Isobaric fission yields

In addition to measuring the variation of mass yield, the variation of fission yield in isobaric mass chains as a function of the proton number has bear studied. In Figure 14.10, "individual yield data are presented for the A = 93 chain. In gmeral, the charge distribution yields follow a Gaussian curve with the maximum displaced several units below the value of Z for stable nuclides with the same A. For A = 93 the yield is largest for Z = 37 and 38 most probable charge, Zp) compared to the stable value of Z = 41. 

In general, these parameters depend on the mass number of the isobaric chain considered. In the region of normal asymmetric fission (>99% of the fission yields), e.g., AZ can be given as a linear function of the mass of the heavier fi-agment ... 

The columns contain isotones. The fission yields for are given for several mass chains (i.e., isobars situated along the lines shown by the slanted arrows). Stable isotopes are shaded and list natural abundances in percentage. (The upmost cells show the stable and primordial Sm isotopes.) See also O Table of Nuclides in this volume s appendix. 

As an illustration of the way to disentangle the events that had taken place 2 billion years ago, the measurement of the neodymium isotopes (142-146,148, and 150) wiU be presented. It is important to know that neodymium remained in the rocks without migrating. In addition, it is advantageous that the content of natural neodymium in the minerals is small. This content could be determined since Nd is practically not formed in nuclear fission. As it results from the systematics of fractional fission yields (see Chap. 4 in Vol. 1), the (independent, direct) yield of Nd is very small. An alternative formation by the P decay of more neutron-rich nuclides of the same mass (i.e., isobars) is not possible because the direct precursor Ce is stable. Consequently, the content of the mineral in Nd reflects the amount of natural neodymium not produced by fission. Using the known isotopic composition of natural neodymium, the contributions of natural origin of all neodymium isotopes could be subtracted. This is illustrated in Table 57.1 (Columns 1-3). 

A couple of features stand out in Figure 17.1. First, is the fact that some of the nuclides considered have relatively short half-lives, and unless detection is achieved promptly, their usefulness declines. Secondly, the low activity yield of Cs compared to Cs and Cs is worthy of note. This is because Cs is shielded from the A = 134 isobaric precursors by the stable Xe. The yield shown is the direct fission yield, a factor of 8000 lower than the chain yield leading to Cs. There is a similar situation with regard to Cs, which is shielded hy Xe. However, the half-life of Cs is so short (13.16d) that the activity created by fission is only slightly lower than that of Cs. 

Unfortunately, precise knowledge of the distribution of direct yield among several competing isobars is generally not available furthermore, the radioactive half-lives involved are frequently completely unknown since the fission process gives rise directly to between 300 and 400 radioactive species, and the separation of such a complex mixture usually involves a time which is quite long compared with the lifetimes of interest. We do know that each isobaric chain is formed directly as a number of different isobars and that the width of the isobaric yield distribution is such that to account for 90% or more of a chain one must consider at least three or perhaps four chemical elements. 

The yield of any given nuclide in fission is called its independent yield. It can be shown that the independent yield of isobars in fission has a Gaussian form ... 

In discussions of fission, one frequently hears the terms cumulative yield and independent yield. The independent yield of a nuclide is just what it appears, the yield of that nucleus as a primary fission product. Because the fission products are all (3 emitters, they decay toward the bottom of the valley of (3 stability, populating several different members of an isobaric series, as, for example, with A = 140 fragments ... 

The yield of each member of the isobaric series integrates, by virtue of the intervening (3 decay, the yields of its precursors. Such yields are referred to as cumulative yields. For example, the cumulative yield of the mass 140 chain in the thermal neutron-induced fission of 235U is 6.25%. 

Podosek et al., 1994 Takaoka et al., 1996) the discrepancy arises in geological interpretation rather than analytical uncertainties. f Fission produces several isotopes of both Xe and Kr (those with no stable isobars of lower atomic number) see Table 1.5 for yields and compositions. 

The mass distribution curves in Figs. 8.13 to 8.15 give the total yields of the decay chains of mass numbers A. The independent yields of members of the decay chains, i.e. the yields due to direct formation by the fission process, are more diflicult to determine, because the nuclides must be rapidly separated from their precursors. Only a few so-called shielded nuclides (shielded from production via decay by a stable isobar one unit lower in Z) are unambiguously formed directly as primary... 

P Z) is the relative independent yield and C is a constant with a mean value of 0.80 + 0.14. This charge distribution is plotted in Fig. 8.16 for the fission of by thermal neutrons and holds for all mass numbers. For even numbers of Z the yields are systematically higher than those for odd numbers of Z. Zp, the most probable value of Z, is about 3 to 4 units lower than the atomic number of the most stable nuclide in the sequence of isobars. Nuclides with Zp are obtained with about 50% of the total isobaric yield, nuclides with Z = Zp + 1 with about 25% each and nuclides with Z = Zp + 2 with about 2% each. 

With the development of fast chemical separation techniques and physical techniques that allows one to differentiate between different elements of an isobaric decay chain, information could be obtained on the fission product distribution prior to P decay. The corresponding yields are called independent or primary product yields. 

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... 

Figure 1.30 The location of fission products on the Nuclide Chart, indicating regions of high independent yield. The inset shows how data are presented for the cumulative yield of each isobar...

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