Energy levels of nuclei

Mossbauer spectroscopy is based on transition between energy levels of nuclei with different values of the nuclear spin quantum number /. When a nucleus emits a y-ray, the energy of the emitted radiation is lowered by the recoil of the nucleus. Conversely, the energy needed for absorption is higher than that needed for transition, because the absorbing nucleus absorbs energy in the recoil process. For nuclei tightly bound in solids, however, the effective mass of the emitter and... 

Fig. 13. Energy levels of nuclei participating in thermonuclear reactions during the helium burning stage in red giant stars (after [13]). Survival of both 12C and 16O in red giants, from which terrestrial abundances result, depends upon the fortuitous circumstances of nuclear level structures and other properties of these nuclei...

Most f3 decompositions (either or e ) are accompanied (immediately followed) by the emission of y rays. The (3 decomposition may take place to one or more of the excited states of the product nucleus, which then drops to the normal state by y emission. A simple example is shown in Figure 20-10. A great amount of information about energy levels of nuclei has been obtained by measuring the wavelengths of the photons (the y rays) and the maximum kinetic energy of the /8 rays (the maximum corresponds to zero energy for the neutrino). 

Fig. 5.10 Energy levels of nuclei and simulated Sn Mossbauer spectra for hyperfine fields of 0, 5, 10, and 15 T...

Nuclear magnetic resctnance involves the transitions between energy levels of the fourth quantum number, the spin quantum number, and only certain nuclei whose spin is not zero can be studied by this technique. Atoms having both an even number of protons and neutrons have a zero spin for example, carbon 12, oxygen 16 and silicon 28. 

Active Figure 14.2 Four - molecular orbitals in 1,3-butadiene. Note that the number of nodes between nuclei increases as the energy level of the orbital increases. 

The properties of 7-rays are indistinguishable from those of x-rays of the same wavelength, but they do differ in origin. A 7-ray is emitted by a nucleus upon the occurrence of a quantum transition between two energy levels of the nucleus. For our purposes, only the 7-rays originating in radioactive nuclei need be considered. 

SR. A. Kenefick and R. K. Sheline, Phys. Rev. 135. B939 (1964), have described the energy levels of Smla, with N= 90, as representing the transition between spherical and highly deformed nuclei. 

Saturation If the Rf field is applied continuously, or if the pulse repetition rate is too high, then a partial or complete equalization of the populations of the energy levels of an ensemble of nuclei can occur and a state of saturation is reached. 

Thus, the Zeeman interaction occurs only with nuclei that possess a spin greater than zero, and it yields 27+1 energy levels of separation = yB Urr. The Hamiltonian is described by... 

Nature s helping hand in this matter came from the fact that the energy levels of the three crucial nuclei could be fine-mned to boost the reaction probability, with the fortunate consequence that carbon and the heavier nuclei could then be produced in significant quantities. Since energy levels are purely quantum features of nucleon systems, one could only rejoice at nature s delicate touch. 

Any external electric field is minute in comparison with the internal field generated by the system of electrons and nuclei inside a molecule. The effect of the operator (8.4) is therefore always much smaller than the electronic energy of the molecule. In most cases, the effects of electric-field perturbations are also much smaller than the vibrational energy of the molecule. The interaction with an external DC field can thus be treated as a perturbation to the vibronic energy levels of molecules. 

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