nuclear fission


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nuclear fission

the splitting of an atomic nucleus into approximately equal parts, either spontaneously or as a result of the impact of a particle usually with an associated release of energy

Nuclear fission

An extremely complex nuclear reaction representing a cataclysmic division of an atomic nucleus into two nuclei of comparable mass. This rearrangement or division of a heavy nucleus may take place naturally (spontaneous fission) or under bombardment with neutrons, charged particles, gamma rays, or other carriers of energy (induced fission). Although nuclei with mass number A of approximately 100 or greater are energetically unstable against division into two lighter nuclei, the fission process has a small probability of occurring, except with the very heavy elements. Even for these elements, in which the energy release is of the order of 200 megaelectronvolts, the lifetimes against spontaneous fission are reasonably long. See Nuclear reaction

Liquid-drop model

The stability of a nucleus against fission is most readily interpreted when the nucleus is viewed as being analogous to an incompressible and charged liquid drop with a surface tension. Long-range Coulomb forces between protons act to disrupt the nucleus, whereas short-range nuclear forces, idealized as a surface tension, act to stabilize it. The degree of stability is then the result of a delicate balance between the relatively weak electromagnetic forces and the strong nuclear forces. Although each of these forces results in potentials of several hundred megaelectronvolts, the height of a typical barrier against fission for a heavy nucleus, because they are of opposite sign but do not quite cancel, is only 5 or 6 MeV. Investigators have used this charged liquid-drop model with great success in describing the general features of nuclear fission and also in reproducing the total nuclear binding energies. See Nuclear binding energy, Nuclear structure

Shell corrections

The general dependence of the potential energy on the fission coordinate representing nuclear elongation or deformation for a heavy nucleus such as 240Pu is shown in Fig. 1. The expanded scale used in this figure shows the large decrease in energy of about 200 MeV as the fragments separate to infinity. It is known that 240Pu is deformed in its ground state, which is represented by the lowest minimum of 7–1813 MeV near zero deformation. This energy represents the total nuclear binding energy when zero of potential energy is the energy of the individual nucleons at a separation of infinity. The second minimum to the right of zero deformation illustrates structure introduced in the fission barrier by shell corrections, that is, corrections dependent upon microscopic behavior of the individual nucleons, to the liquid-drop mass. Although shell corrections introduce small wiggles in the potential-energy surface as a function of deformation, the gross features of the surface are reproduced by the liquid-drop model. Since the typical fission barrier is only a few megaelectronvolts, the magnitude of the shell correction need only be small for irregularities to be introduced into the barrier. This structure is schematically illustrated for a heavy nucleus by the double-humped fission barrier in Fig. 2, which represents the region to the right of zero deformation in Fig. 1 on an expanded scale. The fission barrier has two maxima and a rather deep minimum in between. For comparison, the single-humped liquid-drop barrier is also schematically illustrated. The transition in the shape of the nucleus as a function of deformation is schematically represented in the upper part of the figure.

Plot of the potential energy in MeV as a function of deformation for the nucleus 240 Puenlarge picture
Plot of the potential energy in MeV as a function of deformation for the nucleus 240Pu

Experimental consequences

The observable consequences of the double-humped barrier have been reported in numerous experimental studies. In the actinide region more than 30 spontaneously fissionable isomers have been discovered between uranium and berkelium, with half-lives ranging from 10-11 to 10-2 s. These decay rates are faster by 20 to 30 orders of magnitude than the fission half-lives of the ground states, because of the increased barrier tunneling probability (Fig. 2). Several cases in which excited states in the second minimum decay by fission are also known. Normally these states decay within the well by gamma decay; however, if there is a hindrance in gamma decay due to spin, the state (known as a spin isomer) may undergo fission instead.

Schematic plots of single-humped fission barrier of liquid-drop model and double-humped barrier Introduced by shell correctionsenlarge picture
Schematic plots of single-humped fission barrier of liquid-drop model and double-humped barrier Introduced by shell corrections

Fission probability

The cross section for particle-induced fission σ(y, f) represents the cross section for a projectile y to react with a nucleus and produce fission, as shown by the equation below. The quantities σR(y), Γf and Γt are the total

reaction across sections for the incident particle y, the fission width, and the total level width, respectively, where Γt = Γf + Γn + Γy + · · · is the sum of all partial-level widths. All the quantities in the above equation are energy-dependent.

When the incoming neutron has low energy, the likelihood of reaction is substantial only when the energy of the neutron is such as to form a compound nucleus in one or another of its resonance levels. The requisite sharpness of the “tuning” of the energy is specified by the total level width Γ. The nuclei 233U, 235U, and 239Pu have a very large cross section to take up a slow neutron and undergo fission because both their absorption cross section and their probability for decay by fission are large. The probability for fission decay is high because the binding energy of the incident neutron is sufficient to raise the energy of the compound nucleus above the fission barrier. The very large, slow neutron fission cross sections of these isotopes make them important fissile materials in a chain reactor. See Chain reaction (physics)

Postscission phenomena

After the nuclear fragments are separated, they are further accelerated as the result of the large Coulomb repulsion. The initially deformed fragments collapse to their equilibrium shapes, and the excited primary fragments lose energy by evaporating neutrons. After neutron emission, the fragments lose the remainder of their energy by gamma radiation, with a lifetime of about 10-11 s. The variation of neutron yield with fragment mass is directly related to the fragment excitation energy. Minimum neutron yields are observed for nuclei near closed shells because of the resistance to deformation of nuclei with closed shells. Maximum neutron yields occur for fragments that are “soft” toward nuclear deformation.

After the emission of the prompt neutrons and gamma rays, the resulting fission products are unstable against ß-decay . For example, in the case of thermal neutron fission of 235U, each fragment undergoes on the average about three ß-decays before it settles down to a stable nucleus. For selected fission products (for example, 87Br and 137I) ß-decay leaves the daughter nucleus with excitation energy exceeding its neutron binding energy. The resulting delayed neutrons amount, for thermal neutron fission of 235U, to about 0.7% of all the neutrons given off in fission. Though small in number, they are quite important in stabilizing nuclear chain reactions against sudden minor fluctuations in reactivity. See Neutron

nuclear fission

(new -klee-er) A process in which an atomic nucleus splits into two smaller nuclei, usually with the emission of neutrons or gamma rays. Fission may be spontaneous or induced by neutron or photon bombardment. It occurs in heavy elements such as uranium, thorium, and plutonium. The process is accompanied by the release of large amounts of energy.

Nuclear Fission

 

the splitting of an atomic nucleus into several lighter nuclei—“fragments”—usually two fragments of comparable mass.

In 1938 the German scientists O. Hahn and F. Strassmann established that the bombardment of uranium with neutrons produces nuclei of alkaline-earth elements, in particular Ba nuclei. Somewhat later, the Austrian physicists L. Meitner and O. Frisch showed that the 235U nucleus is split up by a neutron into two fragments. They introduced the term “nuclear fission,” alluding to the similarity of the observed effect to cell division in biology. They were also the first to provide a qualitative explanation of nuclear fission.

In the first stage of fission, the nucleus undergoes a gradual change of shape, in the course of which a neck forms, linking the as yet incompletely formed fragments (Figure 1, a and b). The length of the stage (10–14 to 10–18 sec) depends on the intensity of the excitation of the fissioning nucleus. The neck gradually grows thinner, and at some instant, known as the scission point, breaks (Figure l,c). The resultant fragments fly apart in opposite directions with high energy (Figure 1,d).

The deformation of the nucleus during fission is accompanied by a change in its potential energy (Figure 2). A certain energy must be expended to overcome a potential barrier, known as the fission barrier, so that the nucleus may attain the shape preceding the scission point. This energy is usually imparted to the nucleus from the outside by some nuclear reaction, for example, upon the capture of a neutron. Fission is observed for all nuclei heavier than Ag, although the fission probability is many times higher for the heaviest elements. In the case of 235U, even thermal neutron capture produces fission (seeTHERMAL NEUTRON).

Figure 1. Fission of 235U nucleus, containing 92 protons and 143 neutrons. A neutron captured by the 235U nucleus transforms it into 236U; the resulting deformation leads to the splitting of the nucleus.

In 1940, G. N. Flerov and K. A. Petrzhak (USSR) observed spontaneous fission in which tunneling penetration through the potential barrier occurs (seeTUNNEL EFFECT). Spontaneous fission is a form of radioactive decay of nuclei (seeRADIOACTIVITY) and is characterized by a half-life (the fission period). The probability of spontaneous fission depends on the height of the fission barrier.

Figure 2. Fission barrier and sequence of shapes passed through by fissioning atomic nucleus

For uranium isotopes and for elements close to uranium, the fission barrier is about 6 megaelectron volts (MeV). The height of the barrier and, consequently, the period of spontaneous fission of nuclei depend on the ratio Z2/A (Figure 3). Upon a change of Z2/A from 34.3 for 232Th to 41.5 for 260Ku, the period of spontaneous fission decreases by a factor of about 1030.

The fission of heavy nuclei is accompanied by the release of energy. Owing to the strong forces of electrostatic repulsion, the nucleons in heavy nuclei are not as strongly bound as in the fragment nuclei in the middle of the periodic system of the elements. Therefore, the mass of a heavy nucleus is greater than the sum of the masses of the fission fragments. The difference in masses corresponds to the energy released upon fission (seeRELATIVITY, THEORY OF). A considerable part of this energy is released as kinetic energy of the fragments, equal to the energy of electrostatic repulsion of the two contacting fragments at the instant when the nucleus splits in two (Figure l,c). The total kinetic energy of the fragments increases somewhat with increasing Z of the fissioning nucleus and reaches about 200 MeV for the nuclei of U and the transuranium elements. The fragments quickly slow down in a medium, causing the medium to heat up, generating ionization, and destroying the structure of the medium. After the proper chemical treatment, characteristic tracks of fission fragments can be observed under a microscope. The conversion of the kinetic energy of the fission fragments to thermal energy (heating of the surrounding medium) is the basis of the various uses for nuclear energy (for example, the nuclear chain reaction and nuclear explosion).

At the scission point, the fragments are strongly deformed, but as they move apart the deformation decreases, which increases the internal energy of the fragments. Subsequently, the excitation energy of the fragments decreases as a result of the emission of neutrons and gamma quanta (Figure 1,d). When the excitation energy of the fragments drops below the energy required to break off a neutron from the nucleus, neutron emission ceases and intense emission of gamma quanta begins. On the average, eight to ten gamma quanta are observed per each fission event.

Since the neck of the nucleus can break in different ways, the mass, charge, and excitation energy of the fragments vary from one fission event to the next. The number v of neutrons emitted during fission also varies. When U is bombarded with slow neutrons (see NEUTRONS, SLOW), the number v of neutrons per fission act is about 2.5. For heavier elements, v increases. The realization of v much greater than unity is a very important condition. In fact, it is this that makes possible the nuclear chain reaction and the accumulation in nuclear reactors of the energy released in the course of fission on macroscopic scales. The neutron energy spectrum can be taken as approximately Maxwellian with an average energy of ~ 1.3 MeV.

The nuclei formed during fission are overloaded with neutrons and are radioactive (isotopes of Ba and other elements). The ratio between the number of protons Z and the number of neutrons N = AZ in the nuclei depends on the excitation energy of the fissioning nuclei. With sufficiently strong excitation, the ratio of N and Z in the fragments usually remains the same as in the initial fissioning nucleus. In the case of low excitation energy of the fissioning nucleus, the neutrons and protons are distributed between the fragments in such a way that approximately the same number of beta decays occurs in each of the fragments before the fragments are converted to stable nuclei. In isolated cases (about 0.7 percent of the total number of fissions), an excited daughter nucleus formed during beta decay emits a neutron. The emission of the neutron from the excited nucleus is a fast process (t < 10–16 sec), but it is delayed with respect to the moment when the nucleus splits by a time that may reach tens of seconds; the neutrons emitted in this way are called delayed neutrons.

Fission is called asymmetric when the ratio of the masses of the most frequently arising fragments is ~ 1.5 (Figure 4). As the excitation energy of the nucleus increases, symmetric fission, the splitting of the nucleus into two fragments of approximately equal mass, begins to play an increasingly greater role. Asymmetric fission is typical of some spontaneously fissioning nuclei, such as U and Pu, but the fission approaches symmetric fission as A increases. This is most pronounced for 256Fm. Fission into three fragments, usually accompanied by the emission of alpha

Figure 3. Dependence of the periods T of the spontaneous fission of nuclei in the ground state on the ratio Z2/A

particles, nuclei of 6He, 8He, Li, Be, and so on, is obse rved much less frequently. The limiting case—fission into three equal fragments—has been observed upon the bombardment of nuclei with accelerated heavy ions, such as 40Ar.

Figure 4. Mass spectrum of fission fragments of a 235U nucleus upon the capture of slow neutrons

A theoretical explanation of nuclear fission was first given by N. Bohr and J. A. Wheeler (United States) and, independently, by Ia. I. Frenkel’ (USSR), who developed the liquid-drop model of the nucleus, according to which the nucleus is likened to a drop of electrically charged incompressible liquid. The nucleons in the atomic nucleus are acted upon by nuclear forces of attraction that are in balance with the electrostatic forces of repulsion between the protons that tend to tear the nucleus apart. Deformation of the nucleus disrupts equilibrium; however, as this is happening, forces arise that try to return the nucleus to its initial shape, similar to the surface tension of a liquid drop. The deformation of the nucleus during fission is accompanied by an increase in its surface, and, as in a liquid drop, the forces of surface tension increase, impeding further deformation. After crossing the top of the fission barrier, the formation of two drops of smaller size becomes energetically advantageous, and from this instant the formation of fission fragments proceeds rapidly and irreversibly. A reduction in the fission barrier for nuclei with large Z2/A shows up clearly in a reduction of the period of spontaneous fission.

The liquid-drop model describes only the averaged properties of nuclei. In reality, the nature of the fission process may also depend considerably on the internal structure of the nucleus and the state of the individual nucleons. In particular, because of this, the fission barrier is greater for nuclei with an odd number of nucleons than for the adjacent even-even nuclei (nuclei with even Z and N). The increase in the barrier has an especially appreciable effect on the periods of spontaneous fission of nuclei: the periods of spontaneous fission of even-even nuclei on the average are 100 times shorter than the periods of spontaneous fission of the adjacent nuclei with odd N.

The increase in the fission barrier owing to an odd nucleon can be seen from an example of the fission of uranium isotopes. The fission of 238U nuclei becomes fairly probable only in cases in which the kinetic energy of the neutrons exceeds a certain threshold, whereas in the case of 235U, even the capture of a thermal neutron increases the excitation energy of the compound nucleus of 236U above the fission barrier (Figure 5). The influence that the structure of the nucleus has on fission can be seen by comparing the periods of spontaneous fission of odd-even nuclei. Instead of a regular increase in the period of spontaneous fission with the mass of the nuclide, a sharp reduction in the period of spontaneous fission is sometimes observed. This effect is especially pronounced at a neutron number of N = 152, which cannot be explained using the liquid-drop model, and is evidence of the influence that the shell structure of the nucleus has on nuclear fission.

Nucleon shells do not only influence the surmounting of the fission barrier but also have an appreciable effect on the last stage of the formation of the fragments at the scission point. The change of a nucleus’ shape during fission occurs gradually (compared with the motion of nucleons in the nucleus), and as a result the nucleon orbits are adiabatically reorganized. Measurements of the mass spectrum of the fragments and their total kinetic energy, as well as the dependence of v on the ratio of masses of the fragments, show that nucleon shells form in the fragments before scission.

A. Bohr’s idea of the existence of “channel effects” exerted a considerable influence on the development of concepts of the fission process. It was found that upon fission caused by fast particles, the fragments fly apart anisotropically but always symmetrically relative to an angle of 90° with respect to the particle beam causing the fission. Close to the fission threshold, rather strange angular distributions of fragments are observed, which often change abruptly upon a comparatively small change in the energy of the particle captured by the nucleus. Bohr explained these effects in 1955 as a manifestation of quantum fission channels associated with individual states of the internal motion of nucleons in a strongly “cooled” nucleus at the instant when the energy barrier is overcome (the internal energy of excitation decreases here by the amount of the fission threshold). The study of fission channels has become one of the important sources of information about the structure of the intrinsic quantum states of the nucleus close to the fission threshold.

A new form of metastable (isomeric) state of nuclei with high probability of spontaneous fission was discovered in 1962 at the Joint Institute for Nuclear Research (USSR). About 30 nuclei (isotopes of U,Pu, Am, Cm, Bk) are known for which the probability of spontaneous fission in the isomeric state is greater than in the ground state by a factor of about 1026. It is probable that the shape of the nucleus in the isomeric state differs strongly from the shape of the nucleus in the ground state (isomerism of nuclear shape). In 1968 sub-barrier fission resonances were observed upon the capture of neutrons by 240Pu and 237Np nuclei. Phenomena

Figure 5. Dependence of the fission cross section on the energy of neutrons: (1) 235U and (2) 238U

of spontaneous fission from the isomeric state and the presence of sub-barrier fission resonances are explained by a model proposed by V. M. Strutinskii (USSR), which explains the formation of nucleon shells in strongly deformed nuclei. The model leads to the shape of the fission barrier shown in Figure 6, with an additional minimum of potential energy upon the deformation of the nucleus. The existence of this minimum may explain the nature of spontaneously fissioning isotopes. The lower state in the second potential well of the fission barrier should be isomeric. Electromagnetic transitions from this state to the ground state (lying in the first well) should be forbidden because of the potential barrier separating the two potential wells. At the same time, the fission barrier for isomeric states is low, which explains the high probability of the spontaneous fission of isomers.

Figure 6. Presumed shape of the potential barrier in the case of spontaneous fission from an isomeric state

Upon the excitation of a nucleus to an energy just below the height of the barrier that separates the two potential wells, the strong mixing of states with different equilibrium deformation begins. The mixing of states with different shapes of the nucleus gives rise to groups of fission resonances separated by distances equal to the spacing between the levels of the compound nucleus at the saddle point.

The strong influence of shell effects on the fission barrier makes it possible to predict certain peculiarities in the transuranium elements as yet not synthesized. According to the liquid-drop model, atomic nuclei with Z2/A > 46 should be unstable and should decay by spontaneous fission within about 10–21 sec. Taking into account the influence of nucleon shells on the fission barrier, one may conclude that the appearance of new filled shells (apparently with Z = 114 and N = 184) will be accompanied by an increase in the height of the fission barrier to several MeV. This is the basis for the assumption of an “island of stability” of superheavy transuranium elements close to Z = 114. It cannot be ruled out that the lifetime of some isotopes within this “island” will exceed tens of thousands of years. However, it should be borne in mind that thus far the existence of islands of stability remains a purely hypothetical possibility based on certain assumptions about the details of the structure of the nuclei of superheavy transuranium elements.

REFERENCES

Hahn, O., and F. Strassmann. Naturwissenschaften, 1939, vol. 27, no. 1, p. 11.
Petrzhak, K. A., and G. N. Flerov. Zhurnal eksperimental’noi i teoreticheskoi fiziki, 1940, vol. 10, issue 9–10, p. 1013.
Frenkel’, Ia. I. Zhurnal eksperimental’noi i teoreticheskoi fiziki, 1939, vol.9, issue 6, p. 641.
Petrzhak, K. A., and G. N. Flerov. Uspekhi fizicheskikh nauk, 1961, vol. 73, issue 4, p. 655.
Strutinskii, V. M. “Delenie iader.” Priroda, 1976, no. 9.
Lichman, R. B. “Delenie iadra.” In Fizika atomnogo iadra i plazmy. Moscow, 1974. (Translated from English.)

nuclear fission

[′nü·klē·ər ′fish·ən]
(biology)
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