By Aram Mekjian (auth.), Michel Baranger, Erich Vogt (eds.)
As a lot by accident as through layout, the current quantity comes in the direction of having a unmarried subject than any of our previous volumes. That topic is the homes of nuclear energy capabilities or, however, the matter of line spreading. the road spreading or power functionality ideas are crucial for the nucleus as a result of its many levels of freedom. the outline of the nucleus is approached by utilizing version wave functions-for instance, the shell version or the collective model-in which one has truncated the variety of levels of freedom. The query then is how heavily do the version wave capabilities correspond to the particular nuclear wave services which take pleasure in the entire levels of freedom of the nuclear Hamiltonian? extra accurately, one perspectives the version wave services as vectors in a Hilbert area and one perspectives the particular wave features as vectors spanning one other, greater Hilbert area. Then the query is: how is a single-model wave functionality (or vector) unfold one of the vectors resembling the particular wave capabilities? for instance we think about a version country that's a shell-model wave functionality with a unmarried nucleon extra to a closed shell. any such version kingdom is termed a single-particle wave functionality. on the power of the single-particle waVe functionality one of many real nuclear wave services might resemble the single-particle wave functionality closely.
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Extra info for Advances in Nuclear Physics: Volume 7
Furthermore, because of the long lifetime of the compound state, the compound nucleus will have "forgotten" how it was formed by the time it decays. This result leads to Bohr's assumption that the decay of the compound nucleus is independent of the mode of formation. This independence hypothesis coupled with the picture of the immediate sharing of energy among all the nucleons formed the basis of a statistical description of nuclear cross sections in which thermodynamical concepts are introduced to describe the compound nucleus (Wei 37).
The essential idea behind the interpretation of the giant resonance behavior is that the single-particle states of the incident nucleontarget nucleus system spread their strength over the dense spectrum of states of the whole nucleus, with states far removed from the position of the simple states receiving only a small amplitude from this state and the nearby states receiving a much larger amount. The strength distribution obtained by Lane et al. (LTW 55) for the intermediate coupling situation has the form of Eq.
In the limit of weak mixing due to rapid decay, the distribution of widths will have one pronounced level with a width given by r o, where ro can be obtained from the eigenvalue equation r} - ro = rJ,J coth(nro/2D). When the situation applies ro ~ D, coth(nro/2D) is close to unity so that ro = rdt - ri,J' Moreover, when the distribution is summed over the levels, the following sum rule is obtained: (46) For the case rdt ~ ri,J, the sum is just rJ,J, so that ro = rdt - Lv rv' At the other extreme, that of strong mixing, rd~!