. . . . . . i S $ T OF .. ORNLP 1082 ha : " .. la . . EEEEEEEE ||1.25 L4 L MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 . . . 4 ' .. ... . -7. . a LY . the 172 . .. . . mult 9. NEREY 4 19. . 1 - '* . A . " . . S. : HS at ., . . 1 .. " * * :' * T: ........ ... 2 4 . 1 t . LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representa- tion, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report For that the use of any information, appa- ratus, method, or process disclosed in this report may not infringe privately owned rights; or the B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. 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ELIT. . > 19 . 3 : 1 11. CH * NE LA T E V PRO YA VA - TL * * it Lt IR 12 4. ST TUT 13 17 'S . ...... ++ - 4. ORNL-8-108! LOTIEP MAR 23 1065 Corp. 65020109 Channel Analysis of Neutron Induced Fisşion of Even-Even Isotopes Near Threshold R. W. Lamphere, Physicist Oak Ridge National Laboratory Oak Ridge, Tennessee MASTER 1. Introduction Since the discovery of fission fragment anisotropy by Winhold, Demos, and Halpern in 1952 (1) many measurements have been made of the angular dis- tribution of fragments from fission induced by various means. Far and away the majority of these have been at high energies, well above the thresholds for fission, so that many channels contribute and statistical methods need be used to analyze the results. The reason for this is, of course, that close to threshold it takes much longer time to acquire a meaningful quantity of data. Very close to threshold where only a few channels are open to fission one can hope to identify these, in terms of I, K, and parity from measure- ments of the fragment angular distribution as function of projectile energy, and use of the theory proposed by A. Bohr. [2] in 1955. According to this theory the nucleus as it passes the saddle point is greatly elongated, say major axis roughly twice that of the minor, to the extent that nearly all the energy brought in by the projectile is concentrated in potential energy of deformation. Under such conditions a structure of K bands will exist based on collective motions, similar to those of the heavy deformed nuclei in and near the ground state. Therefore fission offers perhaps the only means of studying such levels in very highly deformed nuclei. Following the lead of Nilsson [3] one might hope to develop a theory accurate enough to relate the positions of levels et saddle point to levels near ground state LA... 1 -LEGAL NOTICE The report wo preparednu nocount of Governand monpored wert. Mether the United ame, por the Committee, nor way pornou nothing on to the Commodo A. MA U unutraty of prisonetton, pred or implied, we repact to the accu. muoy, completo, wat huloruten unnthorpe, or dont the we of nay laformation, sparti, medtem, or proceso direland Nonport w not to be trgo primately owned right of . D. A an my lastuto da mopot to the w eb, or for women with from the w of my father and marmo, methods, ori produs declared to the report As word tan the above, porno rottes on Wheld at the museli me bude my nuwe I boyut of contractive of the coloration, * ployd met contracte, to the stone that Ini mployut of contracte the Cemlerion, or amplyus of mode contractor propusna, de ates, or pw noo to, any wiarnation port Momployment of contract with Coulohen or womployment will mal contracte, PATENT CLEARANCE OBTAINED. RELEASE TU THE PUBLIC IS APPROVED. PROCEDURES ON EILE IN THE DAYANAN "it". - - un a se malo tornar la materia o momente se d o in momentin e moram of the same nucleus, thus depicting how the levels shift with deformation. This paper is concerned with bombardment of even-even target nuclei of masses from 230 to 240 with monoenergetic neutrons over the energy range close to threshold for fission in each case. The first work of this sort was done at Los Alamos by Brolley and Dickinson [4] on 232Th. The results were later analyzed by Wilets and Chase [5] who showed that fission was occurring largely through a K band with K equal to 3/2. Measurements have been made at Oak Ridge in more detail, on this and other isotopes. For example in the case of 232Th one can now say that the K-band sequence is 1/2 plus, 3/2", 1/2", the bands being separated by a few hundred kilovolts. These measurements have of necessity taken many years to complete due to lack of accelerator time for the project. Results have been analyzed as in the case of 23-y re- ported in 1962. [6] In a 20-minute paper only the highlights can be pre- sented. A more complete report, will be given in a year or two when more experimental data have been collected. en link to materiale dok ne sammen i hen the disputa with her and 2. Method Monoenergetic neutrons from either the Li(p,n) or T(p,n) reaction were directed onto a collimated fission counter as shown in Figure 1. In this case the neutrons originate in a tritium gas target. Figure 2 shows the counter in more detail, and Figure 3 shows one of two identical collimators which are the heart of the apparatus. Fission foils are placed back to back in the counter with a collimator in front of each. A collimator consists of an aluminum disc with a grid of 0.020" diameter holes drilled at 45 degrees to the surface. The collimator has a transmission factor of 1/275. By use of two foils and collimators one measures the relative fragment intensity at two angles, usually O and 90 degrees to the beam. By suitable rotations of the counter intensities at other angles may be measured, but one then needs to add a neutron monitor to the system, and this took the form of a long counter placed at 90 degrees to the beam axis. As expected, one finds symmetry about 90 degrees. However in all experiments it was customary to take readings at 0, 90, 180, and 270 degrees as a check on equipment. Data were always found to be self-consistent and were combined to yield the angular anisotropy, a , defined as o 10°/90°). As previously reported, [6] in the case of 23%u measurements were made at other angles, but were not deemed worth the time required to obtain them with this type of apparatus. Solid state detectors offer a fine way to obtain simultaneous data at many angles and this has been done by Simmons and Henkel [7] in a very extensive work on angular anisotropy from neutron induced fission. Most of their data was -2- 1 taken at energies too far above threshold to yield to channel analyses, and instead was interpreted by use of statistical methods. However, in some cases it does overlap slightly the work reported herein. The target nuclei studied consisted of 230Th, 232Th, 234, 236, 238U, and 240pu. In each case a measure of the angular anisotropy, a, was obtained as a function of neutron energy starting at an energy as low as one could ex- pect to get significant statistics in a reasonable time, and continuing to energies several hundred kilovolts above the f'ission threshold. Then suit- able theoretical expressions were used to ascertain the order in which the various K bands contributed to fission. The levels within the K bands lie very close together, a few kilovolts or in some cases a few tens of kilovolts apart, so that they could not be distinguished individually. Predictions from the optical model indicate that strengths of the airst two or three levels within any given band will overshadow the effects of all others together in determining the angular anisotropy. Probable errors are primarily statistical as there is no background except that 240pu gave a small background from spontaneous fission. Such fragments are distributed isotropically in angle. All l'esults have been corrected for this effect. Although chamber components were made as light as possible, there will be a correction of the order of 5 to 10 percent due to neutrons scattered elastically and inelastically from these components. The uncertainty in this correction is estimated to be not greater than 20 effects. Scattered neutrons are essentially isotropic and so tend to reduce measured departures from isotropy in the fragment distribution. All results have been corrected for this effect which introduces an additional I to 2 percent probable error, to be compounded with the counting statistical error. As far as could be ascertained, other sources of error were negligible. 3. Methods of Analysis A compound nucleus which has been formed by capture of a fast nel cron will decay either by neutron emission or by fission, where neutron emission is much more probable, at least for the cases under consideration here. The theory relating to this is far from exact, particularly for such levels of collective vibration as the so-called beta or gamma types. Also level struc- tures are never known completely for the residual nuclei. This complicates interpretation of angular distribution data in terms of channels in that formu- lae for partial cross sections can only serve as rough guides. The simplest -3- assumption, which may be quite crude, is that rn/Te is independent of K and I of the compound nucleus. Here I is the total angular momentum and remains constant from capture to scission. K is the component of I along the axis of deformation of the nucleus and is generally presumed not to be constant except that during the final oscillation prior to scission K will not change while the nucleus elongates more and more and finally passes over the saddle point. Neutron emission will be expected to occur with highest probability when least energy is concentrateż in potential energy of deformation, hence when deformation is small and K not a good quantum number. For compound nuclei with Jarge I a considerable fraction of the momentum may be carried off as intrinsic spin of the individual fragments. There is some evidence of this from studies of fission induced with charged particles of several MeV energy. However, since the extent to which this occurs is not known, no allowance is made for it in the formulae to be presented. In fact for studies near threshold it is not thought to be a serious obstacle to analysis, but should be borne in mind anyhow, especially for such target nuclei as 232Th and where one is attempting to estimate the effects of the K bands on frag- ment angular distribution well above its rather high fission threshold. The following relations have been discussed in detail elsewhere. [6] The angular distributions of fragments relative to the neutron beam are symetric about 90 degrees and independent of parity. They depend on X, I, and o as follows: W(K,1,0) = { (-1)K + E CEKO Z (41k1, { x)R (cose) (1) From the independence of parity it follows that either of the two allowed values of l for a given I may be taken and the function will be the same. These functions have been plotted and are shown in Figure 4. Note that for K and I equal to 1/2 the distribution is isotropic, and this is the only level that gives this. Also note that for K equal to 1/2 and all possible values of I greater than 1/2 the distribution is forward and backward peaked, and that for all higher values of K the peaking is sidewise regardless of I. These are very important factors in recognizing channels near threshold. For an entire K band the resultant angular distribution is Og (0) = H (21+1) T, " W (KI) where the T, are neutron transmission functions, and for this paper those of Perey and Buck [8] based on a non-local optical potential have been used. Relative strengths of the various K bands may be estimated roughly from the following relations which give the meximum possible strengths : . . "! 02/2 = 1 *2 [1/2 +2 273/2 + 3 935/2 + 4 237/2 + ...] 01/24 = r ** (T+ 2 7,3/2 + 3 ,5/2 + 4 7 7/2 + ...] 03/22 = *** [ 2732 + 3,5/2 + 4 , 7/2 - ...) 03/2+ = 1 * [ 27,3/2 + 3 7,5/2 + 4 7,7/2 + ...] etc. In the hypothetical situation where all compound nuclear decay occurs via fission through one K band the various terms give the strengths of the levels in that band directly. This is still true if fission occurs via two bands of opposite parity. Where like parity bands are competing the common terms represent the sum of the strengths of the various levels of these two bands. The following experimental results are discussed in the light of the fore- going relations. 4. Experimental Results 4.1 230th Figure 5 shows the fission cross section and angular anisotropy for 230th. The cross section curve is preliminary as there still remains a ten percent disagreement between two methods of measuring the quantity of 230TH on the foils used. The curve is either as shown or ten percent higher all along. The cross section was measured relative to 265V and values for 2050 were taken from BNL-325. [9] The procedure followed was similar to that de- scribed elsewhere. [10] Reasons for the rather wide disagreement between the various laboratories in the angular anisotropy measurements at low energy is not known. [7] [11] The forward peaking at the lowest energies is clear indication of a K = 1/2 band. The subsequent sidewive peaking shows a higher lying band with K greater than 1/2 and stronger than the first band. The partial cross -5- sections indicate that the only combination which fits is a K = 1/2+ band followed by a K = 3/2- band. The forward peaking at still greater energies can then only be explained by a third band with K = 1/2-. Thus the K band sequence at sadale point deformation of the compound nucleus 232Th is be- lieved to be 1/2+, 3/2-, 1/2-. As both parity 1/2 bands are already present the forward peaking would be expected to remain at all higher energies as indeed it does. 4.2 232Th Figure 6 shows the angular anisotropy for 2327h; and the fission cross section taken from he Los Alamos work given in BNL-325. Note the coincidence energy wise in the extrema. This leads one to suspect that rn/may vary quite widely in some cases at least from level to level. Despite this, how- ever, the variations in a are so marked that one can make K band assignments on the same basis as for 230Th and one finds the same sequence. Thus for the compound nucleus 238T|ı at sadale point deformation the K band sequence is believed to be 1/2+, 3/2-, 1/2-. There still remains an unsolved question in regard to this nucleus, however. Note that at 1600 keV neutron energy, Los Alamos [12] finds an anisotropy of 0.12 to very good statistics. The Oak Ridge data do not con- firm this, but so far are too incomplete to argue the qi.estion. However, if the Los Alamos point is correct it cannot be explained at all by any of the theory given here. One could only say that there must be some most extra- ordinary selection rules at work regarding inelastic neutron scattering which inhibit formation of the K = 1/2+ states at saddle point once the bombarding neutron energy approaches 1600 keV. We hope to have more measurements of a at Oak Ridge soon, but as only 4 weeks of accelerator time a year are allotted to this project, and count rates are low, it does take a long time to get adequate data to settle such questions as this. 4.3 234U Since the rather comprehensive report [6] published on this nucleus in 1962 additional data on a at lower energies were taken in 1963. The total of all data are shown in Figure 7. The additional data merely serves to strengthen the arguments for the K band sequence given in the 1962 paper. Based on the same reasoning as above, the K band sequence for the compound nucleus 2350 at saddle point deformation is believed to be the same as the preceding two; namely, 1/2+, 3/2-, 1/2-. The picture above about 1100 keV neutron energy becomes clouded by the addition of other channels and the overriding effect of the very strong 1/2- band so that predictions of higher bands cannot be made. However it is interesting to note that the reaction, a(p,f) on 234U by Vandenbosch (13] shows additional structure as indicated in Figure 8. Energy resolution was about the same for both sets of deta, but statistics were con- siderably better for the Oak Ridge points, but points were rather far apart in energy so it may turn out that there really is no disagreement after all. The next -fission experiment scheduled in this program at Oak Ridge is to take more points in order to settle this. The agreement over the rest of the curve is quite good. If there really is a disagreement then one must remember that the deuterons introduce considerably more angular momentum into the compound nucleus, and so may excite more of the available states. However, this usually works the other way, in that where many states are present the curve tends to smooth out and small wiggles disappear. Dr. Vandenbosch will dis- cuss this in more detail later on in the meeting. 4.4 238U The low energy angular anisotropy data for this nucleus is shown in Figure 9. This is another case where more data are needed. To get this data better 236U is required. That used had about 1 percent 235U in it and the background counts from this at the lowest energies amounted to a sub- stantial fraction of the total. Therefore, material is needed having say not over 0.2 percent 2950. A request for a few milligrams of such material has been in for about a year. On the basis of present data it is difficult to make a firm assignment of the first three K bands. A K band sequence of 3/2+, 1/2+, 3/2-, 1/2- will explain the curve as it is shown and is con- sistent with the partial cross sections and angular anisotropies given by the appropriate formulae. However, 5/2+ or 5/2- may be alternate possi- bilities for the first level. More careful calculations concerning this first level are scarcely justified until better data can be obtained between 600 and 400 keV neutron energy. It is quite possible that additional data will show the curve not to dip down in this region in which case the level sequence might turn out to be the same as for the preceding mass numbers. 4.5 238U CV Figure 10 shows the low energy angular anisotropy data for this target nucleus. Note the striking difference compared to lower mass numbers. It is clear that here fisbion is predominantly through channels of K = 1/2 at all energies. As the angular anisotropy is not as large as would be predicted by 1/2 bands alone others of larger K must be present, but so close to the 1/2 band or bands that no level sequence can be predicted. Thus the compound nucleus 2884 at sadale point deformation has low lying K = 1/2 band or bands intermingled with one or more of higher K. The relatively small hump in the curve could be explained by additional strength from a K = 1/2 band in this region or by preferential decay of certain states by neutron emission. 4.6 249pu Figure 12 shows results obtained so far for 240pu, the last nucleus so far studied. Results are meager since only extremely poor quality foils were available so that it took a full two weeks accelerator time to get this much. More data are needed in the lowest energy region. At the lowest energy point the background from spontaneous fission was a substantial fraction of the total count rate. Note the similarity to 2380. Clearly K = 1/2 bands are dominant, although if the curve is correct as shown then the first K band will be one of K greater than 1/2, and the second will be a K equal to 1/2 band. 5. Acknowledgments It is a pleasure to acknowledge the help of George Petit of the Oak Ridge Gaseous Diffusion Plant, who developed a method for the quantitative deposition of thorium and who plated all the thorium foils, as also the special thickly coated foils of 236U and 2380. Tipe 234U and 2350 foils were plated by Ralph Greene of the same laboratory as described elsewhere.. [10] and took data on most of the evening shifts. 16. Bibliography Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. [1] WINHOLD, E. J., DEMOS, P. T., and HALPERN, I., Phys. Rev. 87 (1952) 1139/40. BOHR, A., Proc. Internat. Conf. Peaceful Uses of Atomic Energy, Geneva (1955) Paper P/911. NILSSON, S. G., Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 29, No. 16 (1955). [4] BROLLEY, Jr., J. E. and DICKINSON, W..C., Phys. Rev. 94 (1954) 640/2. [5] WILETS, L. and CHASE, D. M., Phys. Rev. 103 (1956) 1296/7. [6] LAMPHERE, R. W., Nuclear Physics 38 (1962) 561/589. [75 SIMMONS, J. E. and HENKEL, R. L., Phys. Rev. 120 (1960) 198/210. [8] AUERBACH, E. H. and PEREY, F. G. J., Brookhaven National Laboratory Report No. 765 (1962). [9] HUGHES, D. J. and SCHWARTZ, R. B. , Brookhaven National Laboratory Report No. 325 [10] LAMPHERE, R. W. and GREENE, R. E., Phys. Rev. 100 (1955) 763/70. [11] GOKHBERG, B. M., OTROSHCHENKO, G. A., and SHIGIN, V. A., Doklady Akad. Nauk S.S.S.R. 128 (1959) 1157/9. Trans: Soviet Phys. Doklady 4 (1960) 1074/6. [12] HENKEL, R. L. and BROLLEY, Jr., J. E., Phys. Rev. 103 (1956) 1292/5. [13] VANDENBOSCH, R., private comunication, 1964. 7. Figure Captions Figure 1 - Gas target and collimated fission detector setup. Figure 2 - Collimated fission detector. Figure 3 - Collimator surface after completion of drilling. Figure 4 - Theoretical fission fragment angular distributions for fission through pure rotational states, W(K,I). Figure 5 - Fission cross section and fragment anisotropy for neutron induced fission of 230th. Figure 6 - Fission cross section and fragment anisotropy for neutron induced fission of 232Th. Figure 1 - Fission cross section and fragment anisotropy for neutron induced fission of 234. Figure 8 - Fragment angular anisotropy for neutron-induced and deuteron- induced fission of 234u. Figure 9 - Fragment angular anisotropy and fission cross section for neutron induced fission of 238U. Figure 10- Fission cross section and fragment anisotropy for neutron induced".* fission of 238U. Figure 11 - Fragment angular anisotropy and fission cross section for neutron induced fission of 240Pu. Wat witir.is tibi $ ar parking met ..poi www.ind. .. M y wat nume p die ander r dort of . .; : w . ' 1 1. -- 1 11 1 . - . . . , Y . W . SO . . .. .. . Firm create a trends . . : . , . 1 . . R y L. To . i 23 * 1 L . Fig. 1 . 17 qui R ! ? . 2 . 2. 8 KO L . V Y- . CZ - . . 1T PT. ** . . A . ". 22 * ! 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All - 1 * . 我 ​.. . + - - " 民 ​. 中 ​- A ' , 1. 1 收 ​' : - , , . , 世事 ​.. 的​, , CSSET(" 的AK Sky 不好​? . . 我的型​? . 1 " 形久 ​1 ' 多地 ​, 14 , } '' 。 出 ​效 ​, 《我的 ​. .4L ALE F11: 14 一 ​, ' . 4, A . . -- 里了 ​, , * , ,, - 'ally - . 1 . . ; 478 * , NT: Si47人​, 中​, 購物​, 4 ' ' : ; : E · 146 :: : 的这场战 ​, ? ; 成的​, 食 ​} · - , 者 ​表 ​ANEL 11 十 ​身上了​。 : r . 音​, , "." tret . . 1 11 cr.ly, 4.上山 ​非 ​. 1 WAN: 11:11 , 10 UNCLASSIFIED ORNL-LR-DWG 56677 W112,72) NORMALIZATION: Si W Wix,7) dicos 8 ) = 4 2,572) . ... . .. .. . . . . .. W(12,3/2) W172,721 -14- W(K,7) -W15/2,5/27 W15/2,72) =W13/2, 3/2) -W13/2,5/2) W(12,12) . -W172, 12) W1362,5/2 \W132,5/21 W15/2,72) W152,1 W13/2,3/2) (34 - W15/2,512) _:W11/2,12) W132,72) W (12,512) W172,72) W12, 3/2) + W13/2, 512) W15/2, 721 W W172,712) Oo 20 30 4050 8(deg) 60 70 80 90 Fig. 4 ORNL-DWG 65-1050 350 . _^ RUSSIANS - LOS ALAMOS + •• OAK RIDGE 300 oorgaan 250 A= 04 (900) Of (millibarns) -15. * 50 JANUARY 1964+ 500 1000 2500 3000 1500 2000 En (kev) Fig. 5 Of (millibarns) 180 160 200 ORNL-DWG 65–1081 PAL 4000 - vove .. - . - r. NOV. 1962 3500 ..... -. .. 1 1 7 ... . . . . . . of (BNL-325) . . - . . . . . . . 1 - LOS ALAMOS IOAK RIDGE 3000 2500 En (kev) Fig. 6 . . . - .. - - - --.. . - 2000 ... .... .......... ....... 1500 1000 (206) to=0 -16- UNCLASSIFIED ORNL-LR-DWG 38460AR 2 2.00 - - .. . . . U-234 + 1.75 ++ AVERAGE NEUTRON ENERGY SPREAD . 1.50 totatto -. Op .---- |(30°/60°) - 11 . III. . . IT 1. 1. -. .. Y to, (0°)+'0, (90°) +. I 1.25 - 0,(30°/60°) - 07 (30° / 60° - 1.00 - - - - - - - 1. . . . . . . . 1 . . 0.50 • . - ** I . . .. .. JUNE 1963 . . 0.25 FO UA. 4 . OLI 500 1000 3500 - 4000 459 1500 2000 2500 3000 NEUTRON ENERGY ( kev) .. det Fig. 7 -17. ORNL-DWG 65–1128 D ... ln (f) (LAMPHERE) a=of (20) :.. . 0.8 - ****. dlp.f) (VANDENBOSCH) ... • d (pp) : onli) OAK RIDGE onlf) LOS ALAMOS .. co to 500 1000 1500 2000 2500 En (kev) 3000 FEB. 1965 3500 4000 ; Fig. 8 -18- !! og (barns) 0.20 1600 -... ORNL-DWG 65-922 - NOV. 1963 1400 -- -- 1200 . .. ... ... .- - .. CA 1000 En (keV) 800 . Fig. 9 . . - Mal- 4.1. 600 CO OAK RIDGE - LOS ALAMOS 400 - . - .. . - 200 0.25 azor () -19- UNCLASSIFIED ORNL-DWG 63-770 HO. -02. Of (barns) MARCH 1963 0.5 0.5 1.0 2.0 4.5 En (Mev) Fig. 10 ORNL-DWG 64-11281R 2.8 2.4 . a = 0; (300) Of (BNL-325) Of (barns) -21.- OCT. 1964 200 400 600 800 1000 1200 1400 1600 1800 NEUTRON ENERGY (kv) . Fig. 11 - Moimiviera Duben h . L- SESSORS END DATE FILMED 18 / 1865 : :