application/xmlIsotopic and isotonic effects in fission-fragment mass yields of actinide nucleiD.M GorodisskiyS.I MulginV.N OkolovichA.Ya RusanovS.V ZhdanovFission-fragment mass distributionsIsotopic and isotonic effectsPhysics Letters B 548 (2002) 45-51. doi:10.1016/S0370-2693(02)02838-1journalPhysics Letters BCopyright © unknown. Published by Elsevier B.V.Elsevier B.V.0370-26935481-214 November 20022002-11-1445-51455110.1016/S0370-2693(02)02838-1http://dx.doi.org/10.1016/S0370-2693(02)02838-1doi:10.1016/S0370-2693(02)02838-1http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.2PLB19269S0370-2693(02)02838-110.1016/S0370-2693(02)02838-1ExperimentsFig. 1(a) Experimental mass yields Y(M). (b) The same as in (a) in logarithmic scale. (c) UCD fragment neutron-number distributions Y(NF) normalized to 200%. (d) UCD fragment-charge distributions Y(ZF) normalized to 200%.Fig. 2(a) UCD fragment charge distributions from “pure” asymmetric fission for Np and Am isotopic chains normalized to 200%. The data for 238Np formed in the reaction 237Np(n,f) at En=5.5 MeV from Ref. [4]. (b) The same as in (a) in logarithmic scale. (c) Experimental fragment-charge distributions Y(ZF) for the Pa isotopic chain from Refs. [19,20]. (d) The same as in (c) in logarithmic scale.Fig. 3UCD fragment neutron-number distributions Y(NF) for three isotonic chains in linear (left part) and logarithmic (right part) scales. Arrows indicate the neutron numbers NF=52 and 82.Isotopic and isotonic effects in fission-fragment mass yields of actinide nucleiD.MGorodisskiyaS.IMulginaV.NOkolovichbA.YaRusanovaS.VZhdanova∗zhdanov@inp.kzaInstitute of Nuclear Physics, National Nuclear Center, 480082 Almaty, KazakhstanbTver State University, 170021 Tver, Russia∗Corresponding author.Editor: V. MetagAbstractFission-fragment mass distributions for the target nuclei 232Th, 233,235,236,238U, 238,239,240,242Pu, and 244Cm have been measured at an incident proton energy Ep=10.3 MeV, and proton and neutron-number distributions of the fragments have been deduced on the basis of the unchanged-charge-density assumption. It was revealed that the shape of the mass distribution in asymmetric fission strongly depends on the proton number of the compound nucleus and shows only a weak dependence on neutron numbers. It was shown that for nuclei with equal ZCN the asymmetric fission-fragment charge distributions practically coincide, i.e., they are almost independent on NCN. Moreover, for nuclei with equal NCN from isotonic pairs with NCN=144,146, and 148 the fragment neutron-number distributions vary with a change of ZCN. This behaviour of the mass, charge and neutron-number distributions is an evidence for the determinative influence of proton shells on the formation of fragments in asymmetric fission of actinide nuclei.PACS25.85.GeKeywordsFission-fragment mass distributionsIsotopic and isotonic effectsAt present an extensive set of experimental data on mass and energy distributions (MEDs) of fragments in the low-energy and spontaneous fission of nuclei with ZCN=78–104 has been accumulated. The intercomparison of these data shows that the shapes of the fragment mass yields can change drastically in dependence on the nucleonic composition and excitation energy of the fissioning nucleus. A wide variety of shapes for mass and energy distributions can be explained within the multimodal concept [1–5]. In the framework of this concept it is usually assumed that the experimental MED consists of different MEDs for three independent fission modes: one symmetric (S) and two asymmetric—Standard 1 (S1) and Standard 2 (S2). Mode S is mainly conditioned by the liquid-drop properties of nuclear matter, and, therefore, its most probable values of fragment masses M are close to ACN/2. The asymmetric mode S1 with average masses of the heavy fragments MH≈134 and high kinetic energies is due to the formation of spherical heavy fragments with ZFN and NFN close to the magic numbers 50 and 82, respectively. The predominant asymmetric mode S2 is characterized by average masses of the heavy fragments MH≈140, and kinetic energies are by 10–12 MeV less than those of mode S1. Usually the origin of mode S2 is attributed to the deformed neutron-shell closure N≈88 in the heavy fragments, see, e.g., Ref. [6]. However, the results of attempts (for example, Refs. [6,7]) to explain the properties of the experimental fragment mass yields for actinide nuclei by the N≈88 shell do not remove some doubts that the mode S2 is caused by this shell. So, in our opinion, the question about the origin of the predominant part of the asymmetric fission remains open.One possible solution of this problem may consist in the comparative analysis of fragment mass yields from the fission of nuclei with equal ZCN, but different NCN, and vice versa, i.e., for isotopic and isotonic nuclear chains. Such an investigation is the main objective of the present work.The experiment was carried out with the 10.3 MeV external proton beam from the Almaty's isochronous cyclotron. Targets from chlorides of enriched isotopes with thicknesses of 20 to 40 μg/cm2 evaporated on backings of Al2O3 with a thickness of 60 μg/cm2 have been used. The measurements were performed by fast spectrometry and timing of pulses from a pair of Si–Au surface-barrier detectors (E1–E2 method) with the subsequent “time-of-flight” selection of fragments belonging to one fission event [8,9]. The detectors were calibrated with the 252Cf spontaneous fission-fragment spectrum [10], and the MEDs were calculated from the measured pulse distributions according to the standard procedure [11].Unfortunately, experimental information on pre-(νpre) and post-(νpost) fission neutron emission is not available for the majority of the reactions studied here. According to data from Ref. [12], at Ep≈10 MeV we estimate values of νpre≈0.5 that decreases the excitation energy of compound nuclei from ≈15 MeV to average values ∼10–11 MeV. Our estimations of the post-fission neutron-emission corrections based on the data on νpost from Ref. [12] showed that, on a scale of the effects discussed below, these corrections are quite small, and their influence on the fragment mass yields of neighbouring nuclei is approximately the same. Since, for our comparative analysis, only the differences in the values of the pre- and post-fission neutron emission corrections are important, these corrections have not been introduced.In the present work, the MEDs have been obtained for 10 actinide compound nuclei including two isotopic chains with ZCN=93,95 (234,236,237,239Np and 239,240,241,243Am), three isotonic pairs with NCN=144,146,148 (237Np–239Am, 239Np–241Am, 243Am–245Bk), and 233Pa, as well. Partly these data had been used earlier in Ref. [13] for the development of a new approach to the multimodal description of the MEDs.The experimental results are shown in Fig. 1, where, in the left part, the measured mass yields Y(M) are plotted in linear (a) and logarithmic (b) scales. From Fig. 1(a) one can see that for all reactions studied the contribution of symmetric fission is rather small, and the shapes of the MEDs are mainly defined by shell effects that are responsible for the formation of asymmetric fission. The mass-yield curves of the heavy fragments are similar for all nuclei studied, and, as expected, the most probable masses of the heavy fragments are MH≈140. Visible distinctions in Y(M) for different nuclei are observed in the vicinity of their maximums and at symmetry. The higher the asymmetric peaks are, the lower are contributions of symmetric fission. Hence, one can suppose that for the fragment distributions of pure asymmetric fission, obtained by subtracting the contribution of symmetric fission from the measured yields, these differences will decrease.As a whole, the peak positions of the light fragment yields are in accordance with the expected tendency ML≈ACN−140. However, for nuclei with equal ZCN the change in ACN by 4–5 units leads to slight continuous shifts of the peak position of the light fragments. At the same time, the change in ZCN by two units moves these positions discontinuously. Possible reasons of this effect will be discussed below in detail.Another interesting property of the mass-yield distributions Y(M) is demonstrated in Fig. 1(b). In logarithmic scale one can clearly see that the mass-yields of the heavy fragments for MH>145 from different fissioning nuclei decrease with different slopes. There is a clearly defined tendency: the smaller ZCN is, the steeper is the inclination of the mass distribution Y(M). In the complementary light fragment at ML<ACN−145 a different behaviour is observed: mass yields tend to converge, and at ML≈80 the degree of convergence becomes maximal. Such behaviour of the yields, apparently, indicates that in the mass range ACN/2<MH<145 the shapes of the asymmetric peaks are governed by shell closures formed in the heavy fragments. With increasing mass asymmetry, the influence of shell closures in the light fragments grows, and at ML≈80 it becomes predominant. This influence was also demonstrated in Refs. [13,14], where the existence of an other high-energy mode, called Standard 3, which is conditioned by shell effects in the light fragments, has been revealed in the mass yields at ML≈83.Recently, the grouping of the light and heavy fragment mass yields on their left wings was also revealed in Refs. [15,16] for thermal-neutron induced fission of actinide nuclei. In these experiments, for a large group of nuclei the convergence and steep inclination of the mass yields was observed at MH<134 and ML<80. Hence, the authors concluded that at least the tails of the mass yields in asymmetric fission are controlled by spherical shell closures in the heavy and light fragments.In order to reveal the influence of the fragment neutron and proton shell closures on the formation of Y(M) more clearly, we converted the experimental mass yields into the yields of the fragment proton Y(ZF) and neutron Y(NF) numbers. To this purpose, we used the unchanged charge density (UCD) assumption according to which the proton and neutron numbers of the fragments are defined by the relations: ZF=M×(ZCN/ACN) and NF=M×(NCN/ACN). According to the results of Refs. [17,18], at our excitation energies (∼10 MeV) the deviations of the UCD values ZF and NF from the “true” ones are weakly dependent on the composition of the actinide compound nucleus. Even for large mass asymmetry, where these deviations become maximal, their values do not exceed one unit, which is not significant from the viewpoint of the effects being discussed.In Fig. 1(c), after transition from Y(M) to Y(NF), the convergence of the yields on the wings becomes weaker, and the grouping effect for nuclei with equal ZCN in Y(NF) practically disappears. A radically different situation appears for Y(ZF) shown in Fig. 1(d). It can be seen that for all nuclei belonging to one isotopic chain the differences in Y(ZF) are rather small, especially in the tails. Small differences in Y(ZF) at ZF≈ZCN/2 and in the vicinity of the asymmetric peaks are due to the differences in the contributions of symmetric fission and do not change the picture as a whole. Simultaneously, for all nuclei studied the degree of congruence for Y(ZF) at light fragment proton numbers ZFL<32 sharply grows.Thus, taking into account all features mentioned above for the yields Y(M), Y(NF), and Y(ZF) deduced from Fig. 1, one may conclude that the sensitivity of the fragment mass distributions to the change of the compound nucleus charge ZCN is much stronger than to a change of the compound-nucleus neutron number NCN.The grouping effect of the asymmetric-fission charge distributions from the fission of nuclei with equal ZCN seemed to be unexpected and interesting, and we tried to consider it in detail and to verify it by involving the experimental data obtained by other authors [4,19,20].Fig. 2 (in linear and logarithmic scales) shows the UCD asymmetric fission charge distributions Yasym(ZF) for 5 isotopes of Np and 4 isotopes of Am together with the experimental fragment charge yields for 4 isotopes of Pa. We should note that here and further below our data (closed circles— Np isotopes, open ones—Am isotopes) are defined as “pure” asymmetric fission-fragment distributions, normalized to 200%. These distributions have been obtained by decomposing the experimental matrices of mass and total kinetic energy of coincident fragments N(M,Ek) into separate matrices for the independent modes S1,S2,S3, and S in the framework of the multimodal analysis method proposed in Ref. [13]. After decomposition, the matrices for the symmetric mode S were subtracted from the experimental data, and the fragment mass, charge- and neutron-number distributions for the asymmetric fission were obtained. Besides, we show the UCD charge distribution (solid line) re-calculated from the mass yields for the 5.5 MeV neutron-induced fission of 237Np measured in Ref. [4]. One can see that the data from the present work and from Ref. [4] are in good agreement.Figs. 2(a) and (b) show that, after subtracting the symmetric component, the differences of the yields in the vicinity of the peak maximums and at MH≈ACN/2 decrease considerably in full accordance with our expectations. One can see that, in spite of the significant changes in NCN for nuclei from the Np and Am isotopic chains (up to 5), the charge distributions from fission of nuclei with equal ZCN practically coincide. At the same time, the change in ZCN by two units leads not only to strong displacements of the light fragment peak, but also to visible changes in the shape of Yasym(ZF). However, for nuclei with different ZCN these distributions virtually coincide at ZFH≈50 and ZFL≈30 that is close to the magic number 28. Roughly speaking, the charge distributions are limited by these magic numbers, and, therefore, the widths of these distributions are defined by the value ▵Z∼ZCN−50−28.In order to verify the results of the present work, we borrowed the experimental data on direct measurements of fission-fragment charges from Refs. [19,20]. It should be noted that in this experiment the charge distributions have been measured for a large range of fissile nuclei, but in Figs. 2(c) and (d) we only used the data of the heaviest four isotopes of Pa, for which the asymmetric fission contribution is predominant. This allowed to demonstrate the isotopic grouping effect of the charge distribution without any corrections on the contributions from symmetric fission. For isotopes lighter than 229Pa the contribution from symmetric fission shoots up with decreasing ACN, and the manifestation of the grouping effect becomes diffuse. However, according to our estimations, after subtracting the yields of symmetric fission from the experimental ones, the grouping of the asymmetric-fission charge distributions is observed for all isotopes from 224Pa to 232Pa. Moreover, the decomposition of the experimental fragment charge yields into symmetric and asymmetric fission components made by those authors showed that the positions of the heavy-fragment asymmetric peaks stay constant (ZFH≈54) not only for all nuclei from the Pa chain, but also for the isotopic chains of U and Th. So, the reality of the grouping effect in fragment charge yields from the asymmetric fission of isotopes is confirmed by the results of direct measurements of fission-fragment charges. Incidentally, this result argues in favour of appropriateness of the approximations used (non-emissive fission and UCD).In order to clear up the role of ZCN and NCN in the formation of mass yields in more detail, we have analyzed Yasym(NF) for three isotonic pairs, namely: NCN=144 (237Np, 239Am), NCN=146 (239Np, 241Am), and NCN=148 (243Am, 245Bk). These data are presented in Fig. 3 (in linear and logarithmic scales) as a function of the fragment neutron number NF. It is seen that in all three cases for the nuclei with equal numbers NCN the change of ZCN by two units leads to visible shifts of the Yasym(NF) shapes. This confirms the conclusion that the shapes of the fragment distributions are much more sensitive to change of ZCN than to the changes of NCN. At the same time, one should note an interesting feature of Yasym(NF): for all isotonic pairs the crossing of the Y(NF) curves is observed in the vicinities of NFH≈82 and NFL≈52, i.e., close to magic numbers for neutron spherical shell closures. This feature may be either an amusing random coincidence or the consequence of the remaining influence of the spherical neutron-shell closures on the fragment yields. At other fragment neutron numbers NF, including NFH=88, which is usually associated with the origin of the predominant asymmetric mode S2 [15,21], no noteworthy features in the behaviour of Y(NF) were observed.Closing the discussion of Figs. 2 and 3, it is expedient to recall that according to widespread notions the asymmetric fission of heavy nuclei is conditioned by the formation of proton and neutron (spherical and deformed) shell closures in the light and heavy pre-scission fragments. The present investigation of the isotopic and isotonic chains shows that at excitation energies around 10 MeV the predominant role in the formation of asymmetric fission mass yields for actinide nuclei is played by fragment proton shell closures. Moreover, it is clear that at least the wings of the asymmetric fission mass yields are governed by spherical shell closures in the heavy (ZFH=50) and in the light fragment (ZFL=28). In addition, we hold the opinion that the shell closure at Z=50 also plays a key role in the maximum of the fragment mass yields (ZFH≈54). Arguments in favour of this assumption could be found in the results of calculations of the nuclear potential energy in the framework of the shell-correction method [6,22,23]. According to these results, the shell Z=50 is the only sharply pronounced proton shell closure in the relevant proton range Z=48–58, and no other likely contender is present.In our opinion, the main effects discussed above could be explained in the framework of the dumb-bell configuration conception discussed in Refs. [24,25]. Reasoning from the basic ideas of this conception, we suppose that in asymmetric fission the pre-scission configuration is conditioned by two spherical proton clusters with Z=28,50 and a corresponding number of neutrons, joined by an elongated hyperbola-like neck. Then, the pre-scission configurations of all nuclides from the actinide region differ only in the neck volume. For all compound nuclei the appearance of light fission fragments with ZF<28 and heavy ones with ZF<50 requires to destroy these very stable spherical shell closures. This leads to a common limitation of the ZF—regions available for asymmetric fission. Consequently, for nuclei from one isotopic chain the spatial distributions of protons in the pre-scission configuration should be similar, and, therefore, one can expect similarities in the distributions of the neck-rupture probability along the nuclear elongation axis that leads to the observed grouping effect in fragment charge yields from the fission of the isotopes studied. So, this conception of a dumb-bell pre-scission configuration could be useful for the qualitative explanation of some features of asymmetric fission. However, we should note that these notions do not explain the experimental fact that in asymmetric fission of actinides the most probable ZFH approximately equals 54 [20].We should especially note that the isotopic effect of the grouping of charge distributions becomes apparent only at respectively high excitation energies E⩾10 MeV. Our analysis of the data on thermal-neutron induced fission of 232,233,235U borrowed from Refs. [8,26] has shown that the UCD charge distributions for these nuclei converge only on their wings, but visible distinctions are observed in the maximums of the yields. In the spontaneous fission of Pu isotopes at the transition from 236Pu to 244Pu [27] one can observe strong variations in the shape of the mass yields, and, therefore, of their charge distributions. So, one can suppose that in cold and low-energy fission of actinides the shapes of the asymmetric fission-fragment distributions are governed not only by proton shells, but also by neutron shells. 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