(D0) for 142~ A ~158.

Transcription

1 P HY SCAL REVEW C COLUM E 11, NUMB ER 3 MARCH 1975 Tota neutron cross section for "Sm and nucear systematics of the Sm isotopes G. J. Kirouac and H. M. Eiand Knos Atomic Power Laboratory, * Schenectady, New York (Received 5 September 1974) The energy dependent tota neutron cross section of "Sm, a fission product poison, has been measured from therma neutron energies up to about 2.3 kev. The resuts obtained for the therma ( ev) cross section, resonance integra, s-wave eve spacing, and strength function were: 1S b, b, ev, and S = X 10, respectivey. The neutron widths for 120 resonances up to 300 ev were obtained by conventiona anaytic methods and the radiation widths were aso obtained for 13 ow energy resonances. The strength function was derived from resoved neutron resonances and from the average kev cross section. n addition, the Dyson-Mehta 6 3 statistic was ca1cu 1 a ted from the 1eve 1 sequences of Sm isotopes and compared with the prediction of the statistica orthogona ensembe. The eve densities of six Sm isotopes and seven Nd isotopes were used to compute the Fermi eve density parameter a, and these resuts are discussed in ight of the nucear structure. Finay, the systematic behavior of s-wave strength functions in the 142 & A & 158 mass region is examined. NUCLEAR REACTONS 5Sm(n, n), (n, y), E = kev; measured a&(e); deduced ED, g, f&, So, (Dg; O.E. theory test; studied systematics So, (D0) for 142~ A ~158. NTRODUCTON Sm j.s a fj.ssipn prpduct ppj. spn prpduced in therma nucear reactors. t has an evauated "U fission yied of 0.42%%uc and a therma cross section of about b. Because it has a hafife of 93 yr, it accumuates in the core unti it undergoes neutron capture. The ony energy dependent measurement of the "Sm cross section was made by Pattenden using a sampe containing ess than 4 at. %%uo"sm. Neutron resonance widths, but no radiation widths, were reported up to 13 ev. The shape of the ow energy cross section was observed to be strongy non-1/v. n addition tp the importance of "Sm as a fission product poison, it and the other Sm isotopes are interesting from a nucear structure viewpoint. The isotopes of Sm occupy the mass region near the first peak in the spit 4-s giant resonance. They may aso be thought of as transition nucei between neary spherica vibrators (44Sm) and permanenty deformed rotators ("4Sm). n an oversimpified she mode picture, the ground state of the Sm isotopes has two proton hoes in the 2d, g, she and a varying number of neutrons in the 1h, &, or 2f, ~, shes. Since extensive cross section data, incuding resonance parameters, eve spacings, and strength functions, are aready avaiabe for five other Sm isotopes, it is of interest to examine the systematic behavior of these nucear properties. n this work a brief account is given of a standard time-of-fight measurement of the "Sm tota neutron cross section from therma energies to the ow kev range. The resonances are anayzed by both shape and area methods to provide neutron widths and radiation widths " &. Parameters for 120 eves up to about 300 ev are reported and the s-wave strength function S, and eve spacing are determined, The strength function derived from the resoved resonances is aso compared with that obtained from the kev average cross section. Three different averaging intervas are used to iustrate structure in the neutron cross section from ev. The distribution of the eve spacings for Sm isotopes is aso tested against the Dyson-Mehta theory. Finay, systematic trends in the strength functions and eve densities are examined for Sm and isotopes of neighboring eements. Some insight into these trends is obtained from the nucear structure. EXPERMENTAL DESCRPTON cross section of "Sm was The tota neutron measured by the time-of-fight method using the Rensseaer Poytechnic nstitute inear eectron acceerator. Transmission data were obtained over an energy range from 0.01 ev to about 2.5 kev. The standard neutron producing tungsten target and 2.5 cm thick poyethyene moderator were used for the pused neutron source and the fight path was 31.6 m. Neutrons were detected 895

2 896 G. J. KROUAC AND H. M. ELAND TABLE. Sm mass spectrometric sampe anaysis (anaysis performed at Oak Ridge Nationa Laboratory). sotope «~Sm "Sm "Sm 4Sm "Sm "Sm "Sm "Sm "4Sm Sampe concentration (at. o) & & with a 1.3 cm thick Li gass scintiator mounted on an XP-1041 phototube. Two "Sm sampes pus an empty sampe hoder and a notch fiter sampe were automaticay cyced in and out of the neutron beam. The counting data were accumuated in 6144 time channes using an on-ine computer. The "Sm sampes were 1.9 cm diam metaic disks which were prepared at the OBNL Target and sotopes Center. The two sampes weighed and mg and were enriched to at.% "Sm. These weights correspond to &10 and x 10 atom/b for the thick and thin sampe, respectivey. A detaied mass spectrometric anaysis performed at ORNL is summarized in Tabe. Two different sets of data runs were made. The first set was designed to measure the therma cross section and the ow energy resonance region up to about 20 ev; the second provided transmission data with good resoution and counting statistics from 6 ev to above 2 kev. Experimenta parameters for the two measurements are cited in Tabe. Counting statistics for the resonance region ranged from ess than 1% uncertainty at 450 ev and above to about 2.5% at 15 ev. Simiar statistica precision obtained for the therma energy data. The time dependent background was determined from the counting rate at saturated resonances in the notch fiter sampe. The steady state background was measured by adding a thick "B or cadmium fiter to the notch fiter sampe for a few of the runs. Saturated resonances at 2.85 kev, 337 ev, 132 ev, and 18.8 ev in Na, Mn, Co, and W, respectivey, were used for the resonance measurement and at 2.85 kev, 132 ev, and 1.46 ev in Na, Co, and n for the therma measurement. The background was 5% or ess of the open beam counting rate for both sets of measurements. Various sampe-in, sampe-out, and background runs were normaized by means of a thin foi fission chamber detector which was aways in the neutron beam. ANALYSS OF DATA The raw counting data for the two "Sm sampes were corrected for the measured experimenta background and then converted to the standard transmission function (sampe in/sampe out). The counting rates were sufficienty sma so that dead time osses were negigibe. Neutron resonances in the transmission function were anayzed by both shape and area methods, using the Atta-Harvey computer codes. The shape method consists of a three parameter fit for E gi, and the resonance energy, reduced neutron width, and tota width, respectivey. This is ony appicabe when the experimenta resoution broadening and Dopper broadening are ess than the natura width. Thus, shape anaysis coud ony be carried out up to 20 ev where the Dopper broadening becomes comparabe to 1". Since the area in a resonance is to a good approximation, independent of Dopper or resoution broadening, the method of area anaysis was appied to a observed resonances from therma neutron energies up to 300 ev. This provided a verification of those reduced neutron widths determined by shape anaysis. The area method uses TABLE. Summary of experimenta parameters. Burst Time channe Sampes Width Rep. rate distribution Sm(atom/b) Experiment (ns) (pps) No. x width (JLfs) x 103 Resoution at 2 ev 20eV Hesonance x x x x ns/m 2.7 ns/m Therma x x x x ns/m 16.6 ns/m

3 TOTAL NEUTRON CROSS SECTON FOR "Sm AND... TABLE. Resonance parameters for n+ ~5~8m. Shape and area anaysis g0 y ~ (96) {96) gr ~o Area anaysis ony (& 96 mv) g g &o g , O.31~O.O ~ o.16 0, e , the area within resonance dips in the transmission function to determine vaues of g for assumed vaues of F. However, for thin sampes with transmission greater than -VO%%uo, the reduced neutron width is essentiay independent of 1. This situation obtained for neary a of the resonances observed above 20 ev. Resonances in the thin Sm sampe were too sma to be anayzed above 14 ev as this sampe was primariy designed for the therma cross section measurement. Thick and thin sampe data for the "Sm cross section from ev were averaged and then anayzed separatey after a the resoved resonance parameters had been determined. The two

4 898 G. J. KHOUAC AND H. M. E AND sampes yieded the same cross section within statistica uncertainties. A sma (4.4% max) correction was appied to account for at.% "Sm present in the sampes. The cross section cacuated from the resoved resonance parameters was subtracted from the observed cross section and the remaining cross section was fitted by tr ia and error to determine the parameters of the bound states. Ony one bound state resonance was needed to fit the data. The average cross section in the kev range was aso determined from the transmission data, as were the resonance spacing and the strength function. These aspects of the anaysis are discussed separatey ater. RESULTS A. Resonance parameters and epitherma cross section The transmission data were anayzed up to about 300 ev and resonance parameters were determined. Above this energy the transmission dips have become too sma for reiabe anaysis due to the decreased resonance ampitude and the increasing Dopper and resoution broadening. Up to 105 ev it is reasonaby certain that no resonances were missed, at higher energies the fraction of missed resonances increases throughout the anayzed region. Between 200 and 300 ev more than haf of the individua resonances were not resoved. n many cases the fitted fuctuations in the transmission function contain two or more resonances. However, the derived resonance parameters do provide a satisfactory fit to the data and the strength function is constant within statistics for the entire energy range. The resonance parameters are isted in Tabe and Figs. 1-3 compare the experimenta transmission function with that cacuated from the resonance parameters. Radiation widths & were obtained for 13 resonances. The error weighted average vaue of 96 mv is somewhat higher than one might expect for a typica rare earth isotope, but this is probaby due to the very high eve density near the midpoint of fiing the hg/2-2f, &, shes. n genera agreement with this resut, radiation widths determined by Rahn et &. for "Eu and "Eu were 90.0 and 94.8 mv, respectivey. The "Sm radiation widths were constant within 10/0 of the average vaue for most resonances and within 20% for a but one resonance. The neutron capture resonance integra R = fo" v&& &(E)/EdE was computed from the resoved resonance parameters by expicit numerica integration of the cross section. The average ra- 1.0 X x, t.o+x XX C) V) Ct (,Q.~ v x "&x y Q. 2 x t ENERGY ev) FZG. ].. Transmission data and cacuated resonance cross section for "Sm beow 10 ev.

5 1 « TOTA. NEUTRON CROSS SECTON FOR "Sm AND diation width was used where individua vaues were unavaiabe. The resonance integra was determined to be b in good agreement with Pattendens vaue of b. Qur resut incudes a contribution of 170 b for the unresoved resonances above 300 ev. About t3% of the resonance integra comes from resonances beow 12 ev with the 1.09 ev resonance aone contributing 39%. Athough the bound state resonance essentiay makes up the entire therma energy cross section, it contributes ony 91 b to the resonance integra above 0.5 ev. The resonance parameters in Tabe have been compared with Pattendens 1963 resuts. Since his sampes were prepared from fission product Sm containing ess than 4% of "Sm, the resonance dips in transmission are much smaer and more difficut to anayze than in the present measur e- ments. n hindsight, considering the difficuty of working with ow enrichment fission product Sm, his resuts were very accurate. Severa genera comments are in order: (1) The "Sm resonance at 0.46 ev was not observed by Pattenden due mosty to the statistica scatter of the points; however, a hint of its presence is there, (2) The resonance at 5.33 ev which he attributes to "Sm is definitey due to a arge resonance in 4Pm. Extensive resonance data are now avaiabe for Pm and they confirm this assignment as we as expain the arge resonances observed by Pattenden at 40.8, 48.3, and 65.5 ev. (3) The resonance doubet reported by Pattenden at 4.09 and 4.19 ev was accuratey described in our data by a singe resonance at 4.13 ev. The sum of his two reduced neutron widths agrees with our singe reduced width within 5%. (4) The neutron widths reported here for the resonances at 1.09, 1.70, and 2.03 ev are some 15 to 25% arger than those previousy reported. A other resonance parameters agree within the quoted uncertainty. B. Therma energy cross section The measured "Sm tota cross section at therma neutron energies is shown in Fig. 4. A correction for the Sm present in the sampes has been appied. This correction reaches 4.4% at 0.87 ev, the "Sm resonance energy, but is essentiay negigibe away from the resonance. The cross section at ev is b in good agreement with the vaue of b previousy reported by Pattenden. The effect of nearby bound states is extremey important in "Sm. The resoved resonances contribute ony 1.7% to the tota cross section at 0, 0253 ev. This portion of the cross section was subtracted from the measured tota and the remaining part was fitted by tria and error to de « « « « n CO « X CA - Os «« «i J & vxv...)k v =T 11 +~ L~ CO R C 1.1 1TTH.O gee OO , E NE RGY O FG. 2. Fitted transmission data for ~5~Sm between 3.0 and 78 ev. 10 x 0.9 ON i ««11««« X \(..Xv V x x ""CPA , ~, ; X~ X X F NERGY (evj i w..vx v..x & X X Kv~ ~~ ~x &g+1t ~ o v...~ P ERME NTAL ANALY TC FG. 3. Fitted transmission data for Sm above 78 ev.

6 900 G. J. KROUAC AND H. M. ELAND ioo ooo f ) 1 O 000 O oooo wa 0 (oo + EXPERMENTAL 0 RESONA NCE BOUND RESONANCE + BOUND Uaa( Q O = O. Q O.O E NERGY {ev) L.OO FG. 4. The energy dependent therma cross section of 5 Sm. The soid ine shows the fitted cross section as computed from the resoved and bound resonance parameters. The bound state and resonance components are aso shown separatey. termine the resonance parameters of bound states. A good fit, accurate within the statistica uncertainty of the measurement, was achieved by using a singe state at ev. The state aso has sensibe resonance parameters, 100 mv for & and mv for g. Figure 4 shows the bound and resoved components of the cross section. The "Sm cross section is strongy non-1/v even at ev and use of a b 1/u cross section woud overestimate the therma neutron capture rate. C. Cross section in the ow kev energy range n the ev energy range the measured transmission function was used to determine the average cross section. Athough the transmission is typicay greater than 9(P/o in this energy range, the statistica precision in each time channe is better than 2% and thus the computation of an average cross section seemed justified. One difficuty inherent in the determination of the average cross section from high transmission sampes is the evauation and eimination of any systematic base-ine bias due to sma normaization errors between sampe-in and sampe-out runs. However, this bias can be determined by fitting the average cross section to a function of the form A. +B/vE. The constant A contains the unknown bias and the potentia scattering cross section. The coefficient B is directy reated to the strength function. Higher order terms do arise in this expansion, but they were negigibe for "Sm in the ower kev energy range. The constant A. was found to be 39 b which incudes an assumed 8 b of potentia scattering. The strength function determined as above was in exceent agreement with that derived from individua resonance parameters. The average cross section with bias and potentia scattering removed, is shown in Fig. 5 for 25, 51, and 101 point averages. These averages correspond to energy averaging intervas of approximatey 50, 100, and 200 ev at kev. The residua "intermediate structure" which can be seen in the cross section is quite interesting. The fuctuation near 800 ev for exampe contains about 75 compound nuceus resona, ces.. D. Leve density and the Dyson-Mehta 6 statistic The eve density of "Sm just above the neutron sepa. ration energy (-8.30 MeV) was determined from the observed spacing of resonances in the n+"sm tota cross section for neutron energies ev. This region incudes 64 resoved resonances. The eve density was obtained by east squares fitting the cumuative density of states N(E), the usua stair step function, to a straight ine function AE +B. The vaues obtained for the

7 ~ 1 $ 1 TOTAL NEUTRON CROSS SECTON FOR "Sm AN& ) OO , z 0 QP C/! 1! O - PONT! A V ERA G E ~ iii ii i i i~i i i i & O i o i OO, a. 5- PONT AVERAGE i i i i i i i i i & i i! i i i ~ i 25- PONT AVERAGE OOO ENERGY FG. 5. The average tota. cross section for Sm from 100 to 2250 ev. The potentia (hard sphere) scattering cross section has been subtracted. The three averaging intervas correspond to approximatey 50, 100, and 200 ev. zero offset eve spacing 1/B and the average eve spacing 1/4 were 0.7 and ev, respectivey. The average eve spacing vaue of ev corresponds to a "Sm eve density of 5.807&10 states/mev at 8.30 MeV. The above fitting is a necessary preiminary step for the computation of the Dyson-Mehta, (D-M)4, statistic. This statistic is defined as, &max 6, = Min N (E) AE B] de. A & Emax 0 Theoretica vaues for 43 have been derived by Dyson and Mehta based on the statistica orthogona ensembe" (OE). This theory for the statistica properties of the eigenvaues of arge random matrices impies a ong range ordering of eve spacings such that 43 increases ony as in% rather than proportiona to N, which foows from a purey random sequence of spacings (no ong range order) R.ahn et a. and Camarda et al" have recenty tested the 43 statistic on a sequence of eves observed in "2Sm, " Sm, and severa other rare earth neutron cross sections. Good agreement between theory and observation was obtained. The b3 statistic has not yet been tested on eve sequences in the odd & isotopes of Sm nor for Sm. Since extensive resonance data now exist for ~Sm and "Sm (Eiand et a."), for "~Sm (Karzhavina and Popov"), and for "Sm, it is of interest to compute the &3 statistic for these isotopes aso. Tabe V ists these resuts for six Sm isotopes. The ~3 statistic for "Sm and "Sm were incuded in the tabe. For these two isotopes, we used the same eve sequences as did Bahn et &. in order to verify our cacuations. Our resuts are identica to theirs. The second and third coumns of the tabe indicate the number of eves in each sequence and the upper energy imit. The upper energy imit for each isotope, E,was seected by examing the pot of N(E) vs E Since it.is required that the eve sequence be compete up to ",,., this imit was conservativey chosen. Figure 6 shows the function N(E) vs E for "Sm and indicates the seection of E,x=105 ev. The theoretica vaues of 43 and their standard deviations we re computed in accordance with Eqs. (81) and (82), D-M Ref. 10, for the odd A isotopes and Eqs. (58) and (64) for the even A. isotopes. Tabe V shows that the eve sequences for a, six Sm isotopes have the ong range order predicted by the D-M theory. Thus the present new resuts for """"Sm provide further confirmation of the theory. A reasonabe aternative to the D-M theory is the usua (uncorreated) Wig- TABLE V. Summary of resuts for the Dyson-Mehta 63 statistic. Target isotope Emax Observed D-M theory U-W theory D Ref. 4Sm "Sm "Sm "Sm ~~~8m "Sm

8 902 G. J. KROUAC AND H. M. E AND ner (U-W) distribution of eve spacings. Using Monte Caro techniques, Camarda et a." have derived expressions for 4, from the U-W distribution. This resut is given in coumn 6 of the tabe. t can be seen that the observed 4, statistic is in much better agreement with the D-M theory than the U-W resut. However, the standard deviations of the U-W resut are somewhat too arge due to the imited popuation of s-wave resonances to be absoutey concusive. Previous to the present resuts and recent work by the Coumbia group"" and by Coceva et a., " a computed vaues of 4, were much arger than ApM t was generay assumed that this was due to errors in the experimenta eve sequence due to missed weak s-wave resonances or to erroneous incusion of P -wave resonances. This assumption was indeed borne out in our anaysis for "Sm. Our initia seections for N and E for this isotope were 81 and 0 ev, respectivey, because the stair step pot appeared to be a straight ine up to that energy. The seection eads to an observed &, of 1.22 compared to &pm of 0.74~ When N and E werevery conservativey owered to 43 and ev, the resut in Tabe V was obtained, in good agreement with 4p M. E. Strength function The neutron strength function for the n +"Sm interaction was determined by two different methods: (1) from the ow energy resoved resonances and (2) from the average cross section in the kev energy range. Up to 296 ev, 120 resonances have been anayzed in the "Sm neutron tota cross section. Due to the ow P -wave penetrabiity at these energies and the near minimum P-wave strength function in this mass region, it can be confidenty asserted that a of these resonances are s wave. However, due to the nonzero ground state spin for "Sm (=-, ) s-wave resonances form a dua popuation with tota anguar momentum, J =+,, of either 2 or 3. Since resonances with J= 2 or 3 cannot be distinguished by anaysis of the tota cross section, ony the tota s-wave strength function averaged over both 40 ~20- LJ ~(00 LLJ ~8o UJ JJ g) 0 ~ too En (ev) ( FG. 6. Average eve spacing of s-wave neutron resonances in n + ~5~Sm. The points are potted at intervas of five resonances. Note the appreciabe number of unresoved resonances above 110 ev. spin states can be determined. The s-wave strength function So was obtained from the cumuative sum Q g for resoved resonances, divided by the width of the anayzed energy region (i.e., S,=gg /E). t is frequenty stated that this method is insensitive to missed resonances because the missed resonances have sma g vaues and contribute itte to the cumuative sum. For "Sm it can be seen from Fig. 6 that some resonances probaby begin to be undetectabe above 110 ev. The insensitivity of the strength function to weak missing resonances is demonstrated in Tabe V where the S, derived from three 100 ev anaysis subintervas is shown. Athough the apparent eve density drops by more than a factor of 2 from 100 to 300 ev, the strength function is constant within its statistica uncertainty. ndeed, the apparent increase in strength between ev appears to be a rea statistica or intermediate structure fuctuation (see Fig. 5). The same information given in Tabe V is graphicay iustrated in Fig. 7 which shows the function ggf vs E. Athough the pot of the cumuative number of eves (Fig. 6) begins to bend above 110 ev, the strength function remains neary constant. The straight ine in Fig, 7 represents the best vaue of the strength function So = , de- TABLE V. s-wave strength function for Sm. Energy range N Loca eves N Cumuative S,x ].04 Loca S,x 104 Cumuative Best over-a vaue: So= x (energy averaged cross section) ~11+0 ~

9 TOTAL NEUTRON CROSS SECTON FOR "Sm AND termined from the resoved resonances beow 200 ev. A second independent determination of the s-wave strength function was obtained from the measured cross section in the ow kev energy range. A 101 point average (approximatey 200 ev averaging interva) of the cross section was performed in the energy range from ev. This resut was previousy shown in Fig. 5. The averaged cross section was then fitted to a function of the form A+BgE. This resut was originay derived by Feshbach, Porter, and %eisskopf" from the optica mode and was written in terms of the strength function as, 2772K 2 where X, is the waveength of a 1 ev neutron and 8" is the potentia scattering ength. More accurate forms of this equation have since been derived for the higher kev energy, range, but for the present purpose A can be considered a constant and the higher order term in S, is negigibe. The strength function derived from fitting the average cross section was SO = 3.59~10, in good agreement with that derived from the ower energy resoved resonances. Averaging these two determinations of S we obtain SO = && 10 for the best over-a vaue for "Sm. SYSTEMATCS OF Sm LEVEL DENSTES AND STRENGTH FUNCTONS The agreement of known eve sequences in the Sm isotopes with the Dyson-Mehta theory indicates that these sequences are compete. Thus, the eve spacings provide a reiabe measure of the =0 compound nuceus eve density at an excitation energy equa to the neutron binding energy. The mass re gion spanned by the Sm isotopes be gins with a major, N=82, she cosure at "Sm and extends we up into the fiing of the 2f, &, and 1h, &, shes. t is therefore of interest to examine the systematic behavior of the eve density vs neutron number. n order to eiminate the infuence of pairing and excitation energy on the eve density, the Fermi eve density parameter a (MeV ) was derived from the experimentay determined eve density. The Bethe formua, as given by Gibert and Cameron, " was used: Z(i =0) n~ exp2(au)"] a"u" (2J +1)exp- (J+, )/2o] 2(2v)~o where U=B 5 5~ (MeV) is the compound nuceus excitation energy with pairing energy corrections; J is the compound nuceus tota anguar momentum, o = ~Ua A~ is the spin-cutoff factor, and a is the derived eve density parameter (MeV ). The pairing energies determined by Cameron and Ekin" from a semiempiri. ca mass formua were used. Athough the spin-cutoff factor shoud be treated as a second free parameter, we have used the above she mode estimate based on the neutron and proton singe-partice eve spacings. This proc edur e s eems jus tified sine e 0 is neary constant and the eve density is much ess sensitive to o than to &. The resuts derived for the density parameter ) E o N ) 6, 13, 14) n(e V) FG. 7. The s-wave neutron strength function for ~Sm as derived from Zg" vs E. Points are shown at intervas of five resoved resonances. The inearity of Zg vs E, in spite of the arge number of missed resonances above 110 ev, is noteworthy COMPOUND NUCLEUS NEUTRON NUMBER FG. 8, The Fermi eve density parameter a (MeV ) vs the compound nuceus neutron number for Sm and Nd isotopes. The ow vaues for N approaching 82 are expained by she cosure, whie the decreasing vaues above N = 89 appear to be associated with increasing nucear deformation (see text).

10 904 6 J. ~ KROUAC AND H. M. ELAND TABLE V. Leve density parameters for Sm and Nd isotopes. Compound nuc. Target Nuc.. & & (MeV) (MeV) ~n (MeV) ppx 10 (MeV-) (MeV ) "Sm 4Sm Sm "Sm "Sm ~5&Sm ~42Nd 4Nd 44Nd 4Nd "Nd ~4Nd "Nd ~ ~ ~ ~ & by the above procedure are isted in Tabe V aong with the other reevant parameters. The reationship between a and the neutron number is graphicay iustrated in Fig. 8. The eve density parameter demonstrates a we defined maximum at N=89 (2=151 for Sm). A simiar trend was observed by Karzhavina et a." for seven isotopes of Nd. Since they used a different compiation of pairing energies, it was decided to repeat their cacuation using the same pairing energies as for Sm and with the more recent Nd data of Teier and Newstead. " The trend was essentiay the same as seen by Karzhavina et a. This resut is aso shown in Fig. 8 and Tabe V. The behavior of a vs N for the Nd isotopes appears to be in fu agreement with that for the Sm isotopes. The sma vaues for the eve density parameter for neutron numbers approaching N= 82 seems TARGET MASS A 56 FG. 9. The s-wave neutron strength function for Sm and neighboring isotopes in the region of the first peak of the 4-s giant resonance. The curves are intended merey as guides to the eye to i.ustrate the difference between odd and even neutron targets. ceary expained by the she cosure at this magic number. However, the decreasing vaues of a above N=89 are not so easiy expained by she mode arguments. The increase between N = 82 and 89 may be correated with the number of vaence partices or hoes in the f, ~, and h9&, shes. The tendency for the eve density to maximize at the haf fied she and to decrease for fewer partices or hoes is predicted in the work of Rosenzweig." Between N=82 and 89 the Sm and Nd isotopes are spherica, or neary so, and the f7&, shes are ve ry e ose to each othe r in energy, neary degenerate. f these shes are treated as a singe "super she" hoding 18 partices, then the eve density shoud maximize at N=91. However, beginning around N=88 or 89, the target nucei, for exampe "Sm or "Sm begin to be appreciaby deformed. n this case the Nisson eve sequence must be foowed rather than that for a spherica potentia. f we examine the Nisson diagram for 82 & N& 126, there is a definite energy gap at N = 90 for vaues of deformation, , whi. ch are eharaeteri. stic of Sm. This gap simuates the effect of a she cosure and shoud therefore ead to a decreased density. t is possibe that this effect, which arises for deformed nucei, is the cause of decreased vaues of a above N= 89. The strength functions for the Sm isotopes and for neighboring isotopes are iustrated in Fig. 9. These data demonstrate a strong even-odd fuctuation of the strength function in this mass region. f smooth curves are drawn through the even-even and even-odd strength functions, as shown, it becomes cear that the even-odd target strength functions are systematicay arger by neary a factor of 2 in the peak region. The one deviation from this trend is the strength function for ~Nd, but here the uncertainty of the vaue is arge.

11 TOTAL NEUTHON t ROSS SECTON FOR Sm AND These odd-even fuctuations suggest some infuence due to pairing correations and merit further investigation. We thank Barbara L. Hennig for her competent work in the storage, retrieva, and transformation of data and for the construction of a mutitude of computer graphs. The efforts of Leon Love of the Target and sotopes Division at Oak Ridge Nationa Laboratory is gratefuy acknowedged for the separation and production of the metaic 5Sm sampes *Operated for the U. S. Atomic Energy Commission by the Genera. Eectric Company under Contract No. W Eng-52. F. E. Lane and W. H. Waker, in Proceedings of the Second Conference on Neutron Cross Sections and Technoogy, Washington, D. C., March 1968, edited by D. T. Godman (NBS Specia Pubication No. 299, 1968), Vo., p R. J. French, in Proceedings of the Second Conference on Neutron Cross Sections and Technoogy, Washington, D. C., March 1968 (see Ref. 1), p N. J. Pattenden, Nuc. Sci. Eng. 17, 371 (1963). W. H. Waker, Chak River Laboratory Report No. AECL-3037, 1973 (unpubished), Pt,. S. E. Atta and J. A. Harvey, Oak Ridge Nationa Laboratory Report No. ORNL-3205, 19 (unpubished). F. Rahn et a., Phys. Rev. C 6, 251 (1972). J. W, Codding, Jr., R. L. Tromp, and F. B. Simpson, Nuc. Sci. Eng. 43, 58 (1971). G. J. Kirouac et a., Nuc. Sci. Eng. 52, 310 (1973). 9K. K. Seth et a., Phys. Rev. 110, 692 (1958). "F. J. Dyson and M. L. Mehta, J. Math. Phys. 4, 701 (1963). F. J. Dyson, J. Math. Phys. 3, 140, 157, 166 (19). H. Camarda et a., in Statistica Properties of Nucei, edited by J. B. Garg (Penum, New York 1972), p ~3H. M. Eiand et a., Nuc. Sci. Eng. 54, 286 (1974). ~4E. N. Karzhavina and A. B. Popov, Joint nstitute for Nucear Research Report No. JNR-P3-5655, 1971 (unpubished). 5H. Feshbach, C. Porter, and V. F. Weisskopf, Phys. Rev. 96, 448 (1954). A. Gibert and A. G. W. Cameron, Can. J. Phys. 43, 1446 (1965). A. G. W. Cameron and R. M. Ekin, Can. J. Phys. 43, 1288 (1965). E. N. Karzhavina et a., Yad. Fiz. 8, 639 (1968) trans. : Sov. J. Nuc. Phys. 8, 371 (1969)]. 9H. Teier and C. M. Newstead, in Proceedings of the Third Conference on Neutron Cross Sections and Technoogy, Knoxvie, Tennessee, 1971 (unpubished), Vo., p N. Rosenzweig, Phys. Rev. 105, 950 (1957); 108, 817 (1957). S. G. Nisson, K. Dan. Vidensk. Se.sk. Mat. Fys. Medd. 29, No. 16 (1955); aso B. R. Motteson and S. G. Nisson, K. Dan. Vidensk. Sesk. Mat. Fys. Skr. 1, No. 8 (1959), H.. Liou et a., Phys. Rev. C 5, 974 (1972). C. Coceva et a., in Statistica Properties of Nucei (see Ref. 12), p. 447.