nuclear reaction


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nuclear reaction

a process in which the structure and energy content of an atomic nucleus is changed by interaction with another nucleus or particle

Nuclear reaction

A process that occurs as a result of interactions between atomic nuclei when the interacting particles approach each other to within distances of the order of nuclear dimensions (≃10-12 cm). While nuclear reactions occur in nature, understanding of them and use of them as tools have taken place primarily in the controlled laboratory environment. In the usual experimental situation, nuclear reactions are initiated by bombarding one of the interacting particles, the stationary target nucleus, with nuclear projectiles of some type, and the reaction products and their behaviors are studied.

Types of nuclear interaction

As a generalized nuclear process, consider a collision in which an incident particle strikes a previously stationary particle, to produce an unspecified number of final products. If the final products are the same as the two initial particles, the process is called scattering. The scattering is said to be elastic or inelastic, depending on whether some of the kinetic energy of the incident particle is used to raise either of the particles to an excited state. If the product particles are different from the initial pair, the process is referred to as a reaction.

The most common type of nuclear reaction, and the one which has been most extensively studied, involves the production of two final products. Such reactions can be observed, for example, when deuterons with a kinetic energy of a few megaelectronvolts are allowed to strike a carbon nucleus of mass 12. Protons, neutrons, deuterons, and alpha particles are observed to be emitted, and reactions (1)–(4)

(1) 
(2) 
(3) 
(4) 
are responsible. In these equations the nuclei are indicated by the usual chemical symbols; the subscripts indicate the atomic number (nuclear charge) of the nucleus, and the superscripts the mass number of the particular isotope. These reactions are conventionally written in the compact notation 12C(d,d)12C, 12C(d,p)13C, 12C(d,n)13N, and 12C(d,α)10B, where d represents deuteron, p proton, n neutron, and α alpha particle. In each of these cases the reaction results in the production of an emitted light particle and a heavy residual nucleus. If the residual nucleus is formed in an excited state, it will subsequently emit this excitation energy in the form of gamma rays or, in special cases, electrons. The residual nucleus may also be a radioactive species, in which case it will undergo further transformation in accordance with its characteristic radioactive decay scheme. See Radioactivity

Nuclear cross section

In general one is interested in the probability of occurrence of the various reactions as a function of the bombarding energy of the incident particle. The measure of probability for a nuclear reaction is its cross section. Consider a reaction initiated by a beam of particles incident on a region which contains N atoms per unit area (uniformly distributed), and where I particles per second striking the area result in R reactions of a particular type per second. The fraction of the area bombarded which is effective in producing the reaction products is R/I. If this is divided by the number of nuclei per unit area, the effective area or cross section σ = R/IN. This is referred to as the total cross section for the specific reaction, since it involves all the occurrences of the reaction. The dimensions are those of an area, and total cross sections are expressed in either square centimeters or barns (1 barn = 10-24 cm2). The differential cross section refers to the probability that a particular reaction product will be observed at a given angle with respect to the beam direction. Its dimensions are those of an area per unit solid angle (for example, barns per steradian).

Reaction mechanism

Various reaction models have been extremely successful in describing certain classes or types of nuclear reaction processes. In general, all reactions can be classified according to the time scale on which they occur, and the degree to which the kinetic energy of the incident particle is converted into internal excitation of the final products. A large fraction of the reactions observed has properties consistent with those predicted by two reaction mechanisms which represent the extremes in this general classification. These are the mechanisms of compound nucleus formation and direct interaction.

Compound nucleus formation is envisioned to take place in two distinct steps. In the first step the incident particle is captured by (or fuses with) the target nucleus, forming an intermediate or compound nucleus which lives a long time (≃10-16 s) compared to the approximately 10-22 s it takes the incident particle to travel past the target. During this time the kinetic energy of the incident particle is shared among all the nucleons, and all memory of the incident particle and target is lost. The compound nucleus is always formed in a highly excited unstable state, is assumed to approach themodynamic equilibrium involving all or most of the available degrees of freedom, and will decay, as the second step, into different reaction products, or through so-called exit channels. The essential feature of the compound nucleus formation or fusion reaction is that the probability for a specific reaction depends on two independent probabilities: the probability for forming the compound nucleus, and the probability for decaying into that specific exit channel.

Some reactions have properties which are in striking conflict with the predictions of the compound nucleus hypothesis. Many of these are consistent with the picture of a mechanism where no long-lived intermediate system is formed, but rather a fast mechanism where the incident particle, or some portion of it, interacts with the surface, or some nucleons on the surface, of the target nucleus. These direct reactions are assumed to involve only a very small number of the available degrees of freedom. Most direct reactions are of the transfer type, where one or more nucleons are transferred to or from the incident particle as it passes the target, leaving the two final partners either in their ground states or in one of their many excited states. Such transfer reactions are generally referred to as stripping or pickup reactions, depending on whether the incident particle has lost or acquired nucleons in the reaction.

Inelastic scattering is also a direct reaction. Whereas the states preferentially populated in transfer reactions are those of specific single-particle or shell-model structure, the states preferentially excited in inelastic scattering are collective in nature. See Nuclear structure, Scattering experiments (nuclei)

Nuclear Reaction

 

the transformation of an atomic nucleus upon interaction with elementary particles, gamma quanta, or another nucleus. The initiation of a nuclear reaction necessitates that particles (for example, two nuclei or a nucleus and nucleon) approach each other to within a distance of ~10−13 cm. The energy of positively charged incident particles must be of the order of the height of the Coulomb potential barrier for nuclei or higher (about 10 megaelectron volts [MeV] for singly charged particles). In this case, nuclear reactions are usually initiated by the bombardment of materials (targets) with beams of accelerated particles. For negatively charged and neutral particles, there is no Coulomb barrier, and nuclear reactions can occur even at thermal energies of the incident particles.

A nuclear reaction is denoted A(a, bcd)B, where A is the target nucleus,a is the bombarding particle, b, c, and d are the emitted particles, and B is the residual nucleus (the lighter reaction products are recorded within parentheses, and the heavier ones outside). A nuclear reaction can frequently proceed in several ways, for example,

63Cu(p, n)63Zn, 63Cu(p, 2n)62Zn, 63Cu(p, pn)62Cu, 63Cu(p, p)63Cu, 63Cu(p, p’)63Cu

The composition of the incident particles is called the entrance channel of the nuclear reaction, and the composition of the particles formed as a result of the nuclear reaction is called the exit channel.

The nuclear reaction is the principal method of studying the structure of the nucleus and its properties (see). However, nuclear reactions are also of considerable importance outside the realm of physics: fission reactions of heavy nuclei and the fusion of light nuclei are the basis of the nuclear power industry, Nuclear reactions are used as a source of neutrons, mesons, and other unstable particles. They provide more than 1,000 radionuclides, which are used in all areas of science, technology and medicine.

The study of nuclear reactions includes the identification of reaction channels, the determination of the probability of the excitation of reactions depending on the energy of the incident particles, and the measurement of the angular energy distributions of the particles formed, as well as their spin, parity, and isotopic spin.

Nuclear reactions conform to the laws of conservation of electric charge, baryon charge, energy, and momentum. Nuclear reactions can occur with the liberation and absorption of energy Q that is about 106 times greater than the energy absorbed or liberated in chemical reactions. Therefore, a change in mass of the interacting nuclei can be noted in nuclear reactions. The energy Q released or absorbed in nuclear reactions is equal to the difference between the sums of the particle masses (in energy units) before and after the reaction (seeRELATIVITY, THEORY OF).

Effective cross section. The effective cross section of a nuclear reaction is the cross-sectional area that must be ascribed to the nucleus so that each incidence of a bombarding particle leads to a nuclear reaction. The effective cross section σ of a nuclear reaction depends on the energy of the bombarding particles, the type of reaction, and the angles of emission and orientation of spins of the particles produced (σ ~ 10–27 to 10–21). The maximum cross section of a nuclear reaction is determined by the geometric cross sections of nuclei σmax = πR2 if the radius R of the nucleus is greater than the length of the de Broglie wave ƛ. For nucleons, ƛ = R when their energy ℰ ≈ 10/A, where A is the mass number. In the low-energy region, ƛ ≫ R, and the cross section of nuclear reactions is no longer determined by R but by ƛ; for example, σmax ≈ πƛ2 for slow neutrons. In the medium-energy region, σmax = π(R + ƛ)2.

Yield. The yield of a nuclear reaction is the ratio of the number of events of the nuclear reaction to the number of particles incident per 1 cm2 of the target. For a thin target and a homogeneous particle flux, the yield of a nuclear reaction W = nσ, where n is the number of nuclei per 1 cm2 of the target. The charged particles lose energy and come to rest as they ionize the target atoms. Their mean free path in targets is of the order of microns or centimeters, depending on the energy. As a result, the yields of nuclear reactions are also small (10–3 to 10–6). The yield is greater for nuclear reactions with high-energy particles. For particles that can cause nuclear reactions at any energy (neutrons, pions), the yield with sufficiently large targets may reach 1.

The products of nuclear reactions are formed in small amounts: a few milligrams per hour for accelerated incident particles and a few grams per hour in powerful nuclear reactors (neutron-induced reactions). As a rule, the concentration of the resultant products is low. The methods of radiochemistry and mass spectrometry are used to isolate and identify these products. The products of nuclear reactions are registered by nuclear radiation detectors.

Mechanisms of nuclear reactions. An incident particle, such as a nucleon, may enter and leave the nucleus at different angles, but with the same energy (elastic scattering). The nucleon may collide directly with a nucleon of the nucleus; in this case, if either or both of the nucleons have an energy greater than that required to leave the nucleus, they may leave without interacting with any of its other nucleons (direct process). There also exist more complex direct reactions, in which the energy of the incident particle is transferred directly to one nucleon or a small group of nucleons in the nucleus (seeDIRECT NUCLEAR REACTION). If the energy introduced by the incoming particle is gradually distributed among many nucleons of the nucleus, the nuclear states will become increasingly more complex. However, after a certain time, dynamic equilibrium will be reached: different nuclear configurations will arise and decay in the resultant system, called a compound nucleus (seeCOMPOUND NUCLEUS). The compound nucleus is unstable and rapidly decays into the final products of the nuclear reaction. If the energy of one of the nucleons in some configurations is sufficient for ejection from the nucleus, the compound nucleus decays with the emission of a nucleon. On the other hand, if the energy is concentrated in a few groups of particles, existing for a short time in the compound nucleus, then there may be the emission of alpha particles, tritons, deuterons, and the like. At excitation energies of the compound nucleus that are lower than the energy for the ejection of particles, the only reaction path is the emission of gamma quanta (seeRADIATIVE CAPTURE OF NEUTRONS). Sometimes particles are ejected before equilibrium is reached, that is, before the formation of a compound nucleus (the mechanism of preequilibrium decay).

The different mechanisms of nuclear reactions vary with respect to duration. The direct nuclear reaction has the shortest time. This is the time it takes for the particle to pass through the region of space occupied by the nucleus (~10–22 sec). The average lifetime of a compound nucleus is considerably longer (10–15 to 10–16 sec). At low energies of the incident particles, the major mechanism of nuclear reactions, as a rule, is the formation of a compound nucleus, with the exception of nuclear reactions with deuterons. Direct processes predominate at high energies.

The nature of the dependence of the effective cross sections σ of nuclear reactions on the energy ℰ of the incident particles σ(ℰ) differs for different mechanisms of nuclear reactions. For direct processes, the dependence σ(ℰ) exhibits monotonic behavior. In the case of nuclear reactions resulting in the formation of compound nuclei, maxima are observed in σ(ℰ) at low particle energies; these maxima correspond to the energy levels of the compound nucleus. In the high-energy region (ℰ ≥ 15 MeV for intermediate-mass and heavy nuclei), the energy levels of the compound nucleus overlap, and the cross section depends mono-tonically on energy. Against this background, broader maxima are distinguished corresponding to the excitation of the isobaric analog states (states of the nucleus in which the isotopic spin is greater than in the ground state), and giant resonances are observed. These broader maxima correspond to the levels of the nucleus that are formed when a nucleus combines with the incident particle and have a simpler structure than the levels of the compound nucleus. The lifetime т of the excited nucleus is related to the total width Γ of the observed maxima by the expression Γ = ℏ/т, where ℏ is Planck’s constant.

Upon the decay of a compound nucleus, the residual nucleus may be formed both in the ground state and in any one of several excited states. The energy spectrum of the decay products of a compound nucleus in the region of higher energies consists of separate lines, and in the low-energy region the emitted particles have a broad maximum. The angular distribution of the final products (in the center of mass system) in the resonance energy region is symmetric with respect to the direction that forms a 90° angle with the direction of the incident particles. In the energy region where the energy levels of the compound nucleus overlap, the quantum characteristics of different levels of the compound nucleus are averaged, and the angular distribution of the emitted particles is spherically symmetric as a rule.

The particles produced in the course of a nuclear reaction are usually polarized. Polarization arises in the case where the beam of bombarding particles is not polarized. On the other hand, if the incident beam is polarized, azimuthal asymmetry of the nuclear reaction products is observed (seePOLARIZED NEUTRONS and ORIENTED NUCLEI).

Neutron-induced reactions. In most cases, nuclear reactions initiated by neutrons occur with the absorption of energy Q. In the (n, p) reaction, Q is low for most nuclei (except 3H and 14N). For the (n, α) reaction, the absorbed energy Q is also low in the case of light nuclei (except 6Li and 10B); only a small amount of energy is released for intermediate-mass and heavy nuclei. Nuclear reactions in which more than two particles are formed proceed with the absorption of energy, equal to the amount necessary for separating a neutron from the nucleus; for example, this energy is about 10 MeV for the (n, 2n) reaction. In this sense, a special place belongs to the reaction of the fissioning of heavy nuclei, which is accompanied by the liberation of a large amount of energy. The fission reaction for some nuclei, for example, 238U, has an energy threshold (neutrons must have sufficiently high energy) associated with the need for overcoming the potential barrier of fission. The nuclei of 235U, 242Am, 245Cm, and 249Cf are fissioned by slow neutrons (see).

The major process for slow neutrons is radiative neutron capture, the (n, γ) reaction. Exceptions are 3He and 14N, for which the major process is the (n, p) reaction, and 6Li and 10Be, for which the (n, α) reaction predominates. In intermediate-mass and heavy nuclei, the potential barrier prevents the emission of protons and alpha particles. The region of energies ℰn of slow neutrons is a resonance region. Most nuclei exhibit resonance capture at ℰn of a few eV or more. At ℰn < 1 eV, the effective capture cross section for most nuclei is inversely proportional to the neutron velocity (the 1/v law).

With increasing neutron energy ℰn, there is a reduction in the probability of resonant capture and an increase in the probability of elastic scattering by nuclei (n, n). When ℰn becomes greater than the energy of the first excited state of the target nucleus (tens and hundreds of keV), inelastic scattering of neutrons is possible (n, n’). When ℰn is of the order of a few MeV, elastic scattering and inelastic scattering of neutrons play a major role; the (n, p) and (n, α) reactions become appreciable, but their cross sections are smaller than the cross section of (n, n’). When ℰn reaches 5–10 MeV, the (n, 2n) reactions play a predominant role.

Proton-induced reactions. The interaction of protons with nuclei is blocked by the Coulomb barrier, and therefore nuclear reactions involving protons are observed only beginning at proton energies ℰp of a few hundred keV for light nuclei and a few MeV for heavy nuclei. At low ℰp, the principal nuclear reaction is the radiative capture of protons (p, γ), as well as the elastic (p, p) and inelastic (p, p’) scattering of protons by nuclei. Nuclear reaction probability is resonant for light nuclei in the region of low ℰp. For intermediate and heavy nuclei, this probability attains a considerable value only in the region of energies where there is no resonance structure. In the region of energies ℰp close to the Coulomb-barrier height, the excitation of a small number of isobaric analog states is observed. The cross section of nuclear reactions has an appreciable value starting from 0.5ℰ0 (ℰ0 is the energy corresponding to the Coulomb-barrier height), and increases monotonically. The (p, n) reaction becomes predominant if a compound nucleus has an excitation energy sufficient for emitting a neutron with an energy of 1 MeV or more. Upon a further increase in ℰp, the residual nucleus may have sufficient energy to emit a second particle. In this case, the (p, 2n) and (p, pn) reactions predominate.

Reactions induced by alpha particles. For alpha particles, the Coulomb barrier is still higher, reaching 25 MeV for heavy nuclei. At this energy of the incident alpha particles, the excitation energy of the nucleus is about 20 MeV, which is sufficient not only to compensate for the binding energy of the emitted nucleon but also to overcome the Coulomb barrier by the emitted proton. As a consequence, the (α, n) and (α, p) reactions are equally probable. Upon an increase in the energy of alpha particles, the (α, 2n) and (α, pn) reactions become most probable. A resonance structure of the energy dependence of the cross sections of these nuclear reactions is observed only in the case of light nuclei and at relatively low energies of alpha particles. The products of the (α, n) reaction are usually beta-active, and the products of the (α, p) reaction are stable nuclei.

Deuteron-induced reactions. Nuclear reactions induced by deu-terons are characterized by the highest yield compared to the other nuclear reactions induced by charged particles. For example, the yield of the reaction 9Be(d, n)10B at a deuteron energy ℰd = 16 MeV reaches 0.02, whereas the yield is of the order of 10–3 to 10–6 for nuclear reactions with other charged particles of similar energies. Nuclear reactions involving deuterons can occur with the formation of a compound nucleus, or they can occur through spallation of the deuteron by the Coulomb field of the target nucleus or through the direct mechanism of stripping. The effective cross sections of these three processes are approximately of the same order. Since the average distance between the proton and the neutron in a deuteron is relatively large and their binding energy is small, it is most probable that upon the bombardment of nuclei by deuterons the nucleus will capture only one of the nucleons of the deuteron, while the second nucleon will continue traveling without interacting with the nucleus. In this case, the nuclear reaction occurs on the surface of the nucleus rather than within the nucleus. The protons and neutrons formed as a result of the deuteron stripping reaction travel mainly in the forward direction. Deuterons accelerated in cyclotrons are extensively used to produce radionuclides and intense neutron fluxes (seeNEUTRON SOURCES).

Nuclear reactions between the lightest nuclei have a considerable yield even at low energies of the incident particles (of the order of 1–10 keV). Therefore, they can be initiated not only by bombarding a target with a beam of accelerated particles but also by heating a mixture of interacting nuclei to a temperature of about 107 kelvins (seeTHERMONUCLEAR REACTIONS).

Reactions induced by high-energy particles (with energies appreciably exceeding the binding energy of the nucleons in the nucleus). Particles with energies of about 100 MeV correspond to ƛ = 0.43 fermi, which is small compared to the average internuclear distance in the nucleus (1.9 fermi). This makes possible “probing” of the nucleus: in a first approximation, it can be assumed that the nucleon entering the nucleus interacts at each instant with only one nucleon as if it were free. An important feature of nuclear reactions induced by high-energy particles is the feasibility of transferring an excitation of about 100 MeV even to a light nucleus.

Upon the interaction of a fast nucleon with a nucleus, the nucleon may be elastically scattered, causing a nuclear reaction. The elastic scattering cross section σel depends evenly on the energy of the incident particles. The total cross section of the interaction of fast nucleons σtot varies from 2πR2 to πR2. At a nucleon energy of greater than 150 MeV, σel = ⅓ σtot, and the cross section of the nuclear reaction σr = ⅔σtot. Thus, the nucleus does not behave as an absolutely absorbing medium (in this case, σel = σr). The angular distributions of elastically scattered particles are similar to a diffraction pattern, and a pronounced forward peaking is observed.

The high energy of an incident particle may be distributed among many nucleons of a nucleus. In this case, some nucleons may acquire an energy sufficient to escape from the nucleus. Upon the interaction of high-energy particles with a nucleus, an intranuclear cascade may develop, resulting in the emission of several high-energy particles and leaving a strongly excited compound nucleus that emits low-energy particles as it decays. The average number of emitted particles increases with increasing energy of the primary particle. Heavier nuclear fragments, such as deuterons, tritons, and alpha particles, may be emitted (with lower probability) along with the nucleons in the nuclear reaction. A nuclear reaction in which various numerous charged particles are emitted forms a multipointed star in a nuclear photographic emulsion. In such reactions, a large number of diverse radioactive products are formed, which are studied by the methods of radiochemistry.

Simpler nuclear reactions are also observed under the effect of fast particles, for example, inelastic scattering (p, p’), the charge-exchange reaction (p, n), the pickup reaction (p, d), and the knock-out reaction (p, 2 p). The contribution of these processes to the total cross section of the nuclear reaction is low (about 10–20 percent). The knock-out proton reaction (p, 2p) has proved to be very convenient for studying the structure of nuclei. The energy loss in a nuclear reaction and the binding energy of a knock-out proton can be determined by measuring the energy of the emitted protons. The distribution of the residual nuclei according to energy shows maxima corresponding to the excited levels of a residual nucleus. The excitation energy of these levels reaches 50–70 MeV, corresponding to hole excitation of deep shells.

Coulomb excitation of nuclei. Protons and heavier ions that move too slowly to overcome the Coulomb barrier create a relatively slowly changing electric field as they approach the nucleus, and the field acts on the protons of the nucleus. In such cases, the nucleus makes a transition to an excited state by absorbing electromagnetic energy, and the incident ion gives up part of its energy. Coulomb excitation is one of the principal means of studying low-lying collective states of nuclei.

Photon- and electron-induced reactions. The excitation of a nucleus by an electromagnetic field (seePHOTONUCLEAR REACTION) can be achieved upon bombardment with gamma quanta. At low energies, the gamma quanta may only experience elastic scattering. At energies greater than those for separating the nucleons from the nucleus, the absorption of a gamma quantum and the emission of nucleons by the nucleus become the major processes. Upon the absorption of gamma quanta with energies of tens of MeV, a compound nucleus is formed as a rule. Direct processes begin to play a large part upon the interaction of a nucleus with more energetic gamma quanta. The effective cross sections of photonuclear reactions are tens or hundreds of millibarns.

Electrons may be elastically and inelastically scattered in interacting with the protons of a nucleus and may also knock protons out of the nucleus. The study of the elastic scattering of electrons has provided detailed information on the distribution of electric charge in the nucleus.

Reactions involving mesons, hyperons, and antiparticles. Mesons may be emitted in nuclear reactions induced by nucleons, whose energy is greater than the threshold energy of meson production. The mesons may also initiate nuclear reactions and participate in the development of an intranuclear cascade. Nuclear reactions involving pions have been studied most extensively. Many nuclear reactions induced by pions are like the corresponding nu-cleon-induced reactions, for example, inelastic scattering (π, π), charge-exchange scattering (π+ π0), (π π0), and knock-out reactions [(π, πp), (π, πn), (π, πd)]. However, there are other nuclear reactions involving pions that do not have analogs in nucleon-nuclear interactions. Among these is the reaction of double charge exchange of pions (π, π+) and nuclear reactions of pion absorption (π, 2n). The study of these reactions makes possible the investigation of the correlation of nucleons in the nucleus.

Nuclear reactions involving heavy ions. For heavy ions (Z > 2) as the incident particles, the potential Coulomb barrier ℰ0 is Z times greater than for protons, and therefore it is necessary that the ion energy corresponding to one nucleon of the nucleus exceed a few MeV (the more so the greater the Z of the target). The effective cross section of nuclear reactions involving heavy protons, with an energy ℰ > 1.2ℰ0, is given by the expression σ = πR2 (1 – ℰ0/ℰ), where

R ≈ 1.4(A1⅓ + A2)

This corresponds to classical representations of the collision of two charged black spheres of radius R. At energies ℰ < ℰ0, the nuclear reaction proceeds by tunnel infiltration through the barrier (seeTUNNEL EFFECT). In this case, σR = (R02/2)(ℏω0/ℰ) In [1 + exp{2π(ℰ – ℰ0)/ℏω0}], where R0 is the sum of the radii of the interacting nuclei and ω0 is the curvature of the barrier. The incident ions may not cause a nuclear reaction but may undergo elastic scattering in the field of Coulomb and nuclear forces. The angular distribution of ions upon elastic scattering (when the ƛ of the ion is of the order of the distance of maximum approach to the nucleus) exhibits diffraction characteristics. At smaller ƛ, the diffraction structure disappears. As a rule, the energy dependence of effective cross sections for nuclear reactions by heavy ions are nonresonant in nature. Elastic scattering is an exception. Resonances with widths of the order of a few MeV are observed, along with a finer structure, in the energy dependence of the effective cross sections of elastic scattering of 6Li by 6Li, 12C by 12C, l4N by 14N, 16O by 14N, and so on in the energy range of ℰ0~ 5–35 MeV.

Nuclear reactions involving heavy ions are characterized by a large number of exit channels. For example, nuclei of Ca, Ar, S, Si, Mg, and Ne are formed upon the bombardment of 232Th with 40Ar ions having energies of 379MeV.

The following distinctions are made among nuclear reactions involving heavy ions: reactions of nucleon transfer, reactions of the transfer of more complex particles, and merging reactions (formation of a compound nucleus). Nuclear reactions involving the transfer of a small number of particles or a small portion of energy are called soft collisions. The theory of such collisions has a great deal in common with the theory of direct reactions. Nuclear reactions involving the transfer of considerable mass or energy are called hard collisions, or deeply inelastic transfers. The angular distributions of the products of these nuclear reactions are sharply asymmetric; light products are emitted chiefly at stríall angles with respect to the ion beam. The energy distribution of the reaction products has a broad maximum. The kinetic energy of the reaction products is close to the height of the exit Coulomb barriers and is virtually independent of the ion energy.

A short-lived intermediate system is formed upon deeply inelastic collisions of nuclei. Despite the exchange of mass and energy, the nuclei of the intermediate system retain individuality as a result of tightly bound cores. Many new nuclides are formed as a result of hard collisions. In such reactions, compound nuclei with high excitation energies (~100 MeV) and angular momenta (~50) may arise. Nuclear reactions that involve the formation of compound nuclei are used in the synthesis of transuranium elements (the combining of Pb and Bi target nuclei with ions of 40Ar, 50Ti, 54Cr, 55Mn, and 58Fe). For example, fermium was synthesized by the nuclear reaction

REFERENCES

Blatt, J., and V. Weisskopf. Teoreticheskaia iadernaia fizika. Moscow, 1954.
Lane, A., and Thomas, R. Teoriia iadernykh reaktsii pri nizkikh energiiakh. Moscow, 1960.
Davydov, A. S. Teoriia atomnogo iadra. Moscow, 1958.
Mukhin, K. N. Vvedenie v iadernuiu fiziku, 2nd ed. Moscow, 1965.
Volkov, V. V. In Trudy Mezhdunawdnoi konferentsii po izbrannym voprosam struklury iadra, vol. 2. Dubna, 1976. Pages 45–65.

I. IA. BARIT

nuclear reaction

[′nü·klē·ər rē′ak·shən]
(nuclear physics)
A reaction involving a change in an atomic nucleus, such as fission, fusion, neutron capture, or radioactive decay, as distinct from a chemical reaction, which is limited to changes in the electron structure surrounding the nucleus. Also known as reaction.
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