Nuclei Coulomb excitation

Figure 10.23 Schematic illustration of the l dependence of the partial cross section for compound nucleus (CN), fusionlike (FL), deep inelastic (D), quasi-elastic (QE), Coulomb excitation (CE), and elastic (EL) processes. [From Schroeder and Huizenga (1984, p. 242).]...

Coulombic excitation of Hf and °Hf by 6-MeV a-particles in targets of HfC and HfN at 78 K has shown considerable line broadening which is not a feature of these materials used as absorbers [34]. It may be presumed that the effect is a result of radiation damage associated with the recoil of the excited nuclei. The latter come to rest at lattice sites with one or more lattice vacancies nearby which generate an electric field gradient at the nucleus. 

Ic atomic nucleus Particle ineUstically scattered < 1 Nuclear (coulomb) excitation... 

A technique called Coulomb excitation is used to induce rotationally excited states in nuclei an example of this was shown in Figure 11.7. In order to impart high energy to the nucleus without causing nuclear transformation, heavy ions with kinetic energy below that required for passing over the Coulomb barrier ( j < cb(min)) projectiles. 

The theory of Coulomb excitation is given by many authors, in particular Ter-Martirosyan and Alder and Winther. The interaction potential between the bombarding particle and the nucleus is taken to be... 

The calculation of the Coulomb excitation can be treated by a semi-classical approximation. If v is the velocity, and Zg and Z are the charges on the target nucleus and the bombarding particle respectively, the quantity ri = 2Z Z e l%v is greater than unity, and the cross sections can be calculated from the classical trajectories of the bombarding particles. In general the total cross section for Coulomb excitation for multipole order Z is ... 

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 . 

Schematic picture of the first-order Coulomb excitation of a nucleus from an initial state to a final bound state and its subsequent 7-decay...

Now, in a solid matrix we have a Mossbauer probe of Fe with a lifetime of 140 ns, as is shown in Fig. 6.18. The 14.4 keV first excited state of the Fe nucleus can be fed through different processes, such as electron capture from Co, jS-decay from Mn, Mossbauer absorption of 14.4 keV y-ray, and Coulomb excitation. Subsequently the 14.4 keV y-ray will be emitted resonantly without recoil (Mossbauer effect), while in Fig. 6.18, the Fe atom is jumping between... 

Another well-defined configuration of the classical three body Coulomb problem with unambiguous quantum correspondence is the collinear antisymmetric stretch configuration, where the electrons are located on opposite sides of the nucleus. In contrast to the frozen planet orbit, the antisymmetric stretch is unstable in the axial direction (G.S. Ezra et.al., 1991 P. Schlagheck et.al., 2003), with the two electrons colliding with the nucleus in a perfectly alternating way (Fig. 3 (left)). Hence, already the one dimensional treatment accounts for the dominant classical decay channel of this configuration. As for the frozen planet, there are doubly excited states of helium associated to the periodic orbit of the ASC as illustrated in Fig. 3 (left). 

The isomer shift, S, is the consequence of the Coulomb interaction between the positively charged nucleus and the negatively charged s-electrons. Since the size of the nucleus in the excited state differs from that in the ground state, the Coulomb interaction energies are different as well. The isomer shift is therefore a measure of the s-electron density at the nucleus, and yields useful information on the oxidation state of the iron in the absorber. Isomer shift values are expressed in velocity units, mm/s, and are usually given with respect to the peak position of a reference such as metallic iron. Table 5.2 lists a few isomer shift values of common iron compounds. 

Moreover, since the new atomic nucleus produced is in an excited nuclear state, it has an excess of energy to get rid of, whether by emission of neutrons and y-rays, or by fission (Figure 14.2) (If the energy of the bombarding particles is too low, they do not possess enough energy to overcome the Coulombic repulsion between them.)... 

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