Fission symmetric

FIGURE 17.22 The fission yield of uranium-235, Note that the majority of fission products lie in the regions close to A = 90 and 130 and that relatively few nuclides corresponding to symmetrical fission (A close to 117) are formed. 

Let us consider first the low-energy fission of the lighter fissionable elements, in the neighborhood of Pb208. These elements (gold, thallium, lead, bismuth), when bombarded with particles such as 20-Mev deuterons, undergo symmetric fission, the distribution function of the products having a half width at half maximum of 8 to 15 mass-number units (20). 

I assume that in the process of fission both the mantle and the core undergo splitting. The core could split between the two middle rings, which would result in symmetric fission. 

There is no structure for an elongated core intermediate between that shown in Fig. 11, with three inner-core spher-ons, and that shown in Fig. 12, with four. The transition between these structures is calculated by use of Eq. 1, with n, = 22, to occur at nt = 69, that is, at N = 138. It is accordingly an expectation from the close-packed-spheron theory that, as observed, 90Ac13a2- 7 (formed by bombardment of Re- 20 with 11-Mev protons) gives a three-humped fission product distribution curve (23), which has been interpreted (24) as showing that both symmetric fission and asymmetric fission occur. 

Asymmetric fission is observed in the spontaneous decomposition of sCf1Ji(15M and other very heavy nuclei. We may ask when the transition to symmetric fission would begin. The next elongated core, in the series represented in Figs. 11 and 12, would contain 31 spherons, and the transition to it should occur for 28 spherons in the core of the undistorted nucleus, that is, at N = 163 (calculated with use of Eq. 1). We conclude that lftf,Lw,(i,20 and adjacent nuclei should show both asymmetric and symmetric fission. 

As already mentioned, asymmetric fission prevails strongly. This is illustrated for in Fig. 5.17 the fission yields are in the range of several percent for mass numbers A between about 95 to 110 and about 130 to 145, and below 0.1% for symmetric fission (A 120). The fission yields are the average numbers of nuclei with a certain mass number A produced per fission. Because two nuclei are generated, the sum of the fission yields amounts to 200%. 

In Fig. 8.13 the yield of fission products obtained by thermal fission of is plotted as a function of the mass number A (mass distribution). The maxima of the yields are in the ranges of mass numbers 90-100 and 133-143. In these ranges the fission yields are about 6%, whereas symmetrical fission occurs with a yield of only about 0.01%. The peaks in the mass distribution curve A = 100 and at 4 = 134 are explained by the fact that formation of even-even nuclei is preferred in the fission of the even-even compound nucleus It should be taken into account that the sum of the fission yields is 200%, because each fission gives two fission products. 

The influence of the energy of the neutrons on the mass distribution of the fission products is shown in Fig. 8.15 at higher neutron energies, the probabihty of symmetric fission increases strongly. 

Increase of symmetric fission is also observed at lower atomic numbers Z. It prevails at Z < 85, and at Z = 89 ( Ac) symmetric and asymmetric fission have nearly the same probability, which results in three maxima in the mass distribution. Three maxima are also observed in the fission of Ra by 11 MeV protons or by y rays. 

A nucleus does not always split in the same fashion. There is a probability that each fission fragment ( 4, Z) will be emitted, a process called fission yield. Figure 3.20 shows the fission yield for fission. For thermal neutrons, the asymmetric fission is favored. It can be shown that asymmetric fission yields more energy. As the neutron energy increases, the excitation energy of the compound nucleus increases. The possibilities for fission are such that it does not make much difference, from an energy point of view, whether the fission is symmetric or asymmetric. Therefore, the probability of symmetric fission increases. 

The single-well curve in Figure 14.14a predicts symmetric fission whereas the double-well curve (Fig. 14.14b) leads to the correct prediction of asymmetric fission and a thin neck. Incorporation of shell effects in the fission model also leads to the prediction that the half-lives of very heavy nuclides (Z 106) must be longer than the simple liquid-drop model would indicate. This has led to a search for "super heavy" elements with Z = 110-118. 

The SF process that results in two nearly equal mass fragments (a process called symmetric fission ) has been observed in Fm (1.5 s). More commonly, SF occurs as asymmetric fission, a split of the parent radionuclide into two unequal large FF. As in neutron-induced fission, many different asymmetric mass (and charge) divisions with varying yields can result, with mass numbers from about 70 to 170, each with many isotopes. Hundreds of different nuclides can be produced. Figure 2.1 displays the predominantly asymmetric mass yields as a function of mass number (dubbed mass-yield curves ) that have been measured for several SF and neutron-induced fission nuclides. 

Even though the formation of two fission products of equal mass (half the mass of the fissioning nucleus, symmetric fission ) would be most exoenergetic, experimentally (as will be shown later) the mass ratio of the two fission products is normally found to be approximately 1/3 to 2/3 ( asymmetric fission ). 

A model, based on the construction of a potential energy surface from a combination of liquid drop terms for protons and neutrons as a function of deformation and shell corrections, has been published by Wilkins, Steinberg, and Chasman (Wilkins et al. 1976). In the model, a specific excitation energy (nuclear temperature) is assumed at scission and the probability to reach this specific state is calculated. The general trends of mass-yield curves in the fission of very different nuclides from "Po to Fm and for different excitation energies of the fissioning nucleus from 0 MeV (spontaneous fission) to highly excited fission reactions are reproduced correctly. In particular, the transition from the symmetric fission of (the compound nuclei) Po to a triple-humped mass-yield curve for Ra to double-humped yield curves for and Cf and, finally, a partial return to symmetry for Fm is... 

Figure 4.13 shows yield curves for various nuclei undergoing spontaneous fission. In the case of spontaneous fission, the barrier is crossed by tunneling. As a consequence, the excitation energy at scission is very small. The figure shows that the yield of symmetric fission is extremely low (below the limit of detection), as one would expect. 

Cumulative plot of the mass yields for thermal-neutron-induced fission of obtained by summing the yields from very asymmetric fission to symmetric fission for fission products (+) and fission fragments ( ). The numbers of prompt neutrons emitted [vi and for light and heavy fragments, respectively, can be obtained from the horizontal distances between the curves using slight corrections for curvature from (Terrell 1962)... 

The fact that not N - 50 (the magic number for isolated nuclei) but iV = 48 is the critical number has to do with the fact that the forming fragment is not an isolated nucleus but is part of a scissioning system. In this context, it is worth remembering that in the transition from asymmetric fission to symmetric fission the limiting neutron number is 158 for Fm (Z = 100) and 154 for Rf (Z = 104) (O Fig. 4.16), i.e., a few neutrons less than 164, which would represent twice the magic number of 82. 

In contrast to this observation, the shell closures for protons (Z = 28, and Z = 50) are practically not influenced by the rest of the scissioning nucleus The transition from asymmetric fission to symmetric fission takes place exactly at Fm Z = 100 (2 x 50) (O Fig. 4.16) and the hump at mass 70 (O Fig. 4.23) also occurs exactly at Z = 28. In this context, it is worth mentioning that - in the framework of astrophysical studies of the r-process (see Chap. 12 in Vol. 2) - it has been revealed that the energetic effect of closed neutron shells is quenched in extremely neutron-rich nuclei (Pfeiffer et al. 2001). 

So far, essentially mass-yield curves were dealt with. Each point of such a curve represents the formation cross section of isobaric nuclei of mass number A, composed of different combinations of protons and neutrons. Because heavy, fissile nuclei are generally more neutron rich than stable nuclides with about half their mass, fission products are generally also more neutron rich than stable nuclides of the same mass, even after the loss of a few prompt neutrons. (Example The symmetric fission of the compound nucleus (Z - 92, N -144) would form two/raiment nuclei of Pd (Z = 46, iV= 72). Assuming the emission of one prompt neutron, the corresponding primary fission product would be Pd. The stable isobar in mass chain with A = 117 is, however, Sn (Z -50, N- 67). As a consequence, the nucleus Pd would have to undergo a sequence of four P decays to reach stability.) Thus, the products... 

In the r on of symmetric fission or in the neighborhood of shell closures, the four parameters behave differently and show some abrupt changes. The behavior of the four parameters mentioned, as a function of the fission fi- ment mass and also as a function of the mass, charge, and excitation energy of the fissioning nuclide, is the subject of the fission yield systematics mentioned (Wahl 1988, 1989 IAEA 2000). A version (YCALC) of the model calculations is attached to ref. IAEA 2000, and it is also available for downloading (YCALC 2003). 

Schematic representations of all of the measured mass-yield distributions (normalized to 200% fragment yield) for SF of the trans-Bk isotopes are shown in Fig. 18.13 (Hoffinan and Lane 1995). It is interesting to observe rather sudden changes from asymmetric to symmetric fission as reflected by the mass distributions changing from asymmetric to symmetric mass distributions as the neutron number increases toward N 160 for the elements Fm Z = 100), No (Z= 102), andRf(Z= 104).

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