Fission asymmetric

Summary.—The assumption that atomic nuclei consist of closely packed spherons (aggregates of neutrons and protons in localized Is orbitals—mainly helions and tritions) in concentric layers leads to a simple derivation of a subsubshell occupancy diagram for nucleons and a simple explanation of magic numbers. Application of the close-packed-spheron model of the nucleus to other problems, including that of asymmetric fission, will be published later.13... 

Close packing of spherons provides a simple explanation of nuclear properties, including asymmetric fission. 

Fig. 12. (Left) An outer core of 21 spherons surrounding a linear inner core of four. (Right) The same core with a portion of the mantle, illustrating asymmetric fission.

The observed width of the distribution functions in mass number of the fission products indicates that the spherons that lie in the plane of the fissure are essentially randomly distributed between the two daughter nuclei, as discussed below for asymmetric 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. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

This observation, along with the observation that the lower edge of the heavy fragment peak is anchored at A = 132 has suggested that the preference for asymmetric fission is due to the special stability of having one fragment with Z = 50, N = 82, a doubly magic spherical nucleus. 

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%. 

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. 

As an example, the mass distribution of the products obtained by the bombardment of with " Ar is plotted in Fig. 8.24. The curve is explained by superposition of the processes described above only few nucleons are transferred by quasielastic reactions (a), and many nucleons by deeply inelastic processes (b). Fusion followed by fission of highly excited products leads to a broad distribution of fission products around l/2(y4i + A2), where A and Ai are the mass numbers of and Ar, respectively (c), and asymmetric fission of heavy products of low excitation energy gives two small maxima (d). 

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. 

Because asymmetric fission is more common than symmetric and the emerging fission fragments have non-spherical form, the numerical value derived above is not very accurate. However, the concq>t of a critical value of Z lA is inqwrtant. A more sophisticated treatment results in the equation... 

Strutinsky developed an extension of the liquid drop model which satisfactorily explains the fission isomers and asymmetric fission. For such short half-lives the barrier must be only 2-3 MeV. Noting the manner in which the shell model levels vary with deformation ( 11.5, the "Nilsson levels"), Strutinsky added shell corrections to the basic liquid-drop model and obtained the "double-well" potential energy curve in Figure 14.14b. In the first well the nucleus is a spheroid with the major axis about 25 % larger than the minor. In the second well, the deformation is much larger, the axis ratio being about 1.8. A nucleus in the second well is metastable (i.e. in isomeric state) as it is unstable to y-decay to the first well or to fission. Fission from the second well is hindered by a 2 - 3 MeV barrier, while from the first well the barrier is 5 - 6 MeV, accounting for the difference in half-lives. 

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. 

The fission reaction Na - Na i + Nas has been studied [79], modelling the fissioning cluster by axially symmetric jellium shapes corresponding to two spheres smoothly joined by a portion of a third quadratic surface of revolution [80]. This family of shapes is characterised by three parameters the asymmetry, A, that is fundamental to the description of asymmetric fission, the distance parameter, p, which is proportional to the separation between the emerging fragments, and the deck parameter, A, which takes into account the neck deformation. 

Whether this step is accompanied to some extent by a primary photodissociation to B2H , + H2 is not yet certain. The evidence for it is compatible with experiment, but not compelling. The formation of B2H[+ is also assumed in the hexafluoroacetone-sensitized photolysis (152), but here the B2H1+ is supposed to arise from the condensation of 2BH2 produced from asymmetric fission of B2Hg as the primary step. 

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 ). 

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). 

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 ... 

In this mass region of normal asymmetric fission, the parameters mass ratio of heavy and light fragments. 

Numerical values of the parameters mentioned (for the yield range of normal asymmetric fission ) are given inO Table 4.2. 

The discovery of an odd-even effect in the (again, very asymmetric) fission of lighter odd-Z fissioning systems studied in inverse kinematics (Steinhauser et al. 1998) has confirmed the findings obtained in thermal-neutron-induced fission. 

It is interesting to note that the spectra of ternary particles extend to different atomic numbers, which coincide nearly with the size of the neck that results from the postulate extracted from the mass yield and nuclear charge distributions. To correlate the data, it has been postulated that the two spheres of the dumbbell configuration shown in O Fig. 4.11 for the fission of are practically the same for all asymmetrically fissioning nuclei from Z= 90 to about 99 and, consequently, that the variation in the neutron/proton numbers of the different compound nuclei must be connected with the size of the neck. O Fig. 4.29 is the direct experimental proof for this assumption in the fission of uranium, the neck size is (92 — 82 =) 10 protons in the fission of californium, the neck size is (98 — 82 =) 16 protons. The situation is similar for neutrons and for the total mass. This is, however, less convincing due to prompt neutron emission. 

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