
* One-half the full neutron energy spread. t Errors quoted as the standard deviation in the absolute value of the cross section.
energy spread associated with the datum point above it, and the solid line represents theoretical calculations which are discussed later in detail. The arrows on the abscissa represent energy levels in the target nucleus. 4.2 Error analysis The principal sources of error associated with these measurements are summarized in Table 3. Unless noted, all uncertainties discussed in this paper are in terms of standard deviation and the errors related to each were estimated as a percentage uncertainty. Many of the values listed in Table 3 are the range of values for all measurements, whereas the quoted values on the reported results have been determined on the basis of each individual measurement. Uncertainties in the neutron source-to-target distance and in the shape of the proton beam spot deserve particular consideration because they affect both the neutron energy and neutron flux. As was previously mentioned, the lithium targets were evaporated on the inside of a tantalum cup which was rotated during proton bombardment. This cup is constructed concave toward the proton beam so that unless the proton beam is focused exactly in the center of the beam pipe, the circle of lithium
4.50
N. D. DUDEY, R. R. HEINRICHand A. A. MADSON TABLE 2.-CAPTURE
CROSS SECTIONS OF 60Ti
Neutron energy
Energy* spread
Cross7 section
otev)
@eV)
(mb)
140 230 337 355 413 448 486 523 550 571 605 650 702 749 808 847 897 929 1025 1096 1177 1206 1292 1363 1428 1540 1645
51.5 52.2 34.9 65.1 37.0 48.3 44.1 49.7 49.9 50.4 45.7 51.6 47.0 53.4 52.8 55.3 54.2 73.3 75.1 748 78.0 65.9 79.1 68.0 82.7 70.7 106.1
1.132 0.768 0.563 0.414 0.246 0.211 0.382 0.285 0.472 0.553 0.593 0.518 0.591 0.443 0.559 0.577 0.595 0.528 0.745 0.753 0606 0.730 0.808 0.867 0.730 0.989 0.741
& f f rt f f f f i * ,. f f * f f f & f f f f f f * + f
0131 0.075 0051 0.036 0.031 0.019 0.038 0.026 0.042 0.050 0.063 0.045 0.056 OMO 0.054 0.052 0.055 0.053 0.089 0.067 0.056 0.059 0.079 0073 0.066 0.106 0.110
* One-half the full neutron energy spread. t Errors quoted as the standard deviation in the absolute value of the cross section.
atoms bombarded will not be precisely perpendicular to the proton beam. The result will appear as an uncertainty in the neutron source-to-target distance. The extreme variation in this distance was measured and maintained at about O-8mm. The size of the proton beam striking the lithium target was measured by stopping the protons in quartz and measuring the dimensions of the beam from the quartz fluorescence. This beam spot area is subject to a slight uncertainty since the outline of the quartz fluorescence is not sharp and the protons are probably not uniformly distributed throughout the area. A propagation-of-error analysis indicates that an error of 5 per cent in the sourceto-target distance and a 10 per cent error in the area of the beam spot will result in an error of i 13 per cent in the calculated solid angle and a 6 18 per cent error in the factor which relates the flux on the fission foil to the flux averaged over the titanium and vanadium targets. The influence of these uncertainties upon the final cross section values has been evaluated with the aid of Nucaps. We have reprocessed all of our vanadium data by changing the source-to-target distance by 1.6 mm. The average effect was a 1.6 per cent change in the average neutron energy seen by the target and a 10.4 per cent change in the calculated neutron flux averaged over the target. Secondly, we reprocessed all the vanadium data assuming a point source of protons and hence a point source of neutrons. Again averaging over all vanadium targets, we found that
451
Fast neutron capture by vanadium and titanium
1 .
THIS
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FIG. 5.-Capture
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FIG. 6.-Capture
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(keV)
cross section of 50Ti.
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452
N. D. DUDEY, R. R.
HEINRICHand A. A. MADSON
TABLEJ.--ESTIMATESOF UNCERTAINTIES IN THE ABSOLUTE VALUES OF THE CAPTURECROSSSECTION; FOR V AND Ti Per cent error (Standard deviation) Source of uncertainty
Detection efficiency Ge(Li) NaI(T1) Decay scheme Neutron scattering zs5U(n,f) cross section* Counting statistics Sourceto-target distance (0.8 mm) Dimensions of proton beam spot Neutron energy
5W(n,y)5W
zt3 *4 +2 *(z) ‘(z:) 5 (l-4)
5oTi(n,y)51Ti *5 f5 *2 ZIJ f4 i(l-3) ?c (3-10) *lo f (14)
* Includes effects due to uncertainties in neutron energy, number of fission foil atoms, and isotopic composition.
the average neutron energy increased by 5.5 per cent and the neutron flux increased by 2.6 per cent. Since the corrections for the beam spot size were made to an estimated accuracy of f18 per cent, the overall influence of this uncertainty upon the reported cross sections is about i-1 per cent. The effects of source-to-target distances are more difficult to assess. Our measurements were uniformly averaged over this variation in distance because the rate of rotation was large compared to the irradiation time; thus in principle, the error in flux and average neutron energy would be negligible and the spread in neutron energy would be increased by at most 1.6 per cent. We conclude that the combined effect of these two dimensional uncertainties results in a f2 per cent uncertainty in both the average neutron energy and neutron flux seen by the vanadium target. Combining these uncertainties with those shown in Table 3, we estimate the uncertainty in the mid-point or average neutron energy to be f3 per cent on the fission foil, and f4 per cent on the vanadium and titanium targets. Errors associated with the determination of the neutron flux involve fission-counter counting statistics, fluctuations in the beam current, uncertainties associated with the fission cross sections, the effects of a 3 per cent error in the neutron energy upon the fission cross section, the uncertainty in the number of atoms in the fission foil, and the solid angle corrections. The secondary gold monitor foils sandwiching the target provide an additional check on the neutron flux averaged over the sample target and enable realistic error assessments. The average number of neutrons seen by the two gold foils surrounding the target corresponds to the average number of neutrons seen by the target. The difficulty with flux determinations based upon gold is the uncertainty in its capture cross section (see for example BARRY (1964) and HARRIS (1965)). This error may be as large as 15 per cent, W. P. POENITZ (Private communication). However, using the recommended gold cross-sections (HUGHES, 1966) we found the neutron flux based on gold to be 6 per cent lower than the values determined from235U when averaged over all titanium and vanadium measurements. Thus, the neutron intensities determined from the two monitors agree well within the estimated uncertainties. Where the agreement between the two monitors was within f6 per cent, the flux determined by the 235U monitor alone was used in the calculations. For the few measurements in
Fast neutron capture by vanadium and titanium
453
which the gold and 235Umonitors did not agree within +6 per cent, a weighted flux average was used. In this weighted average the influence of the 235Umonitored flux was about four times greater than the flux monitored by gold. As a result, the total uncertainty in the neutron flux seen by the titanium and vanadium targets has been evaluated to be between f5 and i8 per cent. The principal errors associated with counting arise from uncertainties in the detector calibrations. Larger errors are estimated for the NaI(TI) detector because of uncertainties resulting from spectral resolution of the 152E~ and l@‘Tb used for the relative efficiency determinations. Overall counting errors are estimated to contribute about f6 per cent error in the final cross sections. Additional uncertainties result in the correction for proton beam current fluctuations. This correction factor is thought to be accurate to &lo per cent. A f10 per cent uncertainty has also been assigned to the second group correction factor. Both of these correction terms were normally small (less than 10 per cent). The uncertainties on the cross sections reported in Tables 1 and 2 have been individually evaluated but on the average are &8.5 per cent in the absolute cross section for 51V and 9.9 per cent for 50Ti. 4.3 Comparison with other experimental results No other capture cross sections have been reported for 50Ti over the energy range covered by these experiments. Cross sections of 2.3 f O-6mb at 24 keV and 0.56 mb at 2.5 MeV have been reported by VERVIER(1959) and PASECHNICK(1958), respectively, which are in agreement with reasonable extrapolations of our results. The neutron-capture cross sections of 51Vhave been reported by STAVISSKII (1962) and JOHNSRUD(1959) over the same energy region as those reported here. Their data have been renormalized to the values recommended by HUGHES(1966) and are compared to our results in Fig. 5. Stavisskii’s values were actually measured relative to the 12’I(n, r) cross section which was in turn measured relative to “5U(n,f). He estimates the 12’1cross section accuracy to be f2 to f5 per cent, and we estimate the renormalized 235U(n,j) cross section to 13 per cent. Johnsrud’s values were obtained by counting relative to the 51V thermal (n, r) cross section, which when renormalized to 5.0 b is probably accurate to f3 to *5 per cent. Neither author reports total uncertainties on his results. Between 140 keV and about 500 keV, our values are about 25 per cent above the other two measurements. LYON(1959), using a photoneutron source, has reported a measurement at 195 keV relative to l151n(n, y). This point is in excellent agreement with our data. Above 500 keV our values are about 10 per cent above Johnsrud’s and 30 per cent above Stavisskii’s. The overall discrepancies are probably not outside the limits of the combined errors. We have shown that neglecting the effect of proton-beam spot size would lower our values by about 3 per cent. The use of absolute detector calibration, rather than counting relative to a thermal cross-section, decreases our errors by l-2 per cent, but other correction factors are not directly comparable. Definite structure is observed in our values which was not apparent in the previous measurements and the significance of this structure will be discussed in the next section.
454
N. D. DUDEY,
R. R. HEMRICH
and
A. A.
MADSIN
5. DISCUSSION 5.1 Theoretical considerations
One of the purposes of measuring these reactions was to examine the accuracy with which theoretical models employing a consistent set of parameters could be used to predict the reaction cross sections. The formalism for describing energy-averaged compound nuclear cross sections was originally developed by WOLFENSTEIN (195 1) and HAUSER(1952). MARGOLIS(1952) and LANE (1957) extended the theory to include fast neutron capture and most recently MOLDAUER(1964) has applied R-matrix theory and included neutron-width fluctuation corrections to calculate energy-averaged cross sections. Numerous authors (RAE, 1958; NEMIROVSKY, 1963; GRENCH, 1967; and STUPEGIA,1968) have compared the results of various forms and modifications of the theory to experimentally measured fast-neutron capture cross-section values. TABLE~--FIXED OPTICALAND STATISTICAL MODEL PARAMETERS
Parameter Real well depth Imaginary well depth Rear welf r, 1 &in-orbit well deoth seal diffuseness ’ Imaginary diffuseness Imaginary well rO Spin-orbit rO Level density parameter a Spin cut-off parameter u Neutron binding energy in S1Ti Neutron binding energy in ?
Value 46 MeV 14 MeV 1.25 f 7 MeV 0.65 0.47
f f
1.25 f 1.25 f A/8 (Me%-’ 3 6.319 MeV 7.309 MeV
We have performed theoretical calculations for the capture cross sections of slV and 50Ti using the theoretical description of MOLDAUER (1964). The results of these calculations are shown as the solid lines in Figs. 5 and 6. The computations were performed with the Nearrex computer code (MOLDAUER, ENGELBRECHT and DUFFY, 1964) and with optical model transmission coefficients obtained from the Abacus-II code (AUERBACH,1962) using a local potential. The details of the calculation have been given elsewhere (STUPEGIA,1968 and MOLDAUER,1964). Thevaluesof theparameters used in the calculations are summarized in Table 4, the optical model parameters are similiar to the recommendation of MOLDAUER(1963). In this formalism the only free parameter is Q/D, the ratio of the observed average radiation width to the observed level spacing at the neutron binding energy for states populated by S-wave neutrons only. The parameter, I’y/D, was varied to give a visually determined best fit to the experimental data. The extracted values of I’y/D are 1.5 x 10e4 for neutron capture by 61Vand 3.5 x 10m6for capture by 50Ti. The 51Vdata is fit reasonably well by this description up to about 1400 keV; however, the agreement between theory and experiment for 50Ti is poor. The calculation using the Nearrex code is a numerical method for computing energy averages of integrated compound nuclear capture cross sections. It is only expected to describe the general behavior of the capture cross section. Figure 5 shows that a consistent set of parameters can be used to describe the 51Vcross section
Fast neutron capture by vanadium and titanium
455
up to about 1400 keV. Above about 1 MeV the calculated values are low, principally because of 1 > 0 contributions from the incoming neutrons. The high energy region of the aV reaction could be fit better by increasing the level density by the parameters a, CJ,or a pairing energy. However, it is not the purpose of this study to examine the influence of several parameters. The significant feature of the measured reactions is the sizeable fluctuations of the cross section about a smooth average. The presence of resonance structure in capture cross sections is adequately explained by the Breit-Wigner formula when l?y/D Q 1. Both 50Ti and slV have filledf; neutron shells; therefore, the relatively large level spacing in these nuclei might result in resonance phenomena being observable up to several hundred keV. If the energy spread of the neutron beam is sufficiently narrow, the result is that a complete statistical averaging of the levels is not obtained. Thus, as the neutron energy is varied, fluctuations in the number, width, and interferences of the levels being excited could appear as fluctuations in the observed cross sections. MOLDAUER(1967) has pointed out that if a sufficient number of levels are excited to obtain a statistical average, the occurrence of strongly absorbing channels can be expected to give rise to a broad distribution of resonance widths and strengths which could result in cross section fluctuations or intermediate structure resonances. A third explanation of the structure would be the presence of doorway states in which the entrance channel is coupled with only a relatively few 2-particle l-hole states. These are in turn coupled to the compound nuclear states. This would result in an ‘accidental’ correlation of resonance contributions observable as intermediate structure in relatively poor resolution cross section measurements. It might be expected that doorway state resonances would be relatively broad (approximately 100 keV) and would have spacings of about 100-200 keV (FESHBACH,1967). Although quantitative predictions of the observed structure in the capture cross sections is very difficult, the the theoretical evidence that structure could exist is abundant. ROHR (1967) has measured the total neutron cross section of aV between 20 and 200 keV and reports an S-wave neutron level spacing of 9.78 keV after correcting for missed levels. BAUMAN,BILPUCHand NEWSON(1962) have reported the total neutron cross section of 50Ti between 40 and 390 keV and find an S-wave level spacing of 123 & 50 keV. From this data and our extracted values of I’y/D, we obtain an average radiation width I’y of 1.5 eV for 51V and 0.6 eV for 50Ti. Radiation widths extracted from neutron capture data are indirectly determined; therefore, they are dependent upon the applicability of the model and the functional dependencies of the calculations. 5.2 Conclusions The fast neutron capture cross sections of 50Ti and 61Vhave been measured. The low cross sections relative to other reactor structural and fuel-cladding materials would suggest a V-Ti alloy is acceptable for reactor applications. The measurements indicate pronounced structure in the capture cross sections extending up to nearly 1 MeV which is not described by the theoretical calculations. Since codes such as Nearrex are often used in reactor design calculations to predict unmeasured capture cross sections, it is important that users of such calculations be aware of the limitations and reservations inherent’ in the results.
456
N. D. DUDEY, R. R. I-~NRICH and A. A. MADMEN
Acknowledgments-The authors gratefully acknowledge the assistance of C. BUX;G for numerous hours of sample counting, J. W. WILLIAMS for help in target preparation, and Drs. A. B. SMITH, P. A. MOLDAUER, and C. E. CROUTHAMEL for helpful discussions. We wish to thank the operating crews of the 4 MeV Van de Graaff for their cooperation and help. REFERENCES AU~RBACH E. A. (1962) Abacus II, unpublished. BARRYJ. F. (1964) J. nucl. Energy 18, 491. BAUMANC. D., BILPUCHE. G. and NEWMAN H. W. (1962) Ann. Phys. 17,319. FESHBACH H., KERMAN A. K. and LEMMER R. H. (1967) Ann/s Phys. 41,230. GRENCHH. A., Coop K. L., MENU)VEH. 0. and VAUGHN F. J. (1967) Nucl. Phys. A94,157. HARRISK. K., GRENCHH. A., JOHNSON R. G. and VAUGHN F. J. (1965) Nucl. Phys. 69,37. HAUSERW. and FESHBACH H. (1952) Phys. Rev. 87,366. HUGHESD. J. and SCHWARTZ R. B. (1966) Rep. No. BNL-325 (2nd Edn), Suppl. No. 2. JOHNSRUD A. E., GILBERTM. G. and BARSCHALL H. H. (1959) Phys. Rev. 116,927. LANEA. M. and LYNNJ. E. (1957) Proc.phys. Sot. A7O,SS7. LYONW. S. and MACKLINR. L. (1959) Phys. Rev. 114, 1619. MARG~LIS B. (1952) Phys. Rev. 88,327. MOLDAUER P. A. (1963) Nucl. Phys. 47, 65. MOLDAUER P. A. (1964) Phys. Rev. 135, B642. MOLDAUER P. A. (1967) Phys. Rev. Letts. 18, 249. MOLDAUER P. A. (1964) Rev. mod. Phys. 63, 1079. MOLDAIJER P. A., ENGELBRECHT C. A. and DUFFYG. J. (1964) Rep. No. ANL-6978. NEMIROVSKY P. E. and YELAGINY. P. (1963) Nucl. Phys. 45, 156. PASECHNIK M. V., BARCHUK I. F., TOTSKYI. A., STREZHAK V. I., KOROLOV A. M., HOPMAN Y. V., L~VCHEKOVA G. N., KOLTYNINE. A. and YANKOVG. B. (1958) Proc. 2nd Znt. Co@ peaceful Uses atom. Energy 15, 18. RAE E. R., MARG~LIS B. and TROUBETZKOY E. S. (1958) Phys. Rev. 112,492. ROHRG. and FRIEDLAND E. (1967) Nucl. Phys. A104,l. S~IW H. W. (1960) Rep. No. ORNL-2883. STAVISSKII Y. Y. and TOL~TIKOV V. A. (1962) J. nucl. Energy 16,496. STUPEGIA D. C., SCHMXDT M., KEEDYC. R. and MADMEN A. A. (1968) J. nucl. Energy 22,267. VERVIER J. F. (1959) Nucl. Phys. 9, 569. WOLFENSTEIN L. (1951) Phys. Rev. 82,690.
FAST NEUTRON N.
CAPTURE BY VANADIUM TITANIUM*
AND
D. DUDEY, R. R. HEINRICH and A. A. MADSON
Argonne National Laboratory,
9700 South Cass Avenue, Argonne, Ill. 60439, U.S.A. (Received 17 April 1969)
Abstract-Fast neutron capture cross sections of 51V and 5oTi have been measured by the activation method as a function of neutron energy between about 150 keV and 1.7 MeV. These cross sections were measured relative to both the zseU(n, f) cross section and the lg7Au(n, y)1“8A~ cross section. Neutrons were produced by the rLi(p, n)‘Be reaction from a Van de Graaff accelerator. The uncertainties on the absolute activation cross sections are rt8.5 per cent for Y and 59.9 per cent for 6oTi and were evaluated with the aid of a computer code which is described. A complete error analysis is given. The data have been compared with calculations based upon the statistical compound nucleus model of nuclear reactions. The significant feature of the measured reactions is the sizeable fluctuations of the cross section about a smooth average which cannot be described by the theoretical calculations. Possible explanations for this observed structure are given. 1. INTRODUCTION
of fast-neutron processes is essential to the design and development of fast-breeder reactors. Accurate measurements and calculations of neutroncapture cross sections for structural and fuel-cladding material are essential to the understanding and description of neutron energy and flux degradation processes occurring in nuclear reactors. Alloys of vanadium and titanium are one of the types of fuel-cladding materials being considered for future fast reactors. At present, only a few measurements have been reported by JOHNSRUD (1959) and STAVISSKII (1962) for fast-neutron capture on vanadium over the energy range of principal interest to fast-reactor design (10 keV-3 MeV). No measurements have been reported for the capture cross sections on titanium between 30 keV and 2.5 MeV. For these reasons we have measured the neutron capture cross sections of 51Vand “Ti as a function of neutron energy between about 150 keV and 1.7 MeV. In addition to the direct practical application to reactor technology, capture cross sections are of considerable importance in evaluating theoretical models which may be used to calculate these and other important nuclear parameters. The statistical model has been widely used with varying degrees of success to predict nuclear properties, including energy-averaged cross sections. The work presented here provides a means for examining the accuracy of the statistical model of nuclear reactions. The 51Vand 60Ti capture cross sections were measured by means of the activation technique. The samples were irradiated in a monoenergetic neutron beam and the radioactive products were identified and counted from their characteristic gamma rays. The results are compared to theoretical values calculated from a self-consistent set of optical model and statistical model parameters. These parameters have been derived from other independent experiments and are expected to describe adequately the reactions reported in this work.
AN UNDERSTANDING
* Work performed under the auspices of the U.S. Atomic Energy Commission. 443
N. D. DUDEY, R. R. HEINRICH and A. A. MADSON
444
2. EXPERIMENTAL
2.1 Irradiations The monoenergetic neutrons were produced by means of the ‘Li (p, n)‘Be reaction using the Argonne 4 MeV Van de Graaff accelerator. The lithium targets were prepared by evaporating metallic lithium onto the inside of a 0.025 cm thick tantalum cup. The target thicknesses were measured by the proton stopping power in lithium at the reaction threshold. During irradiations the targets were rotated at speeds up to 600 rev/min and the tantalum cup was sprayed with a fine mist of cooled alcohol to reduce local heating. This permitted beam current intensities as large as 50 ,uA to be run for up to 6 hr without experiencing any serious deterioration of the lithium. Typical irradiation times for the vanadium and titanium, however, were about 30 min. “‘U
FOIL
ROTATING Ta CAP
t FISSION
FIG. l.--Schematic
COUNTER
drawing of experimental arrangement
for fast neutron irradiations.
The targets were irradiated in the form of a natural metallic disc of 1 cm dia. Thicknesses varied between O-130 cm and O-270 cm for vanadium and 0.250 cm and O-263 cm for titanium. Isotopic abundance of 51Vwas 99.76 per cent and that of 50Ti was 5.34 per cent. The purity of the target materials was examined by thermal neutron activation and high resolution Ge(Li) detectors were utilized to assure that no impurities were present which would interfere with subsequent counting. The targets were usually sandwiched between gold secondary monitor foils of about 0.0013 cm thickness and placed in direct contact with the backing material of a 235Ufission monitor. These packets were irradiated with and without a 0.0165 cm cadmium cover in order to examine the effects of room-scattered low energy neutrons. A schematic diagram of the experimental arrangement is shown in Fig. 1. All targets were irradiated at 0” to the proton beam axis. The size of the proton beam spot was measured for each irradiation and varied between O-151 cm2 and 1.080 cm2. The integrity of the lithium targets was continuously monitored for each proton energy by comparing the number of fissions per PC of protons striking the tantalum cup as a function of time. Neutron source-to-fission counter distances varied between 1.0 cm and 2.5 cm.
Fast neutron capture by vanadium and titanium
2.2 Neutronjlux
445
monitoring
The gold foils sandwiching the targets were intended as secondary monitors and their thicknesses were kept sufficiently small to assure that only a negligible number of neutrons would be removed from the beam. The primary neutron flux monitor was a 235U fission chamber similar in construction to that described by FRIGERIO(1965). This chamber is of lightweight construction to minimize backscatter and is operated as a flow counter with P-10 gas at 2-3 psig. The 235Uwas vacuum evaporated onto a 0.013 cm platinum backing foil which served as one plate of a parallel-plate ionization chamber. Under experimental conditions, fission spectra similar to the pulse-height
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distribution shown in Fig. 2 were obtained. The 235U deposit was sufficiently thin enabling the alpha particle and fission counts to be clearly resolved. By minimizing electronic noise, sufficient fission-fragment resolution was obtained to observe the typical ‘double-humped’ fission fragment distribution. In addition to recording the pulse-height spectra, all fission fragments above -10 MeV energy were integrated and recorded as a function of time. These data enabled corrections to be made for neutron flux variations throughout each individual irradiation. The efficiency of this chamber was estimated to be 98 per cent of 271 geometry and 99 per cent of the fragments measured are above the ~10 MeV cut-off. The 235Ufission foil was 1 cm dia. and weighed 285 ,ug. This amount was determined both by weighing and by alpha pulse analysis. Isotopic composition was 93.34% 235U, 10.35 % 2W, 4.83 % 236Uand 5.15 % 238U, and was determined by mass spectrometry and alpha pulse analysis. The number of 235U atoms on the foil are thought to be known to better than 1 per cent.
446
N.
D. DUDEY, R. R. HEINRICHand A. A. MADSON
2.3 Gamma-ray counting of irradiated targets
The decay scheme characteristics pertinent to the “V (n, y) %V and 50Ti (n, r) SITi reactions are shown in Figs. 3 and 4, respectively. The gamma rays of energy l-434 MeV were counted in the case of 62Vand O-320 MeV for 51Ti. The irradiated samples were counted either on a 2 x 1 in. NaI(T1) detector at about 45 per cent geometry or on a 20 cc Ge(Li) detector at about 25 per cent counting geometry. Both gamma-ray detectors were coupled to a 4096-channel pulse-height analyzer. The samples were
7.309
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-
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1.81 1.6,
0.93
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FIG.
3.-Level and decay characteristics of ‘IV and 9,
in a multi-spectrum scaling mode such that 16 individual counts of 256 channels each were recorded with a dwell time variance sufficient to provide l-3 per cent counting statistics at the peak of interest. The initial counts were started about O-8min after the end of the irradiation and the activity was followed over a period of at least three half-lives. Detector calibration was accomplished in the following manner. System linearity and relative detector efficiency were determined from the known gamma-ray energies and branching ratios of 152E~-154E~and laoTb. The relative efficiencies were converted to absolute values by normalizing to calibrated standards of s7Co, 13’Cs, lWs, “Mn and Wo. These standards were prepared from absolutely calibrated solutions obtained from Amersham Radiochemical Center and National Bureau of Standards.
counted
447
Fast neutron capture by vanadium and titanium
Duplicate standards of @‘Coand gomYcalibrated in our laboratory by y-y coincidence counting, and 13’Cs calibrated mass spectrometrically were also used to aid integrity to the efficiency curves. Each counting standard was prepared in the form of a pellet having the same diameter, thickness and similar matrix composition as the actual vanadium and titanium target samples. Independent sets of pellet standards were prepared for the NaI(T1) and Ge(Li) detectors because of their different intrinsic efficiencies. e
1
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5oTi + n
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2.66
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FIG. 4.-Level and decay characteristics of 50Tiand 61Ti. 3. RESULTS Experimental cross section calculation considerations
A computer code Nucaps has been written to perform many of the required corrections and to carry out the necessary computations to transform the raw data into capture cross sections. The essential features of Nucaps are described only superficially here. The proton energy incident upon the lithium target is computed from the potentiometer setting of the Van de Graaff energy magnets at the operating condition and the settings at the (p, n) reaction threshold. The proton energy loss or spread in proton energy throughout the lithium target is determined from a range-energy relationship of protons on lithium. The spread in neutron energy and the angle subtended by the
448
N. D. DUDEY,R. R. HEINRICH and A. A. MADSON
sample target and fission foil are computed from several parameters: the proton energy and energy spread, the area of the proton spot, the area of the target, the distance between the neutron source and target, and finally, a kinematic calculation of the neutron energy as a function of proton energy and angle. Average energies of the neutrons incident upon the fission foil, the gold secondary monitor foils, and both the front and back of the sample target are independently calculated and a correction made for the angular distribution of neutrons. The number of neutrons incident upon the 235Umonitor foil is computed from the (n,f) cross section, the total number of observed fissions, the duration of the irradiation, and the weight and isotopic composition of the 235Ufoil. Since the fission foil was only 93.34 per cent 235U, it was necessary to correct for (n,f) contributions resulting from =U, 23sU and 23*U. All fission cross section values were taken from those recommended by HUGHES (1966). The neutron flux incident upon the gold monitor foils and on each sample target was determined by computing the solid angle intercepted by a sample and appropriately relating this value to the solid angle and the neutron flux intercepted by the fission foil. The solid angles were computed from approximate solutions to integral equations determined by JAFFEY(1954) and take into consideration the area and thickness of both the neutron source (lithium target) and the sample targets. The computer code also corrects the gamma-ray counting data for decay during the counting time, fits the data by the least-squares method to the appropriate halflives, and computes the counting rate at the end of the irradiation with the associated error. The number of radioactive atoms produced in the irradiation is computed from the decay rate, half-life, duration of the irradiation, detector efficiency, and decay properties of the nuclide. The capture cross section is then computed from the number of target atoms determined from the weight, isotopic abundance and chemical composition of the sample target, the neutron flux on the target, and the number of product atoms produced in the irradiation. Two additional corrections not yet incorporated into Nucaps were also made. Above neutron energies of -700 keV, a second group of low energy neutrons are produced in the ‘Li(p, n)‘Be reaction. The intensity of this second group relative to the first group is a function of both energy and angle. The calculated cross sections have been corrected for this second neutron group by means of the data reported by BEVINGTON (1961) and A. B. SMITH(Private communication). Corrections were made for variations in neutron intensities during each irradiation and were in general f2 to +4 per cent. No corrections were made for neutron scattering or self-absorption. A worse case calculation of the sample scattering correction factor following the procedure of SCHMITT(1960) indicated less than a 2 per cent correction for the vanadium targets and much less than a 1 per cent correction for the titanium targets. 4. RESULTS 4.1 Capture cross section results The capture cross sections for 51Vand 50Ti are given in Tables 1 and 2, respectively. These data together with the results of previous investigations are shown in Figs. 5 and 6. The error bars indicate the rms standard deviation in the absolute values of the cross sections, the horizontal bars at the bottom of the figures represent the neutron
Fast neutron capture by vanadium and titanium
449
TABLEI.-CAPTURE CROSSSECTIONS OF 9 Neutron energy ocev)
Energy* spread WV)
139 163 170 204 240 272 326 337 377 379 402 444 472 503 511 577 645 727 789 848 898 939 985 1048 1125 1197 1292 1385 1488 1659
79.4 79.9 31.9 51.6 51.6 78.9 80.1 35.3 53.5 84.5 37.0 37.2 45.4 59.4 9@3 93.4 89.4 92.2 53.6 96.5 98.4 99.9 56.9 104 107 109 79.2 86.1 83.5 92.1
Cross? section G-W 11.98 8.68 11.87 5.81 5.09 4.80 4.90 4,66 3.37 3.24 3.87 4.19 2.66 2.47 2.11 2.14 2.23 1.92 2.52 1.69 1.67 1.94 2.38 1.95 1.72 1.77 2.21 1.68 2.01 2.65
f k f zt
0.87 0.65 1.07 0.50 ??0.47 5 0.42 * 040 i 0.38 k 0.29 f 0.27 i 0.28 & 0.38 rt 0.23 rt 0.23 i 0.16 i 0.17 5 0.17 5 0.15 i 0.23 f 0.15 f 0.13 f 0.18 f 0.17 f 0.19 * 0.16 f 0.16 * 0.19 A 0.16 * 0.20 & 0.20
* One-half the full neutron energy spread. t Errors quoted as the standard deviation in the absolute value of the cross section.
energy spread associated with the datum point above it, and the solid line represents theoretical calculations which are discussed later in detail. The arrows on the abscissa represent energy levels in the target nucleus. 4.2 Error analysis The principal sources of error associated with these measurements are summarized in Table 3. Unless noted, all uncertainties discussed in this paper are in terms of standard deviation and the errors related to each were estimated as a percentage uncertainty. Many of the values listed in Table 3 are the range of values for all measurements, whereas the quoted values on the reported results have been determined on the basis of each individual measurement. Uncertainties in the neutron source-to-target distance and in the shape of the proton beam spot deserve particular consideration because they affect both the neutron energy and neutron flux. As was previously mentioned, the lithium targets were evaporated on the inside of a tantalum cup which was rotated during proton bombardment. This cup is constructed concave toward the proton beam so that unless the proton beam is focused exactly in the center of the beam pipe, the circle of lithium
4.50
N. D. DUDEY, R. R. HEINRICHand A. A. MADSON TABLE 2.-CAPTURE
CROSS SECTIONS OF 60Ti
Neutron energy
Energy* spread
Cross7 section
otev)
@eV)
(mb)
140 230 337 355 413 448 486 523 550 571 605 650 702 749 808 847 897 929 1025 1096 1177 1206 1292 1363 1428 1540 1645
51.5 52.2 34.9 65.1 37.0 48.3 44.1 49.7 49.9 50.4 45.7 51.6 47.0 53.4 52.8 55.3 54.2 73.3 75.1 748 78.0 65.9 79.1 68.0 82.7 70.7 106.1
1.132 0.768 0.563 0.414 0.246 0.211 0.382 0.285 0.472 0.553 0.593 0.518 0.591 0.443 0.559 0.577 0.595 0.528 0.745 0.753 0606 0.730 0.808 0.867 0.730 0.989 0.741
& f f rt f f f f i * ,. f f * f f f & f f f f f f * + f
0131 0.075 0051 0.036 0.031 0.019 0.038 0.026 0.042 0.050 0.063 0.045 0.056 OMO 0.054 0.052 0.055 0.053 0.089 0.067 0.056 0.059 0.079 0073 0.066 0.106 0.110
* One-half the full neutron energy spread. t Errors quoted as the standard deviation in the absolute value of the cross section.
atoms bombarded will not be precisely perpendicular to the proton beam. The result will appear as an uncertainty in the neutron source-to-target distance. The extreme variation in this distance was measured and maintained at about O-8mm. The size of the proton beam striking the lithium target was measured by stopping the protons in quartz and measuring the dimensions of the beam from the quartz fluorescence. This beam spot area is subject to a slight uncertainty since the outline of the quartz fluorescence is not sharp and the protons are probably not uniformly distributed throughout the area. A propagation-of-error analysis indicates that an error of 5 per cent in the sourceto-target distance and a 10 per cent error in the area of the beam spot will result in an error of i 13 per cent in the calculated solid angle and a 6 18 per cent error in the factor which relates the flux on the fission foil to the flux averaged over the titanium and vanadium targets. The influence of these uncertainties upon the final cross section values has been evaluated with the aid of Nucaps. We have reprocessed all of our vanadium data by changing the source-to-target distance by 1.6 mm. The average effect was a 1.6 per cent change in the average neutron energy seen by the target and a 10.4 per cent change in the calculated neutron flux averaged over the target. Secondly, we reprocessed all the vanadium data assuming a point source of protons and hence a point source of neutrons. Again averaging over all vanadium targets, we found that
451
Fast neutron capture by vanadium and titanium
1 .
THIS
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FIG. 5.-Capture
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(keV)
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FIG. 6.-Capture
ENERGY
(keV)
cross section of 50Ti.
I
t,j I700
452
N. D. DUDEY, R. R.
HEINRICHand A. A. MADSON
TABLEJ.--ESTIMATESOF UNCERTAINTIES IN THE ABSOLUTE VALUES OF THE CAPTURECROSSSECTION; FOR V AND Ti Per cent error (Standard deviation) Source of uncertainty
Detection efficiency Ge(Li) NaI(T1) Decay scheme Neutron scattering zs5U(n,f) cross section* Counting statistics Sourceto-target distance (0.8 mm) Dimensions of proton beam spot Neutron energy
5W(n,y)5W
zt3 *4 +2 *(z) ‘(z:) 5 (l-4)
5oTi(n,y)51Ti *5 f5 *2 ZIJ f4 i(l-3) ?c (3-10) *lo f (14)
* Includes effects due to uncertainties in neutron energy, number of fission foil atoms, and isotopic composition.
the average neutron energy increased by 5.5 per cent and the neutron flux increased by 2.6 per cent. Since the corrections for the beam spot size were made to an estimated accuracy of f18 per cent, the overall influence of this uncertainty upon the reported cross sections is about i-1 per cent. The effects of source-to-target distances are more difficult to assess. Our measurements were uniformly averaged over this variation in distance because the rate of rotation was large compared to the irradiation time; thus in principle, the error in flux and average neutron energy would be negligible and the spread in neutron energy would be increased by at most 1.6 per cent. We conclude that the combined effect of these two dimensional uncertainties results in a f2 per cent uncertainty in both the average neutron energy and neutron flux seen by the vanadium target. Combining these uncertainties with those shown in Table 3, we estimate the uncertainty in the mid-point or average neutron energy to be f3 per cent on the fission foil, and f4 per cent on the vanadium and titanium targets. Errors associated with the determination of the neutron flux involve fission-counter counting statistics, fluctuations in the beam current, uncertainties associated with the fission cross sections, the effects of a 3 per cent error in the neutron energy upon the fission cross section, the uncertainty in the number of atoms in the fission foil, and the solid angle corrections. The secondary gold monitor foils sandwiching the target provide an additional check on the neutron flux averaged over the sample target and enable realistic error assessments. The average number of neutrons seen by the two gold foils surrounding the target corresponds to the average number of neutrons seen by the target. The difficulty with flux determinations based upon gold is the uncertainty in its capture cross section (see for example BARRY (1964) and HARRIS (1965)). This error may be as large as 15 per cent, W. P. POENITZ (Private communication). However, using the recommended gold cross-sections (HUGHES, 1966) we found the neutron flux based on gold to be 6 per cent lower than the values determined from235U when averaged over all titanium and vanadium measurements. Thus, the neutron intensities determined from the two monitors agree well within the estimated uncertainties. Where the agreement between the two monitors was within f6 per cent, the flux determined by the 235U monitor alone was used in the calculations. For the few measurements in
Fast neutron capture by vanadium and titanium
453
which the gold and 235Umonitors did not agree within +6 per cent, a weighted flux average was used. In this weighted average the influence of the 235Umonitored flux was about four times greater than the flux monitored by gold. As a result, the total uncertainty in the neutron flux seen by the titanium and vanadium targets has been evaluated to be between f5 and i8 per cent. The principal errors associated with counting arise from uncertainties in the detector calibrations. Larger errors are estimated for the NaI(TI) detector because of uncertainties resulting from spectral resolution of the 152E~ and l@‘Tb used for the relative efficiency determinations. Overall counting errors are estimated to contribute about f6 per cent error in the final cross sections. Additional uncertainties result in the correction for proton beam current fluctuations. This correction factor is thought to be accurate to &lo per cent. A f10 per cent uncertainty has also been assigned to the second group correction factor. Both of these correction terms were normally small (less than 10 per cent). The uncertainties on the cross sections reported in Tables 1 and 2 have been individually evaluated but on the average are &8.5 per cent in the absolute cross section for 51V and 9.9 per cent for 50Ti. 4.3 Comparison with other experimental results No other capture cross sections have been reported for 50Ti over the energy range covered by these experiments. Cross sections of 2.3 f O-6mb at 24 keV and 0.56 mb at 2.5 MeV have been reported by VERVIER(1959) and PASECHNICK(1958), respectively, which are in agreement with reasonable extrapolations of our results. The neutron-capture cross sections of 51Vhave been reported by STAVISSKII (1962) and JOHNSRUD(1959) over the same energy region as those reported here. Their data have been renormalized to the values recommended by HUGHES(1966) and are compared to our results in Fig. 5. Stavisskii’s values were actually measured relative to the 12’I(n, r) cross section which was in turn measured relative to “5U(n,f). He estimates the 12’1cross section accuracy to be f2 to f5 per cent, and we estimate the renormalized 235U(n,j) cross section to 13 per cent. Johnsrud’s values were obtained by counting relative to the 51V thermal (n, r) cross section, which when renormalized to 5.0 b is probably accurate to f3 to *5 per cent. Neither author reports total uncertainties on his results. Between 140 keV and about 500 keV, our values are about 25 per cent above the other two measurements. LYON(1959), using a photoneutron source, has reported a measurement at 195 keV relative to l151n(n, y). This point is in excellent agreement with our data. Above 500 keV our values are about 10 per cent above Johnsrud’s and 30 per cent above Stavisskii’s. The overall discrepancies are probably not outside the limits of the combined errors. We have shown that neglecting the effect of proton-beam spot size would lower our values by about 3 per cent. The use of absolute detector calibration, rather than counting relative to a thermal cross-section, decreases our errors by l-2 per cent, but other correction factors are not directly comparable. Definite structure is observed in our values which was not apparent in the previous measurements and the significance of this structure will be discussed in the next section.
454
N. D. DUDEY,
R. R. HEMRICH
and
A. A.
MADSIN
5. DISCUSSION 5.1 Theoretical considerations
One of the purposes of measuring these reactions was to examine the accuracy with which theoretical models employing a consistent set of parameters could be used to predict the reaction cross sections. The formalism for describing energy-averaged compound nuclear cross sections was originally developed by WOLFENSTEIN (195 1) and HAUSER(1952). MARGOLIS(1952) and LANE (1957) extended the theory to include fast neutron capture and most recently MOLDAUER(1964) has applied R-matrix theory and included neutron-width fluctuation corrections to calculate energy-averaged cross sections. Numerous authors (RAE, 1958; NEMIROVSKY, 1963; GRENCH, 1967; and STUPEGIA,1968) have compared the results of various forms and modifications of the theory to experimentally measured fast-neutron capture cross-section values. TABLE~--FIXED OPTICALAND STATISTICAL MODEL PARAMETERS
Parameter Real well depth Imaginary well depth Rear welf r, 1 &in-orbit well deoth seal diffuseness ’ Imaginary diffuseness Imaginary well rO Spin-orbit rO Level density parameter a Spin cut-off parameter u Neutron binding energy in S1Ti Neutron binding energy in ?
Value 46 MeV 14 MeV 1.25 f 7 MeV 0.65 0.47
f f
1.25 f 1.25 f A/8 (Me%-’ 3 6.319 MeV 7.309 MeV
We have performed theoretical calculations for the capture cross sections of slV and 50Ti using the theoretical description of MOLDAUER (1964). The results of these calculations are shown as the solid lines in Figs. 5 and 6. The computations were performed with the Nearrex computer code (MOLDAUER, ENGELBRECHT and DUFFY, 1964) and with optical model transmission coefficients obtained from the Abacus-II code (AUERBACH,1962) using a local potential. The details of the calculation have been given elsewhere (STUPEGIA,1968 and MOLDAUER,1964). Thevaluesof theparameters used in the calculations are summarized in Table 4, the optical model parameters are similiar to the recommendation of MOLDAUER(1963). In this formalism the only free parameter is Q/D, the ratio of the observed average radiation width to the observed level spacing at the neutron binding energy for states populated by S-wave neutrons only. The parameter, I’y/D, was varied to give a visually determined best fit to the experimental data. The extracted values of I’y/D are 1.5 x 10e4 for neutron capture by 61Vand 3.5 x 10m6for capture by 50Ti. The 51Vdata is fit reasonably well by this description up to about 1400 keV; however, the agreement between theory and experiment for 50Ti is poor. The calculation using the Nearrex code is a numerical method for computing energy averages of integrated compound nuclear capture cross sections. It is only expected to describe the general behavior of the capture cross section. Figure 5 shows that a consistent set of parameters can be used to describe the 51Vcross section
Fast neutron capture by vanadium and titanium
455
up to about 1400 keV. Above about 1 MeV the calculated values are low, principally because of 1 > 0 contributions from the incoming neutrons. The high energy region of the aV reaction could be fit better by increasing the level density by the parameters a, CJ,or a pairing energy. However, it is not the purpose of this study to examine the influence of several parameters. The significant feature of the measured reactions is the sizeable fluctuations of the cross section about a smooth average. The presence of resonance structure in capture cross sections is adequately explained by the Breit-Wigner formula when l?y/D Q 1. Both 50Ti and slV have filledf; neutron shells; therefore, the relatively large level spacing in these nuclei might result in resonance phenomena being observable up to several hundred keV. If the energy spread of the neutron beam is sufficiently narrow, the result is that a complete statistical averaging of the levels is not obtained. Thus, as the neutron energy is varied, fluctuations in the number, width, and interferences of the levels being excited could appear as fluctuations in the observed cross sections. MOLDAUER(1967) has pointed out that if a sufficient number of levels are excited to obtain a statistical average, the occurrence of strongly absorbing channels can be expected to give rise to a broad distribution of resonance widths and strengths which could result in cross section fluctuations or intermediate structure resonances. A third explanation of the structure would be the presence of doorway states in which the entrance channel is coupled with only a relatively few 2-particle l-hole states. These are in turn coupled to the compound nuclear states. This would result in an ‘accidental’ correlation of resonance contributions observable as intermediate structure in relatively poor resolution cross section measurements. It might be expected that doorway state resonances would be relatively broad (approximately 100 keV) and would have spacings of about 100-200 keV (FESHBACH,1967). Although quantitative predictions of the observed structure in the capture cross sections is very difficult, the the theoretical evidence that structure could exist is abundant. ROHR (1967) has measured the total neutron cross section of aV between 20 and 200 keV and reports an S-wave neutron level spacing of 9.78 keV after correcting for missed levels. BAUMAN,BILPUCHand NEWSON(1962) have reported the total neutron cross section of 50Ti between 40 and 390 keV and find an S-wave level spacing of 123 & 50 keV. From this data and our extracted values of I’y/D, we obtain an average radiation width I’y of 1.5 eV for 51V and 0.6 eV for 50Ti. Radiation widths extracted from neutron capture data are indirectly determined; therefore, they are dependent upon the applicability of the model and the functional dependencies of the calculations. 5.2 Conclusions The fast neutron capture cross sections of 50Ti and 61Vhave been measured. The low cross sections relative to other reactor structural and fuel-cladding materials would suggest a V-Ti alloy is acceptable for reactor applications. The measurements indicate pronounced structure in the capture cross sections extending up to nearly 1 MeV which is not described by the theoretical calculations. Since codes such as Nearrex are often used in reactor design calculations to predict unmeasured capture cross sections, it is important that users of such calculations be aware of the limitations and reservations inherent’ in the results.
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N. D. DUDEY, R. R. I-~NRICH and A. A. MADMEN
Acknowledgments-The authors gratefully acknowledge the assistance of C. BUX;G for numerous hours of sample counting, J. W. WILLIAMS for help in target preparation, and Drs. A. B. SMITH, P. A. MOLDAUER, and C. E. CROUTHAMEL for helpful discussions. We wish to thank the operating crews of the 4 MeV Van de Graaff for their cooperation and help. REFERENCES AU~RBACH E. A. (1962) Abacus II, unpublished. BARRYJ. F. (1964) J. nucl. Energy 18, 491. BAUMANC. D., BILPUCHE. G. and NEWMAN H. W. (1962) Ann. Phys. 17,319. FESHBACH H., KERMAN A. K. and LEMMER R. H. (1967) Ann/s Phys. 41,230. GRENCHH. A., Coop K. L., MENU)VEH. 0. and VAUGHN F. J. (1967) Nucl. Phys. A94,157. HARRISK. K., GRENCHH. A., JOHNSON R. G. and VAUGHN F. J. (1965) Nucl. Phys. 69,37. HAUSERW. and FESHBACH H. (1952) Phys. Rev. 87,366. HUGHESD. J. and SCHWARTZ R. B. (1966) Rep. No. BNL-325 (2nd Edn), Suppl. No. 2. JOHNSRUD A. E., GILBERTM. G. and BARSCHALL H. H. (1959) Phys. Rev. 116,927. LANEA. M. and LYNNJ. E. (1957) Proc.phys. Sot. A7O,SS7. LYONW. S. and MACKLINR. L. (1959) Phys. Rev. 114, 1619. MARG~LIS B. (1952) Phys. Rev. 88,327. MOLDAUER P. A. (1963) Nucl. Phys. 47, 65. MOLDAUER P. A. (1964) Phys. Rev. 135, B642. MOLDAUER P. A. (1967) Phys. Rev. Letts. 18, 249. MOLDAUER P. A. (1964) Rev. mod. Phys. 63, 1079. MOLDAIJER P. A., ENGELBRECHT C. A. and DUFFYG. J. (1964) Rep. No. ANL-6978. NEMIROVSKY P. E. and YELAGINY. P. (1963) Nucl. Phys. 45, 156. PASECHNIK M. V., BARCHUK I. F., TOTSKYI. A., STREZHAK V. I., KOROLOV A. M., HOPMAN Y. V., L~VCHEKOVA G. N., KOLTYNINE. A. and YANKOVG. B. (1958) Proc. 2nd Znt. Co@ peaceful Uses atom. Energy 15, 18. RAE E. R., MARG~LIS B. and TROUBETZKOY E. S. (1958) Phys. Rev. 112,492. ROHRG. and FRIEDLAND E. (1967) Nucl. Phys. A104,l. S~IW H. W. (1960) Rep. No. ORNL-2883. STAVISSKII Y. Y. and TOL~TIKOV V. A. (1962) J. nucl. Energy 16,496. STUPEGIA D. C., SCHMXDT M., KEEDYC. R. and MADMEN A. A. (1968) J. nucl. Energy 22,267. VERVIER J. F. (1959) Nucl. Phys. 9, 569. WOLFENSTEIN L. (1951) Phys. Rev. 82,690.