Anomalous Neutron Yields Confirmed for Ba-Mo and Newly Observed for Ce-Zr from Spontaneous Fission of 252 Cf
B. M. Musangu, A. H. Thibeault, T. H. Richards, E. H. Wang, J. H. Hamilton, C. J. Zachary, J. M. Eldridge, A. V. Ramayya, Y. X. Luo, J. O. Rasmussen, G. M. Ter-Akopian, Yu. Ts. Oganessian, S. J. Zhu
AAnomalous Neutron Yields Confirmed for Ba-Mo and Newly Observed for Ce-Zr fromSpontaneous Fission of Cf B. M. Musangu, A. H. Thibeault, T. H. Richards,
1, 2
E. H. Wang, J. H. Hamilton, C. J. Zachary, J. M. Eldridge, A. V. Ramayya, Y. X. Luo,
1, 3
J. O. Rasmussen, G. M. Ter-Akopian, Yu. Ts. Oganessian, and S. J. Zhu Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Joint Institute for Nuclear Research, RU-141980 Dubna, Russian Federation Department of Physics, Tsinghua University, Beijing 100084, China (Dated: July 16, 2020)We reinvestigated the neutron multiplicity yields of Ba-Mo, Ce-Zr, Te-Pd, and Nd-Sr from thespontaneous fission of
Cf; by (i) using both γ - γ - γ - γ and γ - γ - γ coincidence data, (ii) using upto date level scheme structures, and (iii) cross-checking analogous energy transitions in multipleisotopes, we have achieved higher precision than previous analyses. Particular attention was givento the Ba-Mo pairs where our results clearly confirm that the Ba-Mo yield data have a second hotfission mode where 8, 9, 10, and now 11 neutron evaporation channels are observed. These arethe first observations of the 11 neutron channel. These 8-11 neutron channels are observed for thefirst time in the Ce-Zr pairs, but are not observed in other fission pairs. The measured intensitiesof the second mode in Ba-Mo and Ce-Zr pairs are ∼ % and ∼ % , respectively. Thesehigh neutron number evaporation modes can be an indication of hyperdeformation and/or octupoledeformation in − Ba and in , Ce at scission to give rise to such high neutron multiplicities.
I. INTRODUCTION
Yields of individual correlated pairs in barium (Z =56) and molybdenum (Z = 42) binary fission have beenobserved to undergo fission splits via an extra “hot fis-sion mode” (also called second mode) [1]. In this mode,it has been observed that the Ba-Mo fragment pair emitshigh neutron multiplicities of 7 to 10 neutrons in sponta-neous fission of
Cf [1–3]. To explain this phenomenon,theorists have attributed the presence of this mode to apossible hyperdeformation of , , Ba fragments atscission [1, 4, 5]. This is justified by referring back tothe theory which predicts that a large nuclear deforma-tion is more likely to yield higher neutron multiplicities[6]. Other theorists have raised skepticism, since the hotfission mode has only been observed in Ba-Mo fragmentpairs of
Cf and not in spontaneous fission of
Cm[7]. However, this private communication [7] has neverbeen published.Furthermore, some earlier analysis in spontaneous fis-sion of
Cf did not confirm the second hot mode[8] without reporting the 9 and 10 channel yields (seelater discussion), while others did show some irregularityaround the eight-neutron channel [9–12]. Because of theimportance of understanding this extra hot fission mode,pairs of Ba-Mo, Ce-Zr, Te-Pd, and Nd-Sr have been stud-ied with improved precision using γ - γ - γ - γ as well as γ - γ - γ coincidence data and the latest level structures of thesenuclei. Also, relative intensities of transitions in these nu-clei made available through our work likewise improvedthe accuracy of the analysis. In all cases, careful at-tention was given to transitions of the same energies inmultiple isotopes.Of particular interest in this experiment are the γ -ray transitions to the ground state. Some isotopes have asingle ground state γ -ray transition, but others have mul-tiple ones. The ground state γ -ray transition is generallythe highest intensity γ -ray emitted by an isotope, andall daughter nuclei will emit this γ -ray, excluding the ex-tremely unlikely case they were produced in the groundstate during the fission process. By measuring the in-tensity of ground state γ -rays, it can be deduced howlikely specific isotopes of fission partner isotopes are tobe produced in the spontaneous fission of Cf.If the ground state γ -ray is inconvenient to measure,it is also possible to use a higher transition to make thiscalculation, as long as its intensity relative to the groundstate transition is known. The relative intensities of alltransitions feeding the ground states of the isotopes ana-lyzed in this study were determined based on new levelsschemes with new ground state transitions (especially inodd-even nuclei) [13, 17–24] to produce a new set of ab-solute yields. Some of the γ -rays in the newly publishedlevel schemes are not clearly observed in our data such as Te [25]. The new results confirm a second hot mode inBa-Mo pairs with an intensity of ∼ % and shows ev-idence for a comparable second hot mode in Ce-Zr pairswith an intensity of ∼ % . These result are comparedwith other results [8–12]. II. EXPERIMENTAL SET-UP
The present experiment was done at the LawrenceBerkeley National Laboratory (LBNL) with the Gamma-sphere detector array. A 62 µ Ci Cf source was sand-wiched between two iron 10 mg/cm foils, which wereused to stop the fission fragments and eliminate the needfor Doppler correction. A 7.62 cm in diameter plastic a r X i v : . [ nu c l - e x ] J u l (CH) ball surrounded the source to absorb β rays andconversion electrons, as well as to partially moderate andabsorb fission neutrons. A total of 5.7 × γ - γ - γ andhigher fold γ events, and 1.9 × γ - γ - γ - γ and higherfold γ coincident events were recorded. These γ coin-cident data were analyzed by the RADWARE softwarepackage [26]. More details about the experimental setupcan be found in Refs. [27, 28]. III. METHOD OF DATA ANALYSIS
Quadruple ( γ - γ - γ - γ ) as well as triple ( γ - γ - γ ) coinci-dence data were analyzed to extract the relative yields ofcorrelated fragment pairs in spontaneous fission of Cf.In order to find peaks for the yield computation, a dou-ble or triple gate was set on the most intense coincident γ -rays in a given nucleus (usually the 2 + → + and 4 + → + transitions in case of an even-even product). On thegenerated coincidence spectrum, the transitions in thepartner fragments were clearly identified. The intensitiesof the γ -ray transitions in the partners (usually the 2 + → + in case of even-even nuclei) were corrected for thedetector efficiencies and internal conversion coefficients(ICC) of the γ -rays involved in the selection and usedalong with other transitions feeding into the ground stateto extract the relative yields for the considered parti-tions. In the case of odd nuclei, all the known transitionspopulating the ground state were summed proportionallyaccording to their intensities.Additionally, if there is a presence of an isomeric statein the level scheme structure of a given nucleus, thetransitions populating into that isomeric state were con-sidered by adding the contribution of those transitionspopulating that state according to its time scale. Thiswas done to avoid underestimating the yields. Spe-cific examples will be given in the discussion section.A two-dimensional matrix was created from the initialdata by selecting the γ -ray coincidences occurring within1 µ s time window. The peaks observed in this two-dimensional spectrum arise from the coincidences be-tween the γ -ray emitted promptly by both complemen-tary fission fragments of different fragment pairs. IV. EXPERIMENTAL RESULTS ANDDISCUSSION
Fission spectra are very complex and this type of anal-ysis is difficult and prone to errors caused by randomcoincidences and background. As such, we found somepeaks unusable because of contamination or similar tran-sition energies found in other isotopes. Cross-checks bygating on a series of isotopes as well as gating on their fis-sion partners have been done to determine possible con-tamination and the accuracy of the current result. Inaddition, to measure yields in these cases, we used peaksfound in higher transitions and scaled them appropri- ately. For example, Table I contains this information forthe Sr-Nd pair. In order to calculate the scaling factor,we set a clean gate with no contamination on energy tran-sitions of other isotopes and measured the intensities ofthe ground state transitions and of the higher transitions.By taking the ratio of these intensities, we compute thescaling factor needed.
TABLE I. A list of isotopes whose ground state transitionenergies were difficult to measure (because of similar groundstate energies or not clearly observed in our data) and whatenergy transition we measured instead in Nd-Sr fragmentpairs. The scaling factor is the relative intensity of the mea-sured transition to the ground state transition; we divided theyield of the transition by this factor to correct it.
Isotope Gate Ground Measured Scalingstate (keV) (keV) factor Sr Nd 814.6 859 0.46 Sr Nd 836.7 1089.1 0.23 Sr Nd 814.8 977.5 0.49
The yield matrix for tellurium (Z = 52) and palladium(Z = 46) in Table II, displays the expected pattern wherethe highest yields are concentrated in the center of thematrix, along the 4 neutron channel diagonal, runningfrom the bottom left to the top right corners. The yieldmatrix was normalized by using the normalization con-stant of
Pd in Wahl’s table [31]. This pair has a lot ofisomeric states and many of the level schemes are incom-plete. Therefore, the yields are incomplete (see Fig. 1).The yields for the other studied element pairs in Fig. 1display a similar pattern as expected. However, as seenin Fig. 2 (a), where the spectrum was gated on both the373.7 and 574.5 keV transitions in
Pd, there is no ev-idence for the 9 and 10 neutron channel at 1150.6 keVin
Te and at 974.4 keV in
Te, respectively, for theTe-Pd pairs. Whereas, there is clear evidence of the 8neutron channel at 1279.1 keV in
Te which fits nicelywith the simple curve in Fig. 1.In the Nd-Sr yields matrix in Table IV, we left mostof the items in the
Nd and
Nd columns blank be-cause those isotopes are very weakly populated in thespontaneous fission of
Cf, making it difficult to mea-sure energy transitions of interest. Some similar energies,such as the ground state transitions of
Sr and
Nd(129.8 keV and 129.7 keV, respectively), are not distin-guishable. To resolve this, we set a gate on both the 2 + → + and 4 + → + transitions of Sr 129.8/287.9 keVand compared the intensity ratios of its partners’ transi-tions of interest to another double gate on 2 + → + and4 + → + transitions of Sr 144.3/289.4 keV. The 129.7keV peak from
Nd was contaminated as well as someof the other peaks of interest. Therefore, the gate on
Sr was avoided. Isomeric states had to be consideredin the case of , Nd. In
Nd, the isomeric state at1298.0 keV is weakly populated therefore, the transitions
TABLE II. New yield matrix for tellurium and palladium from the spontaneous fission of
Cf.Yield Pd Pd Pd Pd Pd Pd Pd Pd Pd Te 0.010(1) 0.0029(4) 0.017(2)
Te 0.05(1) 0.042(5) 0.006(1) 0.010(1)
Te 0.036(4) 0.06(1) 0.07(1) 0.19(2) 0.018(2) 0.016(2)
Te 0.0022(3) 0.016(3) 0.035(4) 0.14(2) 0.09(1) 0.15(2) 0.005(1) 0.008(1)
Te 0.0021(3) 0.015(2) 0.16(2) 0.33(4) 0.78(9) 0.28(3) 0.24(3) 0.007(1) 0.006(1)
Te 0.003(1) 0.017(2) 0.11(1) 0.20(2) 0.27(4) 0.05(1) 0.040(5) 0.0013(3)
Te 0.021(3) 0.06(1) 0.29(4) 0.24(3) 0.22(4)
Te 0.012(2) 0.020(3) 0.12(2) 0.06(1) 0.013(2)
Te 0.014(2) 0.023(3) 0.035(4) 0.005(1) − − Ce-Zr FWHM = 3.1Nd-Sr FWHM = 3.1Ba-Mo FWHM = 3.1Te-Pd FWHM = 2.9Neutron Loss Number R e l a t i v e Y i e l d s ( a r b i t r a r y un i t s ) FIG. 1. The experimental Ba-Mo, Ce-Zr, Te-Pd and Nd-Sryield curves from the present analysis are shown above. Thereis no evidence for the 9, 10 and 11 neutron channels in pairsother than Ba-Mo and the newly observed Ce-Zr. A smoothGaussian fit to the 0-8 neutron channels in Nd-Sr, Te-Pd, Ce-Zr and Ba-Mo. The full width at half maximum (FWHM)was also calculated for each of the yields as shown in thisfigure. feeding into it were not added to the total yields.The
Nd nucleus was reported to have an isomer at1348 keV in [14], which is not observed in the current
TABLE III. A list of the average neutron multiplicities ( ¯ ν ) andthe full width at half maximum (FWHM) for each pair shownin Fig. 1. The average neutron multiplicity distributions arevery close to the accepted values of 3.8 for the spontaneousfission of Cf. Ba-Mo Ce-Zr Te-Pd Nd-SrAve ( ¯ ν ) 3.57 3.62 3.71 3.84FWHM 3.1 3.1 2.9 3.1 data. In that paper, the ground state band transitionswere reported as 72, 163, 243, 328 keV... etc, with a 870keV isomeric transition. In the contrast, both the pre-vious work in [15] and our current data show a 72-163-248 keV cascade for ground state band. In [14], tran-sition energy and levels were also reported in other nu-clei , Sm, , Nd. The energy difference betweentransitions in those nuclei reported in [14] and our cur-rent work, as well as other data recorded in nuclear datasheets is generally within 1 keV. Thus, the big 5 keV en-ergy difference in
Nd between the 243 and 248 keV 6 + → + transition may indicate a wrong isotope assignmentin [14]. Instead, Sm was reported to have an isomerin [16], with 163-243 keV for the first two E2 transitionsfor the ground state band and 870 keV for the isomerictransition. The 1348 keV isomer reported in [14] maybelong to
Sm, but 5 mass number away from
Nd.Further details are needed to understand the reason.According to [17],
Nd the ground state transitionsare 50.0 keV, 120.2 keV and 191.7 keV if our time gateis long enough to cover the isomeric transition. Energiesat 50.0 keV, 70.2 keV, 60.7 keV and 78.0 keV reported in[17] are hard to measure accurately to get accurate inten-sities. Thus, when the ground state transitions are hardto measure we summed up all the next level transitions.In the case of
Nd, we used 88.3 keV, 197.6 keV and158.5 keV in the ground state band and 97.9 keV, 175.8keV and 208.8 keV in the 5/2 + band together. Thesetransition are reported in [17]. Figure. 1 shows a plot ofthe extracted yields against the fission’s neutron channelnumber (see Fig. 1). Also shown in Fig. 2 (b), a triplegate on 129.7, 251.2 and 338.6 keV transitions in Ndis used to show that there is no evidence for the 9 and10 neutron channel at 986.1 keV in Sr and at 858.9 keV
980 1020 1060 1100 1140 1180 1220 126050100150200 (a)1279.1(8n)1150.6(9n)974.4(10n) 373.7/547.5(
Pd)
790 840 880 920 960 1000 − (b)836.7(8n) 986.1(9n)858.9(10n)129.7/251.2/338.6( Nd) C o un t s p e r C h a nn e l
310 330 350 370 390 410 430 4500100200300 (c)410(9n)
Ce161.5/999.4( Zr)
Energy
FIG. 2. Gamma-ray coincidence spectra by gating on (a)373.7 and 574.5 keV transitions in
Pd to show that there isno evidence for the 9 and 10 neutron channel at 1150.6 keV in
Te and at 974.4 keV in
Te, respectively, whereas thereis clear evidence of the 8 neutron channel at 1279.1 keV in
Te which fits to the curve. In (b) a triple gate on 129.7,251.2 and 338.6 keV transitions in
Nd to show that there isno evidence for the 9 and 10 neutron channel at 986.1 keV in Sr and at 858.9 keV in Sr for the Nd-Sr pair, respectively,whereas there is weak evidence of the 8 neutron channel at836.7 keV in Sr. And in (c) a double gate on 161.5 and 999.4keV transitions in Zr to show evidence for the 9 neutronchannel at 410 keV in
Ce for the Ce-Zr pair. in Sr for the Nd-Sr pair, respectively. Whereas there isclear evidence of the 8 neutron channel at 836.7 keV in Sr that fits fits nicely the single yields curve as shownin Fig. 1.In the case of determining the cerium (Z = 58) andzirconium (Z = 40) yield matrix, measurements of mul-tiple γ -rays emitted by the Ce-Zr fission fragment pairsformed in spontaneous fission of Cf were used to ex-tract the yields. Table V below displays the absoluteyields data that were collected. These are new resultsand different from the report given in Ref. [32]. In thisanalysis, most of the transitions of interest were easilyidentifiable with the exception of the 97.5 keV (9/2 − → − ) and 97.4 keV (2 + → + ) from Ce and
Ce,respectively, and
Zr and
Zr also have similar tran-sitions of 97.8 keV (5/2 + → + ) and 98.4 keV (5/2 + → + ), respectively.To avoid possible contamination, a few gates were seton Ce to measure the peaks of interests from its Zrfragment partners. Any contamination of the 98.4 keVtransition from
Zr is avoided since
Zr and
Ceare not fission partners in spontaneous fission of
Cf.However, gating on
Ce would bring in contamination (a) (b)1222(10n) Zr 397.2/709.1 keV(
Ce) (c)1222(10n) Zr397.2/541.2/709.1 keV(
Ce) C o un t s p e r C h a nn e l (d)1222(10n) Zr541.2/709.1 keV(
Ce) (e)1750.4(10n) Zr409.9/503.2 keV(
Ce) (f)1750.4(10n) Zr 258.3/515 keV(
Ce)
Energy (keV)
Ce)
FIG. 3. Gamma-ray coincidence spectra by gating on (a)397.2/541.2 keV, (b) 397.2/709.1 keV, (c) 397.2, 541.2 and709.1 keV and (d) 541.2/709.1 keV transitions in
Ce toshow that there is evidence for the 10 neutron channel at 1222keV in Zr for the Zr-
Ce pair. In (e), a double gate on409.9/503.2 keV transitions in
Ce to show clear evidenceof the 10 neutron for the
Ce and Zr pair at 1750.4 keVby gating on 409.9/503.2 keV. And (f) gives further evidencefor the presence of the 1750.4 keV transition by gating on258.3/515 keV from both
Zr and
Zr. Multiple gates were set onthe Zr fragments to measure the ground state transitionof
Ce. By gating on 109.4/146.6 keV of
Zr, the 97.4keV transition from
Ce is once more avoided. Becausethe channel number between
Zr and
Ce is zero, anypossible contribution from the 97.4 keV of
Ce to the97.5 keV in
Ce can be neglected given that it is very
TABLE IV. New yield matrix for neodymium and strontium from the spontaneous fission of
Cf.Yield Nd Nd Nd Nd Nd Nd Nd Nd Nd Sr 0.004(1) 0.005(1) Sr 0.020(3) 0.019(4) 0.030(5) Sr 0.005(1) <0.05 0.027(5) 0.012(2) 0.022(4) Sr 0.010(2) 0.026(4) 0.09(1) 0.18(3) 0.13(2) 0.047(8) 0.043(7) Sr 0.017(3) 0.033(6) 0.12(2) 0.30(5) 0.11(2) 0.023(4) 0.012(2) Sr 0.040(7) 0.06(1) 0.16(3) 0.23(4) 0.06(1) 0.010(2) 0.005(1) Sr 0.030(5) 0.043(7) 0.06(1) 0.07(1) 0.021(4) Sr 0.010(2) 0.031(6) 0.08(2) 0.044(7) 0.06(1) 0.025(5) 0.009(2) Sr 0.020(4) 0.017(3) 0.015(3)
Sr 0.026(4) 0.006(1)TABLE V. New yield matrix for cerium and zirconium from the spontaneous fission of
Cf. The 8-11 neutron channels arelabeled with neutron numbers as superscripts.Yield Ce Ce Ce Ce Ce Ce Ce Ce Ce Zr 0.003(1) Zr 0.002(1) <0.009 Zr 0.004(1) Zr 0.007(3) Zr 0.011(2) Zr 0.11(2) 0.26(4) 0.33(5) 0.54(9) 0.23(4) 0.17(3)
Zr 0.024(4) 0.16(3) 0.43(7) 0.40(6) 0.40(6) 0.10(2) 0.029(5)
Zr 0.033(6) 0.14(3) 0.22(4) 0.14(3) 0.12(2) 0.03(1)
Zr 0.005(1) 0.07(1) 0.008(1) 0.0013(3) small. Any gate on
Zr brings in contribution fromboth the 97.4 keV of
Ce to the 97.5 keV in
Ce. Onething to consider first is to avoid setting any gate usingthe 97.8 keV in
Zr. This prevents the contributionfrom the 98.4 keV in
Zr. A double gate 216.6/250.9keV was set on
Zr and from this gate three peaks wereof interest, however, only the 158.7 keV one in
Ce anda peak around 98 keV, containing both the 97.4 keV peak(
Ce) and 97.5 keV peak (
Ce), were capable of be-ing measured. Since the ratio between 158.7 keV peak(
Ce) and 97.5 keV peak (
Ce) was already knownwhen determining the yields of
Ce, it was easy to de-duce the portion of the contribution of
Ce from themeasured peak. This meant that the remaining portionbelonged to the 97.4 keV peak (
Ce). This method wasrepeated for
Zr.In the present study we observed evidence of the 9, 10and 11 neutron channels in the Ce-Zr fission pairs. Adouble gate on 397.2 keV and 541.2 keV in
Ce showsevidence for the 10 neutron channel at 1222.9 keV in Zr(see Fig. 3). However, in this gate the intensity is notvery clear. Therefore, we checked for clean transitions togate on in
Ce to avoid contamination and we foundthat other double and triple gates on 397.2, 541.2, 709.1and 585.2 keV were good candidates that can be used toverify this observed peak. As shown in Fig. 3 (a), (b),(c) and (d) all these gates show evidence of the presenceof the 10 neutron channel for the Zr-
Ce fission pair. In part (e) of Fig. 3 there is another clear evidence ofthe 10 neutron for the
Ce and Zr pair at 1750.4 keVby gating on 409.9/503.2 keV in
Ce. To measure theintensity of the 1750.4 keV, we accounted for the presenceof 1751 keV in
Zr (which would make this yield higherthan what it should be) by subtracting the portion of1751 keV from the measured 1750.4 keV in
Ce and Zr pair since we already had the real intensity for that.Part (f) of Fig. 3 gives further evidence for the presenceof the 1750.4 keV.There is a clear 1103 keV peak when gating on
Ce.The intensity of this peak however, is higher than ex-pected. We discovered that this high intensity is due toa strong contamination around this peak from beta decaywhere a 1103 keV transition in
Ce feeds a 1810.2 keVlevel. There is also a clear peak at 258 keV in
Ce whenone gates on Zr. However, for any of the possible gateson Zr, it is difficult to find a good reference peak thathas the expected ratio with the 258 keV peak. Therefore,we measured the 409.9 keV peak which has the expectedratio with the 209.1 keV peak taking into considerationtheir intensities, efficiency, and internal conversion rela-tive to the ground state transitions. Another challengingchannel to measure is the
Ce- Zr. There is a strong1102.8 keV peak feeding into the 4 + level (938.6 keV) in Ce. Hence, the presence of the 11 neutron channelat about the 397.2 keV peak would be influenced by theoverlapping two transitions of 1103 keV in both
Ceand Zr.Upon completion of the matrix yield of the corre-lated fragment pairs of Ce-Zr in the spontaneous fissionof
Cf, the yields were next scaled according to Ter-Apkopian’s independent yield [2] and summed for eachisotope of Ce. This summation and Ter-Akopian’s cal-culated data for Ce-Zr, were both normalized such that
Ce had a value of 100. Then these two data sets werecompared to see if Ter-Akopian’s calculations could beverified. As can be seen in Fig. 1, the present abso-lute yield data Te-Pd, Nd-Sr and Ce-Zr are in agreementwith the previous ones [2], and thus are experimentallyconfirmed with smaller error limits. The results fromthe present study show evidence for an “extra hot fis-sion mode" as shown Fig. 4. This is the first time thismode is observed in Ce-Zr pairs; it is ∼ % of thefirst mode. The observation of this mode in this paircan be explained when one considers that − Ba and , Ce have been determined to be octupole deformed[29, 30, 33–35] and may also have hyperdeformation atscission to give these nuclei high internal energy and inturn gives rise to high neutron multiplicities. The sec-ond curve (6-10 neutrons) in Fig 4 was fitted by restrict-ing the width of the second curve to the width of thefirst curve (0-7 neutron channels) and the position to 8neutron channel. If the unfixed width method is usedinstead, the width of the Ce-Zr first curve is 6 % largerthan the Ba-Mo width. However, the 10 neutron chan-nel in Ce-Zr pair is obviously above the tail of the firstGaussian in either way.The new yields of Ba-Mo are given in Table VI andFig. 1. The 8-10 neutron yields presented in the presentstudy are much lower than both the ones reported ear-lier; contributing ∼ % of the first mode. In thefirst report [1], the second mode was reported to con-tribute ∼ % of the first mode with significantly lowerTKE, 153/189 MeV [1]. The second report to have ob-served this mode [9], reported that it contributed ∼ % .The current experimental data have improved statisticsover the other two experimental data from which the firstand second analysis came. Therefore, one would expectthat the second mode would be more pronounced in thisexperiment. However, this is not the case because withimproved statistics comes more complete level schemesthat provide new insights on possible contamination thatwere otherwise not considered in the previous analysescausing either overestimation or underestimation of theyields. Gating on Ba isotopes and Mo isotopes shouldgive the similar yield results. Such cross-checks were usedin this experiment to investigate the contamination giventhat contaminates are more common in Ba-Mo than inCe-Zr, Te-Pd and Nd-Sr pairs.In detail, in the analysis of Mo-Ba yields, one has to beextra careful when determining the yields of Ba-
Moand the
Ba-
Mo which correspond to the rare 8 and10 neutron channels and the
Ba-
Mo and the
Ba-
Mo yield which correspond to the 4 and 6 neutronchannels. This is because of the possible contamination − − Ce-Zr FWHM = 3.1Ba-Mo FWHM = 3.1Neutron Loss Number R e l a t i v e Y i e l d s ( a r b i t r a r y un i t s ) FIG. 4. The second curve in Ce-Zr was fitted by fixing thewidth of the second curve (presenting the second mode) tothe width of the first curve (presenting the first modes) andalso fixing the position to 8 neutron channel. It contributes ∼ % of the first mode. The second curve in the Ba-Mo fitwas also fitted by fixing the width of the second curve to thewidth of the first curve and fixing the position to 8 neutronchannel. It contributes ∼ % of the first mode. that arise from the unresolved 192.4 keV and 192.9 keV2 + → + transition for Mo and
Mo, respectively(see [8] for similar analysis). In a previous analysis [8],a gate on 602.4/529 keV in
Ba was used to measurethe intensities of 368.6 keV and 371.0 keV transitions in
Mo and
Mo, respectively. In such gate, the 369 keVpeak has ∼
30 counts and is 1/3 (1/14 in our data) of the371 keV one. In contrast, as seen in Fig. 5 part (b), ourdata show ∼ Ba-
Mo yield was overestimated dueto the background fluctuation (10-20 counts) in Ref. [8].A gate was set on the first two transitions of the
Moisotope and the ground state transition (1435.7 keV) of
Ba was measured as well the (8 + → + ) transitionpopulating the isomeric state at 2089 keV level becauseit is very strong in our data. When measuring the yieldsof Ba-
Mo, however, the 192.4 keV from
Mo hasto be avoided to prevent contamination from 192.9 keVfrom
Mo since it is strong and can enhance this yield.Instead, gates on 368 keV and 519 keV transitions from
TABLE VI. New yield matrix for barium and molybdenum from the spontaneous fission of
Cf. The 8-11 neutron channelsare labeled with neutron numbers as superscripts.Yield 138Ba Ba Ba Ba Ba Ba Ba Ba Ba Ba Ba Mo 0.004(1) Mo 0.017(3) 0.005(1)
Mo 0.005(2) Mo 0.009(3) <0.005(1) Mo 0.009(2) Mo 0.008(2) Mo 0.015(3) Mo 0.009(2) 0.020(4) 0.13(3) 0.31(6) 0.57(10) 0.30(6) 0.16(3)
Mo 0.011(3) 0.028(5) 0.14(3) 0.22(3) 0.22(4) <0.09 0.05(1)
Mo 0.008(2) 0.015(3) 0.034(7)
Mo <0.008 0.008(2)
Mo were set and this time only the 1435.7 keV transi-tion in
Ba was measured (see Fig. 6 (a)). Also in Fig. 6(b) is shown the 9 neutron channel seen in the 94.9-138.1keV transitions in
Mo to show the 9 neutron channelat 1435.7 keV in
Ba.Furthermore, unlike in Ref. [8] we did not set a gateusing the 602 keV from
Ba when determining the yieldof
Ba-
Mo pair because 602 keV is present in
Mofrom the 8 + → + transition feeding into the 1725 keVlevel and another weaker 602 keV 8 + → + transitionfeeding into the 2685.4 keV level. This means that settingany gate with 602 keV from Ba to measure desiredpeaks in
Mo would bring in contamination. The otherreason is that 602 keV lies on a complex region associatedwith an inelastic neutron scattering in germanium of thedetectors as discussed in Ref. [10]. This neutron platformis not negligible; the background around this region istoo high and as a result it is in coincidence with everyother peak on the spectra (see Fig. 5 (a)). In Ref. [10],
560 580 600 620 6401000300050007000900011000 C oun t s pe r C hanne l
356 360 364 368 372 376 380
Energy (keV) . . . (a)(b) neutron platform FIG. 5. Gamma-ray coincidence spectra by gating on (a)193.1 and 371.0 keV transitions in
Mo to show the neutroninelastic scattering platform, and (b) 602.4 and 529 keV tran-sitions to show the 369 keV in
Mo and 371 keV in
Mo.Part (b) shows difference between Fig. 1 in Ref. [8] using thesame gate. See text for more details. C oun t s pe r C hanne l Energy (keV) Mo Mo Mo FIG. 6. Gamma-ray coincidence spectra by gating on (a)368.6 and 519.4 keV transitions in
Mo to show evidencefor the 10 neutron channel at 1435.7 keV in
Ba and in (b)another gate on 368.6 and 641.6 keV transitions in
Mo togive further evidence of the 10 neutron channel in the
Ba-
Mo. In (c) a gate on 94.9 and 138.1 keV transitions in
Mo to show evidence for the 9 neutron channel at 1435.7keV in
Ba for the Ba-Mo pair. the 528.2 keV 4 + → + transition was used in the placeof the 602.4 keV in Ba. However, transitions withenergies close to 528 keV are present in
Mo from 7 − → + (feeding into the 2083.8 keV level), Mo from21/2 − → − (feeding into the 1352.9 keV level), Mofrom 6 + → + (feeding into the 1033.48 keV level), and Mo from 6 + → + (feeding into the 564 keV level).Although they are weak transitions, when consideringwhich one to gate on between the Mo and
Ba, theyare comparable in intensities when gating on
Mo whichwould result in contamination but sufficient when gatingon
Ba. Such cases should also be carefully treatedwhen measuring other high neutron channels with lowyields, e.g , Mo-
Ba pairs.Another approach that has been used in the past toresolve this problem is presented in Ref. [11]. In theanalysis of Ref. [11], the intensities of 519 keV (6 + → + transition in Mo) and the 414 keV (4 + → + tran-sition in Mo) were measured instead of the groundstate transitions for the yields. However, there is an-other 414 keV present and strong in
Mo from (15/2) − → (11/2) + (feeding into the 2083.8 keV level). When gat-ing on Ba transitions to measure the 414 keV in Mo,the strong 414 keV transition from
Mo will contam-inate the spectra. Whereas, the 519 keV transition isokay in this case because even though it is present in
Mo it is weaker to contaminate the spectrum. There-fore, a gate on (519/641) keV from
Mo was used tomeasure the 602 keV in
Ba. These two gated transi-tions are located high enough in the
Mo level schemeand have no feeding from the two contaminants (602 keVtransitions mentioned earlier) in
Mo. In this case, weused a local background subtraction which was set higherthan usual to reduce the contribution from the neutronplatform. This too does not completely circumvent theproblems but it gave us a good approximation of whatthe yield should be. For more major overlapping transi-tions in Ba-Mo pairs to be considered when conductingthis analysis refer to Table VII. Through this thoroughexamination of the Ba-Mo yield there is clear evidence ofthe 9 and 10 neutron channel yields as in Fig. 6.The errors are significantly reduced because of the im-proved statistics, the use of quadruple coincidence dataand improved knowledge of level schemes. To calculateall absolute errors, the experimental data were normal-ized to values from Wahl’s tables [31]. Specifically, thesummation of
Ba yields was normalized to Wahl’svalue because it was the strongest yield in our experi-ment. Note that the values from Wahl’s tables only con-sidered ground state γ transitions but we have consideredthe branching ratios from feeding bands. The 15 % errorsfrom Wahl’s data were added to our absolute errors aswell as 5-10 % experiment errors from missing transitionsand contamination in our data.As seen in Fig. 1, a similar deviation from a Gaussianfit to the data for the 0 to 7 neutron emission channelsis seen at neutron numbers 7, 8, 9 and 10 in the Ba-Moyields as observed in [1, 9]. In comparison to these re-sults, a noticeable difference is that in the present analy-sis we have a more complete set of yield pairs; − Moand − Ba. This is not the case for the earlier anal-yses where
Ba is missing in [1, 8, 9] and
Ba in [8].These are very important components of the analysis asthey contribute to the intensity of the second hot mode.Additionally, the 9 and 10 neutron channels were not re-ported in [8] and [11, 12] (same data set in these two) didnot report only the 10 neutron channel. Note that thereis a typographical error in the
Ba-
Mo yield in Ref.[11]. This reported yield is too small (0.007) compared (a)1435.4(11n)
Ba102.8/138.5(
Mo) C o un t s p e r C h a nn e l (b)1435.4(11n) Ba102.8/363.1(
Mo)
Energy (keV)
FIG. 7. Gamma-ray coincidence spectra by gating on (a)102.8 and 135.5 keV transitions in
Mo to show evidencefor the 11 neutron channel at 1435.7 keV in
Ba and in (b)another gate on 102.8 and 363.1 keV transitions in
Mo togive further evidence of the 11 neutron channel in the
Ba-
Mo pair. to Ba-
Mo (102) in the same reference. The secondsmallest reported yield in Ref. [11] was 0.35, which is twoorders larger than the 0.007 value. However, as shown inFig 6, the 9 and 10 neutron channels are present. And inthe current study we have also observed the 11 neutronchannel at the 1435 keV peak in
Ba as seen in Fig. 7.This channel is observed in several gates but in Fig. 7we only show two gates on 102.8/138.5 keV peaks in (a)and 102.8/363.1 keV peaks in (b) and they are both from
Mo. Also in Fig. 4, we show a second Gaussian fitto the 8, 9, and 10 as reported earlier [36] and addedthe 11 neutron channel. In Ref. [36], we fitted a sec-ond Gaussian by means of restricting the peak positionof the second mode to greater than 6 neutrons emitted.However, in the present study we were able to obtain areasonable fit by restricting the peak position of the sec-ond fit to ∼ and width of the second curve was fixedto the width of the first curve. This new analysis of Ba-Mo fission pairs, coupled with the new analysis of Ce-Zryields, which shows a reduced “extra hot mode”, and theTe-Pd and Nd-Sr yields, which do not exhibit 8, 9, 10neutron emissions, confirms the existence of this “extrahot mode" in the Ba-Mo and now found in Ce-Zr yields. V. CONCLUSION
In the present work, new yield matrices were deter-mined for Te-Pd, Nd-Sr, Ce-Zr and Ba-Mo fission part-ners from the spontaneous fission of
Cf. A similar de-viation from the Gaussian fit to the normal fission modewas found in Ba-Mo for the 8, 9, and 10 neutron channelsas found in previous analyses to confirm the existence ofthe proposed “extra-hot-fission” mode. We have also ob-served an “extra hot fission mode” for the first time in
TABLE VII. Part of the major overlapping energies transi-tions in Ba-Mo pairs that could result in contamination. Seetext for more instructions.
Energy (keV) Nuclei E i to E f (keV)110 Mo 458 → Mo 333 → Ba 618 → Ba 110 → Mo 354 → Ba 113 → Mo 796 → Mo 172 → Mo 492 → Ba 463 → Ba 185 → Mo 192 → Mo 193 → Ba 2089 → Mo 354 → Ba 360 → Mo 566 → Mo 979 → Mo 950 → Ba 954 → Mo 1157 → → Mo 2612 → Mo 1882 → Mo 1563 → Mo 1508 → Ba 1130 → → Mo 2326 → → Ba 602 → Ce-Zr pairs. The observation of these modes in bothpairs can be explained by considering that , , Baand , Ce have been determined to be octupole de-formed which can help give these nuclei high internalenergy at scission and in turn gives rise to high neutronmultiplicities. This is in addition to the possible hyperde-formation suggested for these nuclei. Errors are reducedin this newest analysis compared to previous studies be-cause of the greater statistics of the latest Gammasphereexperiment and the use of quadruple coincidences in theanalysis and improved level schemes. A new experimentis being planned to do fission fragment- γ - γ coincidencestudies to investigate details of the fission process andto study new more neutron-rich nuclei. In addition, theinvestigation will study the existence of an “second extrahot mode” observed in Ba-Mo and Ce-Zr fission yields aswell as ascertain whether these second modes are a re-sult of hyperdeformation and/or octuple deformation of , , Ba and , Ce.
ACKNOWLEDGMENTS
The work at Vanderbilt University and LawrenceBerkeley National Laboratory are supported by the USDepartment of Energy under Grant No. DE-FG05-88ER40407 and Contract No. DE-AC03-76SF00098.The work at Tsinghua University was supported by theNational Natural Science Foundation of China underGrant No. 11175095. The work at JINR was partlysupported by the Russian Foundation for Basic ResearchGrant No. 08-02-00089 and by the INTAS Grant No.2003-51-4496. [1] G. M. Ter-Akopian et al ., Phys. Rev. C , 1146 (1997).[2] G. M. Ter-Akopian et al ., Phys. Rev. Lett. , 32 (1996).[3] G. M. Ter-Akopian et al ., Phys. Rev. Lett. , 1477(1994).[4] Yu. U. Pyatkov et al ., Nucl. Phys. A , 140 (1997).[5] R. Donangelo et al ., Int. J. Mod. Phys. E , 669 (1998).[6] U. Brosa et al ., Phys. Rep. , No. 4 167-262 (1990).[7] N. Schultz (private communication) in Ref. [9][8] D. C. Biswas., et al. , Eur. Phys. J. A , 189 (2000).[9] S. C. Wu et al ., Phys. Rev. C , 041601(R) (2000). [10] S. C. Wu et al ., Nucl. Instrum. Methods A , 776(2002).[11] C. Goodin et al ., Phys. Rev. C , 017309 (2006).[12] A. V. Ramayya et al ., Romanian Rep in Phys, , No.2, P. 595-608, (2007).[13] T. Rząca-Urban et al ., Phys. Rev. C , 031305(R)(2013).[14] C. Gautherin et al ., Eur. Phys. J. A , 391âĂŞ397 (1998).[15] W. Urban et al ., Phys. Rev. C , 037301 (2009).[16] G. S. Simpson et al ., Phys. Rev. C , 024304 (2009).[17] G. S. Simpson et al ., Phys. Rev. C [18] J. Marcellino et al ., Phys. Rev. C , 034319 (2017).[19] W. Urban et al ., Phys. Rev. C , 037302 (2006).[20] W. Urban et al ., Phys. Rev. C , 017301 (2012).[21] W. Urban et al ., Phys. Rev. C , 067301 (2009).[22] W. Urban et al ., Phys. Rev. C , 027302 (2005).[23] H. B. Ding et al ., Phys. Rev. C , 054301 (2006).[24] Y. X. Luo et al ., Nucl. Phys. A et al ., Phys. Rev. C , 044322 (2017).[26] D. C. Radford, Nucl. Instrum. Methods Phys. Res. A , 297 (1995).[27] J. H. Hamilton, et al ., Prog. Part. Nucl. Phys. , 635(1995).[28] E. H. Wang, et al. , Phys. Rev. C , 034317 (2015).[29] Y. J Chen, et al. , Phys. Rev. C , 054316 (2006). [30] S. J. Zhu, et al. , Phys. Rev. C , 051304(R) (1999).[31] A. C. Wahl, Nucl. Data Tables , 1 (1988).[32] B. M. Musangu et al ., 6th International Conference onFission and Properties of Neutron-Rich Nuclei, eds. J. H.Hamilton, A.V. Ramayya and P. Talou, World Scientific:Singapore, (2017) pp. 629-632.[33] J. H. Hamilton, et al ., Acta Physica Slovaca , 1, 31-42(1999).[34] B. Bucher, et al ., Phys. Rev. Lett. et al (Submitted to Phys. Rev. C)[36] A. H. Thibeault et alet al