Nuclei, collective excitations

Since the nuclear resonant scattering is a coherent elastic process it is impossible to identify the scattering atom in the sample. Instead, for each individual resonant nucleus there is a small probability that this nucleus is excited. The summation of all these small amplitudes gives the total probability amplitude for a photon to interact resonantly with the nuclei. If the incident radiation pulse is short compared to the nuclear lifetime Tq. these probability amplitudes exhibit the same temporal phase. As a result, a collectively excited state is created, where a single excitation is coherently distributed over the resonant atoms of the sample [44]. The wave function of this collectively excited state is given by a coherent... 

Figure 12.6 Mechanism of action of mineralocortjcoid receptor antagonists in the collecting tubule. Aldosterone enters the tubular cell by the basolateral surface and binds to a specific mineralocorticoid receptor (MNR) in the cytoplasm. The hormone receptor complex triggers the production of an aldosterone-induced protein (AlP) by the cell nucleus (NUC). The AIP acts on the sodium ion channel (ic) to augment the transport of Na+across the basolateral membrane and in to the cell. An increase in AIP activity leads to the recruitment of dormant sodium ion channels and Na pumps (P) in the cell membrane. AIP also leads to the synthesis of new channels and pumps within the cell. The increase in Na+conductance causes electrical changes in the luminal membrane that favour the excretion of intracellular cations, such as K+and H-h. Spironolactone competes with aldosterone for the binding site on the MNR and forms a complex which does not excite the production of AIP by the nucleus.

As an example we treat the decay process of IV.6 in terms of the master equation. The decay probability y per unit time is a property of the radioactive nucleus or the excited atom, and can, in principle, be computed by solving the Schrodinger equation for that system. To find the long-time evolution of a collection of emitters write P(n, t) for the probability that there are n surviving emitters at time t. The transition probability for a... 

As a measure of the shape or the collectivity of the nuclei we use the ratio E4/E2, where E2 and E4 are the excitation energies of the spin 2 and spin 4 states. The value of this quantity is 3 1/3 for a nucleus with a pure rotational spectrum, and 2 for a harmonic vibrational spectrum. 

Among collective models which have been developed for special purposes is the alpha particle model. If it is assumed that the four-structure already apparent in the supermultiplet theory of Wigner has some permanence in an actual nucleus, the methods of molecular physics may be applied to deduce a level sequence (Wheeler ). The S5nnmetry of the system imposes special restrictions on the level spins of the lower excited states. The energies of these states are obtained from a decomposition of the motion into rotation and vibration. The treatment is especially suitable for nuclei of mass number An, but it is not restricted to these 3 and the detailed application of the model to a number of nuclei is discussed in references [7] and [itf]. 

Transition probabilities for rotational levels. The excitation of a high member of the rotational spectrum in an even-even nucleus is followed by a cascade of 2 radiation. In an even-odd nucleus the cascade is less simple because E2 cross-over transitions are possible and the transition between one level and the next can consist of a mixture oi E2 and Mi radiation. If the transition probabilities were comparable with those to be expected of single particle transitions, E2 radiation at these energies (100 kev or less) would be far weaker than Mi radiation. The existence of strong E2 components and the successful competition of the E 2 components in the cross-over transitions is a clear indication of the collective nature of these processes where presumably the whole nuclear charge contributes to the emission of quadrupole radiation. 

It should be noted that if the lowest states in even-even nuclei have a collective origin, similar states might be expected to occur in odd mass number nuclei. None have yet been identified as such in nuclei with A <90. Nevertheless the collective properties of the nucleus have a considerable effect on transition probabilities, for where the lowest states have been excited by Coulomb excitation they have usually been found to have a high E2 transition probability (e.g., the si- d transition in the Te isotopes. Table 6b). The effect persists, as we have seen, even into the closed shell nuclei . 

The formation of a compound nucleus in which the excitation energy is redistributed many times between different degrees of freedom (single-particle states of the nucleons and collective degrees of freedom, like deformations and vibrations) before fission occurs (timescale 10 s). 

Another phenomenon often observed in the NFS time spectra that follows from the collective coherent nuclear resonant excitation is the speedup of the initial decay compared to that of an isolated nucleus [51,52]. The time evolution of the radiative decay for an isolated nucleus is described by... 

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