Nuclear Stability and the Mode of Decay

There are several ways that an unstable nuclide might decay, but can we predict how it will decay Indeed, can we predict if a given nuclide will decay at all Our knowledge of the nucleus is much less than that of the atom as a whole, but some patterns emerge from observation of the naturally occurring nuclides. 

The Band of Stability and the Neutron-to-Proton (N/Z) Ratio A key factor that determines the stability of a nuclide is the ratio of the number of neutrons to the number of protons, the N/Z ratio, which we calculate from (A — Z)/Z. For lighter nuclides, one neutron for each proton N/Z 1) is enough to provide stability. However, for heavier nuclides to be stable, the number of neutrons must exceed the number of protons, and often by quite a lot. But, if the N/Z ratio is either too high or not high enough, the nuclide is unstable and decays. 

Stability and Nuclear Structure The oddness or evenness of N and Z values is related to some important patterns of nuclear stability. Two interesting points become apparent when we classify the known stable nuclides  

Just as noble gases—with 2, 10, 18, 36, 54, and 86 electrons—are exceptionally stable because of their filled electron shells, nuclides with N or Z values of 2, 8, 20, 28, 50, 82 (and N = 126) are exceptionally stable. These so-called magic numbers are thought to correspond to the numbers of protons or neutrons in filled nucleon shells. A few examples are i N = 28), f Sr (A = 50), and the ten stable nuclides of tin (Z = 50). Some extremely stable nuclides have double magic numbers 2He, 0, 2oCa, and Pb (A = 126). 

Problem Which of the following nuclides would you predict to be stable and which radioactive (a) j Ne (b) (c) 9 h (d) leBa Explain. 

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Modes of Radioactive Decay Balancing Nuclear Equations 765 Nuclear Stability and the Mode of Decay 768... 

Radioactivity The ability possessed by some natural and synthetic isotopes to undergo nuclear transformation to other isotopes, 513 applications, 516-518 biological effects, 528-529 bombardment reactions, 514-516 diagnostic uses, 516t discovery of, 517 modes of decay, 513-514 nuclear stability and, 29-30 rate of decay, 518-520,531q Radium, 521-522 Radon, 528 Ramsay, William, 190 Random polymer 613-614 Randomness factor, 452-453 Raoult s law A relation between the vapor pressure (P) of a component of a solution and that of the pure component (P°) at the same temperature P — XP°, where X is the mole fraction, 268... 

The nuclei of some elements are stable, but others decay the moment they are formed. Is there a pattern to the stabilities and instabilities of nuclei The existence of a pattern would allow us to make predictions about the modes of nuclear decay. One clue is that elements with even atomic numbers are consistently more abundant than neighboring elements with odd atomic numbers. We can see this difference in Fig. 17.11, which is a plot of the cosmic abundance of the elements against atomic number. The same pattern occurs on Earth. Of the eight elements present as 1% or more of the mass of the Earth, only one, aluminum, has an odd atomic number. 

Sometimes it is difficult to predict if a particular isotope is stable and, if unstable, what type of decay mode it might undergo. All isotopes that contain 84 or more protons are unstable. These unstable isotopes will undergo nuclear decay. For these large massive isotopes, we observe alpha decay most commonly. Alpha decay gets rid of four units of mass and two units of charge, thus helping to relieve the repulsive stress found in the nucleus of these isotopes. For other isotopes of atomic number less than 83, we can best predict stability by the use of the neutron to proton (n/p) ratio. 

A continuing effort among experimentalists who study nuclei far from beta stability is the measurement of the atomic mass surface As a manifestation of the nuclear force and the nuclear many body system, atomic masses signal important features of nuclear structure on both a macroscopic and microscopic scale It has thus been a challenge to nuclear theorists to devise models which can reproduce the measured mass surface and to predict successfully the masses of new isotopes Both the measured mass surface and that beyond it which can be predicted by these models serve as important input to a variety of fundamental and applied problems, e g, nucleosynthesis calculations, predictions of decay modes of exotic nuclei far from stability, nuclear de-excitation by particle evaporation, decay heat simulations, etc ... 

The mode of radioactive decay is dependent upon the particular nuclide involved. We have seen in Ch. 1 that radioactive decay can be characterized by a-, jS-, and y-radiation. Alpha-decay is the emission of helium nuclei. Beta-decay is the creation and emission of either electrons or positrons, or the process of electron capture. Gamma-decay is the emission of electromagnetic radiation where the transition occurs between energy levels of the same nucleus. An additional mode of radioactive decay is that of internal conversion in which a nucleus loses its energy by interaction of the nuclear field with that of the orbital electrons, causing ionization of an electron instead of y-ray emission. A mode of radioactive decay which is observed only in the heaviest nuclei is that of spontaneous fission in which the nucleus dissociates spontaneously into two roughly equal parts. This fission is accompanied by the emission of electromagnetic radiation and of neutrons. In the last decade also some unusual decay modes have been observed for nuclides very far from the stability line, namely neutron emission and proton emission. A few very rare decay modes like C-emission have also been observed. 

SECTION 21.2 The neutron-to-proton ratio is an important factor determining nuclear stability. By comparing a nuclide s neutron-to-proton ratio with those in the band of stability, we can predict the mode of radioactive decay. In general, neutron-rich nuclei tend to emit beta particles proton-rich nuclei tend to either emit positrons or im-dergo electron capture and heavy nuclei tend to emit alpha particles. The presence of magic numbers of nucleons and an even number of protons and neutrons also help determine the stability of a nucleus. A nuclide may undergo a series of decay steps before a stable nuclide forms. This series of steps is called a radioactive series or a nuciear disintegration series. 

Abstract In this chapter, four topics are treated. (1) Fundamental constituents and interactions of matter and the properties of nuclear forces (experimental facts and phenomenological and meson-field theoretical potentials). (2) Properties of nuclei (mass, binding energy, spin, moments, size, parity, isospin, and characteristic level schemes). (3) Nuclear states and excitations and individual and collective motion of the nucleons in the nuclei. Description of basic experimental facts and their interpretation in the framework of shell, collective, interacting boson, and cluster models. The recent developments, few nucleon systems, and ah initio calculations are also shortly discussed. (4) In the final section, the a- and P-decays, as well as the special decay modes observed far off the stability region are treated. 

Nuclear reactions producing exotic nuclei at the limits of stability are usually very non-specific. For the fast and efficient removal of typically several tens of interfering elements with several hundreds of isotopes from the nuclides selected for study mainly mass separation [Han 79, Rav 79] and rapid chemical procedures [Her 82] are applied. The use of conventional mass separators is limited to elements for which suitable ion sources are available. There exists a number of elements, such as niobium, the noble metals etc., which create problems in mass separation due to restrictions in the diffusion-, evaporation- or ionization process. Such limitations do not exist for chemical methods. Although rapid off-line chemical methods are still valuable for some applications, continuously operated chemical procedures have been advanced recently since they deliver a steady source of activity needed for measurements with low counting efficiencies and for studies of rare decay modes. The present paper presents several examples for such techniques and reports briefly actual applications of these methods for the study of exotic nuclei. 

The final model that accounts for nuclear stabilities must, of course, be the strong force, or rather the residual component of the strong force that works outside of quark confinement. Natural or artificial radioactive nuclei can exhibit several decay modes a decay (N1 = N — 4, Z = Z — 2, A = A — 4, with emission of a 2He4 nucleus), which is dominant for elements of atomic number greater than Pb / -decay or electron emission (N1 = N — 1, Z = Z + 1, A = A this involves the weak force and the extra emission of a neutrino) positron or / + decay (N = N + 1, Z =Z — 1, A = A, emission of a positron and an antineutrino this also involves the weak force) y decay no changes in N or Z, and electron capture (N1 =... 

If a graph is made (Fig. 3.1) of the relation of the number of neutrons to the number of protons in the known stable nuclei, we find that in the light elements stability is achieved when the number of neutrons and protons are approximately equal (N = Z). However, with increasing atomic number of the element (i.e. along the Z-line), the ratio of neutrons to protons, the NIZ ratio, for nuclear stability increases from unity to iqiproximately l.S at bismuth. Thus pairing of the nucleons is not a sufficient criterion for stability a certain ratio NIZ must also exist. However, even this does not suffice for stability, because at high Z-values, a new mode of radioactive decay, a-emission, appears. Above bismuth the nuclides are all unstable to radioactive decay by a-particle emission, while some are unstable also to / -decay. 

In spite of the lower excitation energies obtained in cold-fusion reactions, hot-fusion reactions produce evaporation residues that are more neutron rich, a consequence of the bend of the line of fi stability toward neutron excess. For the purposes of studying nuclei whose stability is more strongly influenced by the spherical 184-neutron shell clostrre, hot fusion is the more viable path. If nuclei were constrained to be spherical, or deformed into simple quadrupole shapes like those that influence the properties of the actinide isotopes with N — 152, one would expect cold-fusion reactions to quickly veer into ZJ space where nuclides would be characterized by very short partial half-lives for decay by spontaneous fission. In fact, there is a region of nuclear stability centered at Z = 108 and N — 162 [12, 19-21], removed from the line of fi stability toward proton excess, where the nuclei derive a resistance to spontaneous fission from a minor shell closure associated with complicated nuclear shapes, making a emission their most probable decay mode [133, 240]. 

Fig. 2.—Proton, Free-induction Decay Signal45 of a Solution of 6-Deoxy-1,2 3,4-di-O-isopropylidene-6-phthalimido-o-D-galactopyranose (54) (0.06 mg) in 4 1 (v/v) Chloro-form-d (Commercial, 100% )-Hexafluorobenzene (0.06 ml) Contained in a Microcell. [The f.i.d. signal was acquired in 419 sec by using the crossed-coil mode with hetero-nuclear, internal, field-frequency stabilization on fluorine-19, with 1,024 pulses at 90 MHz, tp 40 jusec, St 400 /jsec, and 1,024 datum points (for definitions, see text).]...

The decay of radioactive isotopes via electron emission, so-called beta decay, is a well-known phenomenon, hi this mode imstable nuclei that have an excessive number of neutrons, for example can emit fast electrons, particles, in order to attain a stable nuclear configuration. Nuclei with insufficient neutrons, such as can obtain stability by emitting fast positrons, particles (the anti-matter equivalents of electrons). Both processes are classified as radioactive f) decay. In each case, the mass munber of the nucleus remains constant but the atomic number changes. There exist several positron emitting isotopes, of which and in particular... 

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