Cluster Decay - Theory


The quantum tunneling may be calculated either by extending fission theory to a larger mass asymmetry or by heavier emitted particle from alpha decay theory.

Both fission-like and alpha-like approaches are able to express the decay constant = ln 2 / Tc, as a product of three model-dependent quantities

where is the frequency of assaults on the barrier per second, S is the preformation probability of the cluster at the nuclear surface, and Ps is the penetrability of the external barrier. In alpha-like theories S is an overlap integral of the wave function of the three partners (parent, daughter and emitted cluster). In a fission theory the preformation probability is the penetrability of the internal part of the barrier from the initial turning point Ri to the touching point Rt. Very frequently it is calculated by using the Wentzel-Kramers-Brillouin (WKB) approximation.

A very large number, of the order 105, of parent-emitted cluster combinations were considered in a systematic search for new decay modes. The large amount of computations could be performed in a reasonable time by using the ASAF model developed by Dorin N Poenaru, Walter Greiner et al.. The model was the first to be used to predict measurable quantities in cluster decay. More than 150 cluster decay modes have been predicted before any other kind of half-lives calculations have been reported. Comprehensive tables of half-lives, branching ratios, and kinetic energies have been published, e.g. . Potential barrier shapes similar to that considered within the ASAF model have been calculated by using the macroscopic-microscopic method.

Previously it was shown that even alpha decay may be considered a particular case of cold fission. The ASAF model may be used to describe in a unified manner cold alpha decay, cluster decay and cold fission (see figure 6.7, p. 287 of the Ref. ).

One can obtain with good approximation one universal curve (UNIV) for any kind of cluster decay mode with a mass number Ae, including alpha decay

In a logarithmic scale the equation log T = f(log Ps) represents a single straight line which can be conveniently used to estimate the half-life. A single universal curve for alpha decay and cluster decay modes results by expressing log T + log S = f(log Ps). The experimental data on cluster decay in three groups of even-even, even-odd, and odd-even parent nuclei are reproduced with comparable accuracy by both types of universal curves, fission-like UNIV and UDL derived using alpha-like R-matrix theory.

In order to find the released energy

one can use the compilation of measured masses M, Md, and Me of the parent, daughter and emitted nuclei, c is the light velocity. The mass excess is transformed into energy according to the Einstein's formula E = mc2.

Read more about this topic:  Cluster Decay

Other articles related to "theory":

Feudalism - Etymology
... The most widely held theory is put forth by Marc Bloch ... This Germanic origin theory was also shared by William Stubbs in the nineteenth century ... Another theory was put forward by Archibald R ...
Zermelo Set Theory
... Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory ...
Falsifiability - The Criterion of Demarcation
... It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory ... be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable ... Popper claimed that, if a theory is falsifiable, then it is scientific ...
J. Philippe Rushton - Work and Opinions - Application of r/K Selection Theory To Race
... Rushton's book Race, Evolution, and Behavior (1995) uses r/K selection theory to explain how East Asians consistently average high, blacks low, and whites in the middle on an evolutionary scale ... He first published this theory in 1984 ... He theorizes that r/K selection theory explains these differences ...
... Minimax (sometimes minmax) is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case (maximu ... Originally formulated for two-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to ...

Famous quotes containing the word theory:

    A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.
    Lionel Trilling (1905–1975)

    Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.
    —H.L. (Henry Lewis)

    Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.
    Willard Van Orman Quine (b. 1908)