Fissility parameter

Af (or more simply Z"/A) appears as a factor that determines the willingness of nuclei to fission. Therefore, it is called the fissility parameter. A value of Z"/A larger than 39 indicates that the nucleus should be unstable toward (spontaneous) fission. Values of Z"/A larger... 

Another derivation of the fissility parameter goes back to Bohr and Wheeler (Bohr and Wheeler 1939) and (independently) to Frenkel (Frenkel 1939) Oscillations of a nucleus will be unstable if the gain in Coulomb energy surpasses the loss of surface energy. The volume (V) of a sphere is given by... 

The role of the fissility parameter in the stability of nuclei against fission is documented in 0 Fig. 4.4 where the half-lives of heavy nuclei toward spontaneous fission are plotted. As a general trend, one can observe a gradual decrease over 35 orders of magnitude with increasing Z /A in the semilogarithmic plot. At closer look, one can see however that most elements (characterized by their atomic numbers) show a bell-shaped behavior. This deviation from... 

Half-lives for spontaneous fission of heavy elements (characterized by their atomic numbers Z) as a function of their fissility parameters Z /A). (Data from Wagemans 1991a, p 37). The data represent even-even nuclei only... 

Half-lives for spontaneous fission of even-even nuclei (as shown inO Fig, 4,4) open circles) and of odd-4 and odd-odd nuclei full circles) versus the corresponding fissility parameter (Wagemans 1991a)... 

In O Fig. 4.4 only even-even nuclei are plotted. Nuclei with an odd number of either neutrons or protons or both, generally, have longer half-lives, as will be discussed later in the context of the influence of nuclear shell structure on fission. For comparison, the half-lives of odd (i.e., odd-A and odd-odd) and even-even nuclei for spontaneous fission as a function of the fissility parameter are shown in Fig. 4.5. It is obvious that in general the half-lives of odd nuclei are several orders of magnitude longer. 

The dip between the two peaks is most pronounced for the fission of and decreases with increasing mass or rather with increasing fissility parameter (Z M) of the fissioning nucleus. This is in agreement with the expectation that shell effects will become less important with increasing excitation energy of the nucleus at the scission point. 

The ratio of count rates in the two ionization chambers at a known rotational speed of the wheel (800-1,400 rpm) allowed to calculate the half-life of the spontaneously fissioning nuclides. The value obtained was 0.02 s - about lo times shorter than expected for a normal spontaneously fissioning nuclide of this fissility parameter (see O Fig. 4.4). (The shortest-lived normal spontaneously fissioning nuclide that could be considered is pm formed in the reaction ( 0,2n) Fm. Its fissility parameter would be Z /A = 39.7. The half-life extrapolated from the systematics (O Fig. 4.4) would be of the order of 10 -10 s. The species observed here was later identified to be a shape isomer of Am (fissility parameter of 37.3). The ground state of Am decays by P decay and electron capture with a half-life of 16 h.)... 

Half-lives for spontaneous fission from the second minimum of the potential energy curve as shown schematically in O Fig. 4.8 (fission isomers) full points) as a function of the fissility parameter compared to the corresponding half-lives from the ground states open points). The latter points are identical to those in O Fig. 4.4. All data are from the compilation of (Wagemans 1991a)... 

In O Fig. 19.11 the partial fission half-lives of the doubly even isotopes of uranium and beyond are plotted on a logarithmic time scale versus the fissility parameter. In accordance with the expectation from the liquid drop model the dashed line labeled Bld, describing the fission half-life calculated with only the liquid drop barrier Bid, crosses the 2. line at nobeKum. The time Te. is needed for the formation of the electron shell of the atom, the lower time limit considered beyond which a chemical element cannot be formed (Barber et al. 1992). The experimental half-lives follow this general trend. They decrease from uranium to nobelium over more than 20 orders of magnitude, from the age of the solar system down to fractions of seconds. The structure of the isotopic chains of elements from curium to nobelium is caused by a subshell closure at M = 152. 

A change in the half-life systematics occurs at rutherfordium. Fission half-lives become independent of the fissility parameter and stay almost constant. A comparison of the data to the calculated liquid-drop half-lives shows an enhancement of the fission half-lives by about 15 orders of magnitude. This stabilization is caused by a new shell at hassium. 

Fig. 2 Schematic illustration of fission barriers as a function of deformation parameter S for several values of the fissility parameter x. The corresponding nuclear shapes are also indicated...

Fig. 3 Experimental spontaneous fission half-lives for even-even nuclei circles) compared to the prediction of the liquid drop model as a function of the fissility parameter x = 7 jA dashed line). The horizontal dotted line shows the minimum lifetime for the formation of a chemical element. Figure reproduced from [19] with permission...

Spontaneous fission is a decay process in which a nucleus breaks up into two almost equal fragments. Each fission event is accompanied by the release of about 200 MeV energy and the emission of 2-4 neutrons. Fission half-life depends on the fissility parameter Z /A and it is the major mode of decay for many isotopes of elements 100 and beyond. 

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