Decay modes in spontaneous fission

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A654 (1999) 855e-863c

www.elsevier.nl/locate/npe

Decay Modes in Spontaneous Fission F. GSnnenwein a aPhysikalisches Institut, Universit£t T/ibingen, Auf der Morgenstelle 14, D 72076 Tfibingen Spontaneous fission (SF) is considered to be the choice reaction for studying the influence of shell and pairing effects in fission in general, and in particular their impact on the mass and energy distributions of fission fragments. For the time being some 35 SF reactions have been analysed in detail for elements ranging from Pu up to Rf. Going from the lighter to the heavier actinides both, the distributions of fragment mass (or charge) and of total kinetic energy undergo dramatic changes. It is observed in experiment, however, that these distributions may be well described as a superposition of a few fission modes, each with its own characteristic mass an energy pattern. The experimental modes are traced in theory to fine structures in the potential energy surface of a fissioning nucleus, provided shell and pairing corrections to the basic liquid drop model are accounted for. 1. I N T R O D U C T I O N Shell and pairing effects are most pronounced at low excitation energies of nuclei. Spontaneous fission from the ground state of a disintegrating nucleus is, therefore, the best suited reaction to study the influence of shells and pairing in nuclear fission. However, the life times for spontaneous fission (SF) and the competition between fission and alpha decay in the heaviest nuclei impose limitations to experiment, and a detailed analysis of the properties of fragments from SF is only feasible in a well circumscribed region in the chart of nuclides. So far about 35 SF reactions for isotopes from Pu to Rf could be investigated in detail, i.e. the fragment yields Y(A,TKE) as a function of fragment mass A and total kinetic energy (TKE) are fairly well known. Already back in 1951 the differences observed in the excitation functions for symmetric and asymmetric fission prompted speculations about two distinct modes in fission [1]. Though very soon after the discovery of the shell model the idea was put forward that asymmetric fission could be due to shell effects in the fragments, it was not before the advent of the Strutinski shell correction method that a sound theory for asymmetric fission was developed [2,3]. The finding was that the fission barrier is double humped and that the outer barrier is lowered for asymmetric (i.e. pearshaped) deformations. This explains why asymmetric fission is favored compared to symmetric fission, as observed especially at low excitation energies of the fissioning nucleus. The analysis of fission reactions in terms of this two-mode hypothesis has been very successful in the past [4]. In recent years the systematic study of the fragment yields Y(A,TKE) has allowed not only to disclose fine structures in the asymmetric distributions but also to realize 0375-9474/99/$ see front matter © 1999 ElsevierScienceB.V. All fights reserved.

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that different fission reactions exhibit very similar yield patterns. These patterns are well described by a superposition of distinct asymmetric fission modes. Examples are provided in the following for a series of Pu, Cm and Cf isotopes. For some heavy isotopes of Fm, Md and No a striking change in the yield pattern shows up. Just adding one or two nucleons to the fissioning nucleus, the familiar asymmetric yield distribution all of a sudden becomes sharply symmetric, and the average T K E release jumps upwards by some 30 to 40 MeV. It is intriguing to note that this phenomenon, bimodal fission as it has been called, is observed whenever the parent nucleus is close to a combination of two doubly magic 132Sn nuclei. Very recently it has been discovered that the 132Sn cluster also gives rise to a specific decay mode in 2s2Cf(sf). The mode is characterized by a narrow asymmetric mass distribution and an exceptionally large T K E release. This decay may either be viewed as a precursor to bimodal fission in heavier nuclei or as a variant of cluster radioactivity with 2°Spb having been traded for 132Sn. The above mentioned more recent developments are discussed in some detail in the following.

2. S P O N T A N E O U S

FISSION

IN THE LIGHTER

ACTINIDES

It is well established [5] that in SF of the lighter actinides the light mass peak moves with the mass of the parent nucleus while the heavy mass peak stays pretty constant. This has again been confirmed in a remarkably complete series of experiments for SF of the Pu isotopes 236pu, 23Spu, 24°pu, 242pu and 244Pu [6]. In Fig. 1 the mass yields for the heavy peak prior to neutron emission are shown. Sizeable yields in excess of, say, 2% are observed for all isotopes in the mass range 130 through 148. But besides this constancy in the position and width of the mass peak, the lighter and heavier isotopes appear to have dissimilar yield distributions with fine structure peaks near mass 134 and 140, respectively. Surprisingly, in going from 2aSpu to :4°Pu with just two additional neutrons, the fragment distribution changes markedly. A similar observation holds for the Cm isotopes 244Cm, 246Cm and 24SCm [7]. Though in Fig. 2 the post-neutron-emission mass yields for the heavy peak are plotted and, therefore, the comparison to the pre-neutron data in Fig. 1 should be made cautiously, again a rapidly changing fine structure is catching the eye. The locations of the fine structure peaks virtually coincide with those for the Pu isotopes. This gives strong support to a mode analysis of mass distributions which is shown in Fig. 3 for SF of 24°pu [6]. The deconvolution of the asymmetric mass yield in terms of 2 Gaussians (left panel) leads to an excellent fit of the measured data. Each Gaussian may be identified with a mode and it has become customary to adopt the notation introduced by Brosa et al. [8]. The mode centered near heavy fragment mass 134 is called the standard I mode while the one near mass 140 is the standard II mode. In the right panel of Fig. 3 the T K E distribution is displayed together with the equivalent deconvolution into the two standard modes. It should be stressed that it is the standard I mode which carries the larger TKE. To each mode, hence, correspond average values and widths for both, the mass and the T K E distribution. A very ambitious mode analysis for one of the best studied fission reactions, viz.

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2~2Cf(sf), is presented in Fig. 4 [9]. Guided by a theoretical exploration of the potential energy surface (PES) of a deforming 2s2Cf nucleus not less than one symmetric and four asymmetric Gaussian modes have been invoked to describe the fragment mass distribution. In the range of large yields the quality of the fit is quite impressive. However, the logarithmic yield scale in Fig. 4 allows to reveal that far asymmetric yields at levels below about 1% are not satisfactorily reproduced. This may simply be due to the fact that Gaussians are not the appropriate functions for fitting very low yields. 3. B I M O D A L A N D C L U S T E R F I S S I O N Ongoing efforts to push our knowledge of mass and energy distributions of fragments from SF to heavier and heavier nuclei have led to reliable yield data up to heavy Rf isotopes [10]. Especially interesting has been the discovery of the so-called bimodal fission in the heavy Fro, Md and No isotopes [11]. An example is provided for the reaction 26°Md(sf) in Fig. 5 [12]. Inspecting first the TKE distribution in the panel to the right of Fig. 5, is is the very pronounced asymmetry of the distribution which is spectacular since it deviates from the more symmetric Gaussian-like shape usually encountered (see, however, Fig. 3 where the distribution is also clearly asymmetric). The distribution is readily deconvoluted into two components with greatly different average energies. It should be stressed that the high energy component is coming close to the Q-value of the reaction. The mass distribution to the left of Fig. 5 is given separately for events with TKE exceeding 224 MeV or staying below 210 MeV, respectively. For the high TKE component the mass distribution is symmetric and surprisingly narrow. On the other hand, the low T K E component has a broadly symmetric (or perhaps slightly asymmetric) mass distribution. It should be underlined that the phenomenon of bimodal fission is restricted to a quite well defined region in the chart of nuclides where the decaying nuclei are close to two doubly-magic

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t32Sn clusters. The ideal candidate for bimodal fission should then be 264Fm. Intuitively these parent nuclei could indeed split symmetrically while the spherical shape of the clusters could allow for very compact scission configurations and, hence, large TKEs, as observed in experiment. It is tempting to ask the question whether there is a link between the high energy mode of bimodal fission and the standard I mode discussed in the preceding section for the lighter actinides. After all the standard I mode is centered around a heavy fragment mass of about 134 close to a 132Sn cluster and it also carries large TKEs. However, comparing the T K E distribution for 26°Md in Fig. 5 to the one for 24°pu in Fig. 3 it becomes evident that the energies in the high energy mode of bimodal fission and the standard I mode in the lighter actinides are vastly different. Hence, it appears at least doubtful whether there is a generic connection between these two modes. A much clearer conclusion may be reached from the discovery of a peculiarity in the T K E distribution of fragments from 252Cf(sf). In a high resolution study of cold fission in 2s2Cf(sf) the high energy tail of the TKE distributions could be explored mass by mass and charge by charge [13]. Two examples are given in Fig. 6. The left panel shows as a zoom the high energy foothill of the TKE distribution for the fragmentation light mass/heavy mass = 120/132, while the panel to the right is for the fragmentation 102/150 (solid lines). Since besides the masses also nuclear charges could be identified, the yield is decomposed into the contributions from the individual charge splits at fixed mass ratio. The isobaric yields are depicted in Fig. 6 as dashed lines. These are labelled by the charge number of the heavy fragment (the charge of the light fragment then follows as a complement to the charge number 98 of Cf). In addition, on top of the figure, the Q-values for the different charge splits at fixed mass ratio are indicated, the labelling for the charges being the same as for the yield curves. It is seen that for the fragmentations

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on display the highest T K E events exhaust the available energies within a few MeV, i.e. these are cold fission events. Of interest for the question addressed above concerning the interpretation of fission modes is the conspicuous shoulder at the very highest energies for the mass split 120/132 (left panel in Fig. 6). According to the experimental results in Fig. 6 the shoulder is entirely due to the presence of the doubly magic 132Sn as the heavy fragment. Similar structures also show up for a few neighbouring mass splits in the narrow range of mass ratios light/heavy = 122/130 through 118/134. In all these cases it is a magic heavy fragment with Z = 50 and/or N = 82 which is responsible for the shoulder-like bump. The narrow mass distribution for these distinct events recalls the sharp mass peak of bimodal fission (see Fig. 5). Even more striking is the average T K E measured for these events which is perfectly in line with the T K E for the high energy mode of bimodal fission. This is demonstrated in Fig. 7 where the average TKEs for the low and high T K E mode in the Fm, Md and No isotopes are plotted together with the overall average T K E = 184.1 MeV for 2s2Cf(sf) and the average T K E = (228 ± 1) MeV for the events in the high energy shoulder at mass ratio 120/132. The well pronounced structure in the fragment T K E distribution for a narrow but continuous range of masses is taken as justification to envisage an independent and hitherto unknown decay mode of 2s2Cf. In view of the magic fragment clusters being specific for this mode it is proposed to call it a cluster mode. The cluster mode is well to be distinguished from the standard I mode in the lighter actinides. This is readily confirmed from Fig. 4 where the standard I mode is labelled S1. The cluster and the standard I mode have definitely different average values and variances for the mass distribution. Even more convincing are the huge differences for the average energies. For the standard I mode an average T K E of 194.3 MeV is reported [9], while in the cluster mode the average T K E is (228 =k 1) MeV, i.e. a difference in excess of 30 MeV. From experiment it is, hence,

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concluded that the cluster mode should not be mixed up with the standard I mode. By contrast, the cluster decay mode of 252Cf has all the features required to view it as the precursor of bimodal fission in some heavier nuclei. 4. D I S C U S S I O N

In the preceding sections the experimental evidence from SF studies has been given which has led to the notion of fission modes with specific characteristics. The original two-mode hypothesis [1] differentiating only between symmetric and asymmetric fission has nowadays given way to a more elaborate description of fine structures observed for the asymmetric mass yields and their T K E distributions. It is noteworthy that mass distributions from SF of lighter actinides are surprisingly well described by just two asymmetric modes in addition to one symmetric mode. In a landmark paper Wilkins et a1.[14] could show from a calculation of shell and pairing corrections to the liquid drop model that e.g. spherical neutron shells at N = 82 and deformed shells at N = 88 in the heavy fi-agment give rise to substantial energy gains. In a thermodynamical model set up at the scission point for fragments facing each other these energy gains will enhance asymmetric fission in general and specific mass ranges in particular. In consequence, the modes identified in experiment (e.g. for 23°pu(sf) in Fig. 3) should correspond to fragmentations with large gains in shell energy. Since the neutron numbers 82 and 88 most probably are associated with the mass numbers 134 and 142, respectively, it is seen that theory at least qualitatively is capable to account for the experimental observation. In a quite different theoretical approach to fission, elaborate calculations of the potential energy surface (PES) of a deforming nucleus from ground state to scission have been presented by Brosa et al. [8]. A major achievement of this work was to realize that the landscape of the PES is much more complex than thought before. Due to shell and pairing

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effects there is not just a lowering of the fission barrier for asymmetric fragmentations. Instead, these corrections transform the smooth PES from the liquid drop model into a landscape with rough and bumpy fine structures. A special role is played in this theory by individual valleys being separated by ridges leading all the way down to scission. The valleys are characterized by more or less asymmetric and more or less compact scission configurations. Hence, for each valley a distinctive mass ratio and T K E release is predicted. Obviously, there should be a one-to-one relationship between valleys from theory and modes from experiment. In fact, the basic standard I and standard II modes from theory have come into widespread use as guidelines for analyzing experimental data (see Fig. 3). In general the properties of modes predicted by theory conform reasonably well with experiment. It is, however, a delicate point to establish how many relevant valleys or modes there are (see Fig. 4). Even more tough for theory is to predict the relative feeding of the modes. Probably this problem is outside the reach of static calculations. The task will ultimately have to be solved by dynamical calculations of the flow of nuclear matter downhill the PES. These calculations are not yet available with sufficient accuracy. Bimodal fission has been an incentive for several groups in theory to reconsider the PES especially in the vicinity of the fission barrier [15-17] for heavy isotopes of Fro, Md etc. The experimental evidence for a mode with extremely large TKEs could be substantiated by disclosing in the PES a new valley which for symmetric deformations starts close to the barrier and ends up in a compact scission configuration. This valley is, therefore, identified with the symmetric high energy mode of bimodal fission. It is interesting to note that almost 30 years ago it was already realized in theory that in the deformation process of fission the nucleus experiences very early the shell structure of nascent fragments [18].

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This is especially true for the heavy doubly magic fragment 132Sn and some neighboring nuclei which are held responsible for the phenomenon of bimodal fission. More generally this feature makes understandable why models based either on fragment properties at the scission point or on the properties of the PES all the way down from saddle to scission are not at variance. The special role played by some nuclei around ta~Sn in the mass-energy distributions of fission becomes once more manifest in SF of 252Cf [13]. There these nuclei show up in the cluster mode of fission. This mode was in fact predicted by theory prior to experiment and called the supershort mode of 2s2Cf(sf) [8]. The typically very large energies of fragments expected are in excellent agreement with experiment (see Fig. 7). However, one could equally well speculate that the cluster mode of spontaneous fission is closely akin to cluster radioactivity. In cluster radioactivity invariably the heavy partner to the cluster being emitted in centered around 2°Spb. In the cluster mode of fission the magic 20s Pb is just traded for 132Sn [13,19]. In summary it can be stated that mass-energy distributions in spontaneous fission are steered by shell and pairing effects either in the fission prone nucleus or in the fragments. This allows to describe these distributions in terms of only a few decay modes, each with specific characteristics as to fragment masses and energies. A shortcoming of any presentday mode analysis is, however, that fine structures due to odd-even effects in the yields of nuclear charges are not covered. In fact, most theoretical calculations of the PES do not treat neutrons and protons independently and hence odd-even effects of either protons or neutrons are smeared out. Anyhow, in induced fission, at higher excitation energies of compound nuclei the influence of modes based on structural effects in nuclei are fading away until the rather dull fission properties of a pure liquie drop are reached.

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Acknowledgements: Special thanks are due to L. Dematte and F.-J. Hambsch for redrawing figures from their work and for allowing their publication. Part of the work has been supported by the BMBF, Bonn, under contract number 06TU669. REFERENCES

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