. . I OFI ORNL P 1067 . . à A EEEFEEEE EEEEE MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 V. - P .. . T " " '. 1 . " : . . .: : ! 1, . . . . . : Li . . .. " .. - : , , L . . . . . ' . I !T : ' . 1 2 " -,' * ." . . TEXTILE . 7. . . .. . . .'. MTANTO . . . . . . i . i .. -.- . LOW . '' WA Ti . .. .".1. .' + -. . : : ' . PP- :.* 1 . * i .. 7 " . - 1 ! . ... .. . . :. .. . i. . * VI . * '; Ti 2 I 1 T . LEAVES KE . . ' " . T... . - INTM -.- . i. ' -. . , 1 . . . 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, or that the use of any information, appa- ratus, method, or process disclosed in this report may not infringe privately owned rights; or 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. As used in the above, “person acting on behalf of the Commission" includes any em- ployee or contractor of the Commission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employ- ment or contract with the Commission, or his employment with such contractor. * " T .' . J . 1 . . Y . ' 1 . .'. 1...1 .2 y .' . . :- 1 y ' 12 Fr 4 1 13 . - ' T . , . - ; ." . . 1 ' 1 . ..47 Fi .. .. . . . . . - "' , - A 19 . . . .. . . . . : : . ... 13-17 1 . + .. ) : r - 12. -.. , --.. ' . . . . . . -" . 1: : . . . ++r', ', * . . : '' ! . . . -li : . I .:: . . . . . : : đ 15 II i . .” .. L+ '.. L' , - ' ' *.. .! - . . . > '*. L- . ' ' . Ir I. - ? " ' ... t . ,- " . .. ? . . . -'. - . . . . . 1 - .. . . ii . Nyt . 1. . -- . .. 23 . SRL , . ... . . !! !: 26 1, .. " . : . .. . . . " .. ..:: TOR .. : . - .- " - ITO LK. D 22. ORN-P-1067 AOTIES JAA 23 1985 SM-60/5 -LEGAL NOTICE The report w oparu w who comment power wort, Matthews the United here, sor the Commisslun, Min mana seting all of A. MAIN my warm emp tion, and or lapin mo respect to the way. racy, completo , o wadows of the whormation on this report, or that the we of muy information, smart, who a mocens deled in emport may not matting wintown D. Ant. Any liontin with manet w the wo, or for damage tonding to the wo baloration, untun, who own aloud ta the most Al wat in the above, porta notte a wall of the Omanlolo" malainen . Noyno e contractor of the Comminges, play mucha contratos, how extend that wel wmployee of contractor of the Content or played wel contractor property dammame, or more nown to, any wormation to sployee contract will the Counci, a Memployment will contractor Corf - 650301-8 MASTER Sadale Point Rotational States from Resonance Fission of Oriented Huclei" J. W. T. DABBS, F. J. WALTER** and G. W. PARKER Oak Ridge National Laboratory Oak Ridge, Tennessee, USA : 1. Introduction The process of low energy neutron-induced fission can be considered to take place in three regimes. These are (a) capture and subsequent redistri- bution of excitation energy, corresponding to approach to the fiebion barrier; (b) passage over the saddle point (or tunnelling through the barrier); .. (c) scission or breakup. Of these, only (b) represents a relatively simple situation, because (a) and (c) involve large numbers of states and many possible paths. AB A. BOHR [ 17 has pointed out, the situation is considerably simplified during passage through or over the barrier: here, the number of states available to the compound nucleus can be small and these states are thought at be analogous to the collective states near the ground state of a deformed heavy nucleus. The simplification afforded by this picture provides a basis for understanding of the present experiments. A number of experiments [2,3,47 have demonstrated that nuclei of the actinide elements U, Np and Pu can be aligned in the compounds MO, Rb(NOx), simply by cooling a single crystal of the compound. Although there was for some time a question about the direction of the nuclear orientation, this now appears to bave been satisfactorily resolved 4,5). Both 2530 and 2550 are known to have positive nuclear electric quadrupole moments [6 (Q > 0) and both are believed to align with the major nuclear axis in the plane perpendicular to the c-axis of the (pseudo-hexagonal) UO, Rb(NO,), crystal. In both cases, Q-particles were found to be preferentially enitted in the plane perpendicular to the c-axis, with an anisotropy given by W(B) = 1 + (A/T) Po(cos B) THE PUBLIC IS APPROVED. PR YE KAT! PATENT CLEARANCE OBTAINED. RELEASE TV ARE ON FILE IN THE RECEIVING SECTION. ......... .....oru where A had the value -0.073 + 0.013 for 2550 and the value -0.064 + 0.004 for 2334 . One set of measurements has also been made on the anisotropy of fission 11 ah neutrons from the graphite reactor at the Oak Ridge National Laboratory [7). The results showed an anisotropy of the type (1), but with A = +0.035 + 0.009 for 2454 and A ~ 0 for 2550. The present work 18 an extension of these experiments to selected neutron energies in the resonance range, and to lower temperatures where the coefficient of P (coa ) 1 (1) 18 larger, and thus easier to determine. We shall first discuss certain theoretical aspects of the problem, then describe the experimental apparatus and the (interim) results, and finally give the con- clusions which may now be drawa. 2. Theory For present purposes, the compound nucleus during passage over the barrier may be considered to be represented by a suitable sum (over magnetic substates ) of symmetric top wave functions and Worlaby) where a, B: y are the Bulerian angles. The three quantum number indices J, M, and K are those associated with the compound system at the saddle point, K being the projection of the total angular momentum J along the symmetry axis; and M being the pro- Jection of J along the spatial axis, i.e., along the c-axis of the crystal in the present case. In his 1955 paper [ 17 BOHR suggested that small values of K should pre- dominate in low-excitation fission. This argument is based on energetic con- siderations; i.e., those nuclei which have "used up" the least energy in pre- serving angular momentum and parity have more energy which can go into producing deformation. Nuclei in rotational states with low values of K have the largest monents of inertia and thus the smallest energy of rotation for a given J. These nuclei should therefore have a higher probability for fission. In the aligned compound state system the angular distribution wla, B, ~) of the symmetry axis 18 then given for each K by [87 (B) oc Ilocos en PCM). (2) The populations P(H) are determined by the initial nuclear orientation. If the target nucleus has angular momentum quantum numbers J, m ani captures a neutron with spin projection M, Bq. (2) may be written [87 (8) OC Euro f criće sa mundo ) @ cini) - 2 - E- where C 18 a Clebsch-Gordan coefficient. BOHR [ 17 identifies the angular distribution of the fragments after scission with the angular distribution of the symetry axis at the saddle point. Within this ideatification, Iqs. (2) and (3) give an expression for the fragment angular distributions. These ex- pressions may be shown to lead to the following for both the J.) + and J = 9 - cases of slow neutron fission: W (B) = 1 + *74I+1) [fes autres pl25 +32]* s P (cob ) (4) where 8, 18 essentially the alignment parameter Q, of ROSE 7,107. In the present case, the nuclear alignments come from electric quadrupole coupling with a spin Hamiltonian (5) where P 18 the quadrupole coupling constant in cm". The alignment parameter 8, 18 then given in good approximation (117 by i l (21 + 3)! 7* , Phe Są Qe - 23+1 180 2234-32571 (en) (6) where k 18 the Boltzmana constant and T 18 the absolute temperature. Thus in.. the Bohr approximation this formulation leads to an angular distribution which indeed has the form of Eq. (1). (electric quadrupole coupling) and Bleaney (anisotropic magnetic hfs coupling) types, it has been showa [12] that in the angular distributions expected, 1.e., in a more general form of Eq. (1) W(B) = 2 A, C, P. (cos B) (7) v even an expansion of the alignment parameter Q, in powers of 1/T cannot have terms of lower order than (1/T). This point 18' important for demonstrating the absence of Palcos B) terms in the present experiment, where strict linearity of the anisotropy with 1/T 18 found within experimental error. The coefficient of P (COB B) in Eq. (4) contains the parameter | 36€ - J(J + 1)] and thus reverses sign in going from small K values to.values....... K=J. Table I gives values of A for each of the X values which may occur for g-wave neutron Induced fission of 253U and <50. Wheeler in a recent dis- cussion [137 has suggested that certain K values should be important. These values are starred in Table :. [147. ................... even mozas. ... --om.............. TABLE I Calculated A values in Eq. (1) (in °K) corresponding to various J, K values. The assumed values of the quadrupole coupling constant of Eq. (6) are given in each case _235 (Phc/k = .0154°K) 1 9 +0.074* 2330 (Pac/k = .027°K)_ a+ rarity forbidden +0.037 +0.055 -0.037* -1).092 +0.077** +0.058* Parity forbidden +0.065* H 0* OM +0.031** -0.96 5 = -0.108 . * From WHEELER [127. **From WHEELER [127 and Paper SM-60/10, this conference [137. .. . ........ Examination of Table I reveals the fact that the sign and magnitude of. the anisotropy primarily reflects the value of K. and is relatively insensitive to the value of J. Thus measurements of the angular distribution of fission from aligned nuclei should be quite useful in determining at least the average, or effective, value of K associated with rotaticaal states at the sadale point of fission. As 18 now well known, it is also possible to determine J values associated with the compound nucleus (and thus with these same saddile point states) by using the interaction of polarized neutrons and polarized nuclei [157. The existence of these two complementary methods thus gives promise of providing means for resonance-by-resonance studies of the saddle point states in favorable cases. The values in Table I include as a factor the degree of orientation which occurs. in 25500, Rb(NO2)2, Eq. (6). There are three estimates of the coupling constant (Pac/k) presently available. The first 18 .0216°K and was obtained from low temperature specific heat neasurements on a related compound 25500 F, [27. The second was obtained by CHASMAN and RASMUSSEN (16), using our results on 250 alpha particle anisotropy and a correctly phased partial wave analysis [ 37. This gave a value of 0.0277°K for 25300, Ab(NO)z. Since the ratio of the quadrupole moments Q(235)/Q(233) 18 known approximately [17, a value of 0.0154 $ 0.0027ºk can be derived for <5>0, Rb(NOK)z. This value can also be considered as a minimum value of Phc/k, since the alpha anisotropy for the particular choice of partial wave amplitudes 18 very near the maximum for given Phc/k. A similar analysis has recently been made possible by a calcu- lation of SALUSTI [18], who has given another derivation of the partial wave amplitudes in the alpha decay of 50. This calculation in a similar way lowers the possible minimum value of Phc/k for 2990 to 0.0123 t .0022°K. The Chasman-Rasmussen values have been used in Table I to indicate the size of the expected anisotropies. These estimates emphasize the importance of an inde- pendent measurement of Phc/k [197. 3. Apparatus The apparatus for measurement of the fibsion fragment anisotropy as a function of neutron energy and 1/T 18 conceptually simple but somewhat more difficult in practice. A single crystal of 25°VO, Rb(NO3)2, grown with a surface layer of the same material where 2930 was substituted for 2500, was mounted in a variable energy neutron beam in such a way that its c-axis could be rotated with respect to a fløsion fragment detector. The apparatus per- mitted cooling the crystal to temperatures as low as 0.45°K. Figure 1 18 a schematic diagram of the lower end of the cryostat in which the experiment was carried out. The dewar had an outside diameter of • 5 - HIN.. LOVE UNCLASSIFIED ORNL-LR-DWG 74898 TO HePUMPS LIQUID HE BATH (2.2°K) O - ----OUTER VACUUM CASE - - + 11 . -- --- ---OUTER LIQUID N2 BATH 18r I 1 III III i 1 LI 3. 1 770K SHIELD (REMOVABLE) 2.2°K SHIELD 20:1 GEAR BOX AND EXPANSION VALVE- II IT LII . : He3 CONNECTIONS FOR VACUUM GAGES, TO COUNTING CIRCUITS ETC - - - - - ---- - - - - . . CU PLATE COOLED TO 0.45°K- . TIIMITRUNK . .. ILLARY TUBE Hey HEAT EXCHANGE GAS OUT III . I 0.01 mil NI WINDOW- 1 VORb (NO3)3 CRYSTAL - 1 . TI DI 1 + Ht wer - .-. APERTURE IN 2.2°K SHIELD T UL ID . | 1 DI DVD TI LILIT 1 . III : 0.02-10 ev NEUTRON BEAM SHUTTER SI SURFACE BARRIER DETECTOR SIGNAL CABLE 77°K PLATE - . Nuclear Alignment Apparatus. Fig. 1 25 cm and contained two liquid nitrogen baths, a "he bath, and a section (the sample chamber) which was cooled by a continuously operating "He refrigerator. The temperature of the sample chamber was monitored by a carbon resistance thermometer and recorded continuously. A heater on the sample chamber was controlled so that the inverse temperature of the chamber 18 held within 1% of the desired 1/T value. Pre gas surrounded the sample, and provided adequate and reliabl: heat contact to the walls; the pressure of "He was N 25 x 10 mm Hg. The density was thus sufficiently low that (n,p) reactions in the 'He were not important. This technique of gas cooling necessitated development of a thin gas tight window." N foil 2.5 x 10 cm thick (from Chromium Corp. of America) was used, and a dilute coating of 1% VYNS resin in cyclohexanone served to cover the small pinholes in the foll. A mesh support served to Lmprove the ability of the foil to support a pressure differential, although great care had to be taken in this regard. Fission fragments passing through the foil lose 530% in energy, and were detected by a si or de surface barrier detector at 77°K. The 'He refrigerator was unusual in that it operated with a condenser temperature of 2.20°K rather than the usual 1.2°K. The monochromator was a Be single crystal and the 123i reflection was used except at the lowest energies. Soller slits determined the entrance and exit collimations. The energy spread of the monochromator was 2.6% at l'ev and 8.54 at 10 eV. The apparatus was located at the Oak Ridge Research Reactor (30 MW). Even the high flux afforded by this reactor, however, gave counting rates which were quite small in the 1 - 10 eV energy range and it was necessary to operate the experiment continuously for periods up to several weeks per resonance. An automated counting system was developed for this purpose. The low counting rates also dictated the use of the 'He refrigerator; an increase in the size of effect (by increasing 1/T) of a factor a, for example, permits a reduction in counting time of a factor o for a given accuracy . ...Counts were taken in each of two sample positions' (c-axis at oº or 90° with respect to the detector: direction). The counting periods were determined by the integrated neutron flux through the dewar as seen by a parallel plate fission chamber containing 2550 (for measurements on 25u). 4. Results The results given below represent approximately 7 months operation of the experiment. The dependence of the anisotropies (both.. and fission) on 1/T have been measured rather extensively at 0.28 eV. A graph of these values is shown in Fig. 2. The slope of the upper curve of Fig. 2 18 & measure of the -7. UNCLASSIFIED ORNL-LR-DWG 76961 1.15 FISSION AT 0.282 ev – CORRESPONDS TO 14.0.0307), Pz (cos 0) — 1.05 W(0) W100) 1:00 K 4 W(900 1.00 Q-PARTICLES - CORRESPONDS TO - 1 -0.0575%, P (cos e) WHEN CORRECTED FOR U234 CONTENT 0.95 0.90 2.5 0.85 0 0.5 1.0 1.5 2.0 VK) U235 in VO2 Rb (NO3)3 Using Carbon Resistance Thermometer for 1 Values. Fig. 2. coefficient A in Bq. (1). It is the variation in this slope with energy which 18 of interest here. The linear dependence of both the alpha and fission effects on 1/T in Fig. 2 18 a strong indication that the angular distributions are indeed of the form given by Eq. (1); additional confirmation of the absence of Pin terms was found in the behavior of the absolute counting rates at oº and 90°, although those indications are less accurate. The alpha particle anisotropy serves as an excellent monitor of the degree of orientation actually obtained and thus can serve as a basis for normalizing measurements made under various con- -- I . . - - . - - At neutron energies above 1 eV, low counting rates have restricted the measu:ements to energies where large resonance appear in thou cross section. Some analyses Z207 have indicated that the resonance near 2 eV has a different J-value from the bound state and the 0.28 eV resonance. However, this resonance 18 quite small and probably cannot be studied without very prolonged measure- .- - MILY E : --: : - .. . -- - -- - - - - - - - - - - . - - - . - .. . ments, followed by the large resonance at 8.8 ev. Measurements were then carried out from 0.28 eV down to 0.24 eV, the lowest energy available from Be in our monochromator arrangement. There was a sharp change in the anisotropy between 0.14 eV and 0.28 eV. An examination of the fission cross section of u in this region shows that this sharp change corresponds roughly to the change from a very small contribution to the cross section from the 0.28 eV resonance at 0.14 eV to the maximum contribution which occurs near 0.28 eV. The measured points are plotted in Fig. 3 (use right hand scale). 5. Preliminary analysis and discussion Since the observed anisotropy in the neighborhood of the 0.28 eV resonance varied strongly and in a manner which suggested that the variation might be : proportional to the contribution (above "background") to the cross section, a trial analysis was made on this bas18. In the absence of direct measurements of J, resort was made to a multilevel fit to of using parameters recently obtained by Kirpichnikov et al. for the 0.28 and 1.14 eV levels [217, and estimates of the parameters for two assumed bound levels. The bound level nearest E = 0 was assumed to have the same J as the 0.28 eV level, while the other bound level and the level at 1.14 eV were assumed to have spin J' J 1, in accord with Kirpichaikov et al. This choice was made in contradiction to other multilevel fits [207 because of the presence of the observed variation in A. The quantity F(E) = Op(J',8)/[op(J',E) + OP(J,E)] was then cal- culated, and 18 shown as the smooth curve of Fig. 3. The scale for the ob- served anisotropies was adjusted to give an approximate fft of these points - 9 - UNCLASSIFIED ORNL-DWG 64-1837 H0.06 Hi H0.05 UNCORRECTED F(E)=0 111/O (U') to 10) Az (obs) -10- Ho.o3 Ho.o2 III Ho.o. 10-2 10-1 · 100 ENERGY (ev) 1. . *, ." . Fig. 3 7., 19 ., " IT III to the P(E) curve. Such a comparison makes the tacit assumption that only one channel/spin value is operative, i.e., for each spin J there is one particular K value (or more properly, one set of K's). It 18 doubtful that such a relation actually holds, however. The apparent agreement in Fig. 3 may well be illusory. Two other pieces of evidence may be adduced to suggest this. (a) The radio- chemical studies of Faler and Troup give an asymmetric/symmetric fission ratio which clearly does not follow the F(E) curve of Fig. 3. The variation in their ratio bears little relation to the cross-section curve and is particularly flat in the region just below 0.3 ev [227. (b) The same remark may be applied to the results of Moore and Miller, whose result [237 shows yet another variation with energy. It would appear that while results such as the above [22,23 may give strong indications regarding the channels (sadale-point states) associated - actual determination of the angular momentum character of such states. 6. Acknowledgements - We wish to thank L. D. Roberts for his many contributions to the initial conception of the alignment experiment and for the design of the neutron mono- chromator. J. 0. Thomson made several contributions to the cryostat design. We particularly with to thank C. T. Hall who constructed the cryostat. . ll . References 11 [1 [ [9] "Research sponsored by the U. 8. Atomic Bnergy Commission under contract with the Union Carbide 'Corporation. *Now with Radiation Instrument Development Laboratory, Oak Ridge, Tennessee. BOHR, A., Proc. Int. Conf. PUAE, Geneva, 1955, 3 (1956) 151. DABBS, J. W. T., ROBERTS, L. D. and PARKER, G. W., Physica XXIV, (1958) 569. ROBERTS, L. D., DABBS, J. W. T. and PARKER, G. W., Proc. 2nd. Int. Conf. PUAE, Geneva, 1958, 15 (1958) 322. ROERRIS, L. D. and DABBS, J. W. T., Ann. Rev. Nucl. sci. 11 (1961) 175. BANAUER, 8. 1., DABBS, J. W. T., ROBERTS, L. D., PARKER, G. W. ,Phys. Rev. 124 (1961) 1512: HILL, D.L., Handbuch der Physik 39 (1957) 178. ROBERTS, L. D., WALTER, F. J., DABBS, J. W. T. , PARKER, G. W., and THOMSON, J. o., Proc. Int. Conf. Nucl. Structure, Kingston, 1960 (University of Toronto Press, Toronto, 1960) p. 884. Oak Ridge National Laboratory Rept. 2430, (1957) 51. (Available from Office of Technical Services, Dept. of Commerce, Washington 25, D.C.). ROSE, M. E., Elementary Theory of Angular Momentum, John Wiley and Sons, New York (1957). p. 179. The second terms of Eq. (17) of ref. 7 should be multiplied by the factor - (2) + 1)/(23 + 2) to conform to Eq. (4) above; the second terms of the second equation in ref. 6 and of Eq. (216) in ref. 3 contain a numerical error and should be multiplied by a factor 2/3. A more general form is given in ref. 3, Eq. (18). ROSE, M. E., ROBERTS, L. D., DABBS, J. W. T., Bull. Am. Phys. Soc. 1 (1956) 207. WISELER, J. A., chapter on fission in Fast Neutron Physics, Part II,. (MARION, J. B. and POWLER, J. L., eds) Interscience, New York (1963). Values with a double star in Table I are those suggested to be important by MOORE and MILLER (Paper SM-60/10, this conference). We are grateful for a preprint of this paper. ROSE, M. E., Phys. Rev. 25 (1949) 213; Recent works which will illustrate the power of the method can be found in, e.g., STOLOVY, A., Phys. Rev. 134 (1964) 68B, and SHORE, REYNOLDS, SAILOR and BRUNHART, Phys. Rev. (to be published - preprint available as Brookhavea National Laboratory Report 8788). It should be noted that no successful experiments on polarizing either 2530 or 295U have been reported; this may be attributed to the very small nuclear magnetic moments of these isotopes. - 12 - T 147 [15] in the man who ---- "* M1 0 *- .MI . . . - CHASMAN, R. and RASMUSSEN, J. O., Phys. Rev. 115 (1959) 1257. DORAIN, P. B. , HUTCHISON, C. A. and WONG, E., Phys. Rev. 105 (1957) 1307; HUTCHISON, C. A., private communication. SALUSTI, E., Muovo Cimento 20 (1963) 171, and private communication. Attempts to find the quadrupole resonance have been made (HUTCHISON, C.A., Jr., private communication) and are planned (NEWMAN, J. B., private communication). [207 SHORE, F. J. and SAILOR, V. L., Phys. Rev. 112 (1958) 191; VOGT, E., Phys. Rev. 112. (1958) 203; Phys. Rev. 118 (1960) 724. [217 KIRPICHVIKOV, I. V., IGNAT'EV, K. G., and SUKHORUVHKIN, 8. I., Atomnaya Energiya 16 (1964) 211. We wish to thank M. S. Moore for supplying a preprint of this work. FALER, K. T. and TROMP, R. L., Plays. Rev. 131 (1963) 1736. CP. Fig. 6 of ref. 13. [23] Fig. 5, ref. 14. . 2 . M . ) - . . -. - i '. END 1.1 - '- " * T : 1: : : : 2 * " " .. . t' - - ia . i : 21 i 7 L .. 12 . .. DATE FILMED 8 / 17 /65 . .. . . 2 ' . . ! . 1 : :