Special decay modes

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. 

Fission and fusion are different from other radioactive decay modes because they won t happen spontaneously. For this reason, they need some kind of catalyst or special conditions to make them happen. Examples include the... 

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

The behavior of VACF and of D in one-dimensional systems are, therefore, of special interest. The transverse current mode of course does not exist here, and the decay of the longitudinal current mode (related to the dynamic structure factor by a trivial time differentiation) is sufficiently fast to preclude the existence of any "dangerous" long-time tail. Actually, Jepsen [181] was the first to derive die closed-form expression for the VACF and the diffusion coeffident for hard rods. His study showed that in the long time VACF decays as 1/f3, in contrast to the t d 2 dependence reported for the two and three dimensions. Lebowitz and Percus [182] studied the short-time behavior of VACF and made an exponential approximation for VACF [i.e, Cv(f) = e 2 ], for the short times. Haus and Raveche [183] carried out the extensive molecular dynamic simulations to study relaxation of an initially ordered array in one dimension. This study also investigated the 1/f3 behavior of VACF. However, none of the above studies provides a physical explanation of the 1/f3 dependence of VACF at long times, of the type that exists for two and three dimensions. 

When conventional electrodes with diameters between 0.1 and 2 mm are used, the latter quantity has usually decayed to zero after 0.5 ms or less and may be neglected in experiments lasting 1 ms or more. This decay time is reduced to the microsecond time regime when ultramicroelectrodes are used [94,125,202]. According to Eq. (64), which for i = 0 is known as the Cottrell equation, the current approaches zero when the time approaches infinity. However, undisturbed linear diffusion can be maintained only over rather short time intervals unless special precautions are taken (see Sec. II.D.l), and the measurements of current-time curves, called chronoamperometry (CA), are often complicated by additional modes of transport. Therefore, the use of properly shielded electrodes [140] should be considered in chronoamperometric experiments exceeding approximately 1 s. The mathematical formalism for chronoamperometry has been developed also for the application of ultramicroelectrodes [203]. 

The absorption can also be measured by recording core-hole decay products in the case of diluted systems. The inner shell photoionization process can be described as a two-step process. In the first step the photon excites a core hole-electron pair, and in the second step the recombination process of the core hole takes place. There are many channels for the core hole recombination. These channels can produce the emission of photons, electrons or ions, which can be collected with special detectors. The recombination channel that is normally used to record bulk x-ray absorption spectra of dilute systems is the direct radiative core-hole decay producing x-ray fluorescence lines. In Fig. 3 a beam line with an apparatus to record absorption spectra in the fluorescence mode is represented schematically. 

Radioactive decay is a spontaneous nuclear transformation that has been shown to be unaffected by pressure, tenqierature, chemical form, etc (except a few very special cases). This insensitivity to extranuclear conditions allows us to characterize radioactive nuclei by their decay period and their mode and energy of decay without regard to their physical or chemical condition. 

Spectral hole burning results for P870 and P960 of Rb, sphaeroides and Rps, viridis and the temperature dependence of P decay indicate that for the problem at hand the low frequency modes (protein phonons, special pair marker mode(s)) are most relevant. It was recently reported that for strong electron-phonon coupling the electron transfer rate constant has the form... 

Finally we make a few remarks on the mean energy gap value = 300 cm" Table I. First, it is the effective gap for the low frequency modes to accommodate. Second, the fact that the homogeneous width of the nuclear factor, 2yep, is 1000 cm at room temperature means, cf. Eq. 2, that the rate is quite insensitive to significant variations in 2q. It follows that the conclusion that dispersive kinetics for P decay at room temperature is most improbable is not altered by such variations. We see no reason why this conclusion should not apply to the second step (P" H -> P BH") of the two-step mechanism although the special pair marker mode is likely to be silent in this step. 

The sections contain information about ground and excited states, half-life, isotopic abundance, modes of decay as well as energies and intensities of the emitted radiation. Each of the properties is identified by a special code. Missing codes mean that they are not applicable for that nuclide or that no data for these properties are available. For nuclear masses, systematics on Q values for the different modes of decay, p+Zs ratios, half-lives, conversion coefficients, and X rays, see Chapter 1.2.1, p. 6. 

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