By Aram Mekjian (auth.), Michel Baranger, Erich Vogt (eds.)
As a lot by accident as by way of layout, the current quantity comes towards having a unmarried subject matter than any of our previous volumes. That topic is the homes of nuclear power capabilities or, on the other hand, the matter of line spreading. the road spreading or energy functionality thoughts are crucial for the nucleus as a result of its many levels of freedom. the outline of the nucleus is approached through the use of 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 features which take pleasure in all of the levels of freedom of the nuclear Hamiltonian? extra accurately, one perspectives the version wave features as vectors in a Hilbert house and one perspectives the particular wave services as vectors spanning one other, greater Hilbert house. Then the query is: how is a single-model wave functionality (or vector) unfold one of the vectors equivalent to the particular wave features? for example we give some thought to a version nation that's a shell-model wave functionality with a unmarried nucleon additional to a closed shell. this type of version kingdom is termed a single-particle wave functionality. on the power of the single-particle waVe functionality one of many real nuclear wave capabilities may well resemble the single-particle wave functionality closely.
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Extra resources for Advances in Nuclear Physics: Volume 7
P • of such single-particle resonances in a square-well potential of radius R for L = 0 waves are Ii F s. p . = MR2 2kR D s. p • = Ii (51) MR2 :rcKR The K and k are the wavenumbers inside and outside the square well, respectively. The potential scattering model predicted cross sections which varied from nuclear dimensions to much larger values at the single-particle resonance energies. While accounting for the large cross sections Fermi (Fer+ 34) found the model failed to account for the very rapid variations in the slow-neutron cross section (BW 35, FA 35, MT 35, FP 36) and also the large capture cross section.
2. Compound Nucleus Model and the Strong Absorption Model To account for the narrow, closely-spaced resonances seen in highresolution slow-neutron cross sections and the large capture probabilities, Bohr (Boh 36, Boh 37) and also Breit and Wigner (BW 36) introduced the compound nucleus. This scheme stood at the other extreme from Bethe's description of nucleon-nucleus scattering. In Bohr's picture, the incident nucleon, upon reaching the nuclear surface, strongly disturbs the state of the target nucleons by immediately coalescing with them to form a highly complex state of a many-particle system.
12 has associated with it a spin, parity, energy, and width. If the width of each i- resonance is plotted against the location at which it appears in the spectrum of K41, a distribution of widths (MM 67) is obtained which is illustrated in Fig. 13. Now, the resulting distribution has itself several interesting features which are associated with three different regions. The three regions are separated according to their location with respect to the centroid Ea of the distribution. 46 Aram Mekjian They are (1) the near region- IE - Ea I < 20 keY, (2) the far regionIE - Ea I > 200 keY, and (3) the intermediate region-20 keY < I E-Ea I < 200 keY.