Quantization of nuclei

If we would try to find an ontological interpretation of the Bom-Oppenheimer hierarchical type of quantization, surely the concept of quantization of atomic centers would be more adequate description than the concept of quantization of nuclei motion. The question arises how to retrace the simultaneous quantization of the unit system of electrons and nuclei. The author solved this problem in his... 

The commonly accepted pulsar model is a neutron star of about one solar mass and a radius of the order of ten kilometers. A neutron star consists of a crust, which is about 1 km thick, and a high-density core. In the crust free neutrons and electrons coexist with a lattice of nuclei. The star s core consists mainly of neutrons and a few percents of protons and electrons. The central part of the core may contain some exotic states of matter, such as quark matter or a pion condensate. Inner parts of a neutron star cool up to temperatures 108iT in a few days after the star is formed. These temperatures are less than the critical temperatures Tc for the superfluid phase transitions of neutrons and protons. Thus, the neutrons in the star s crust and the core from a superfluid, while the protons in the core form a superconductor. The rotation of a neutron superfluid is achieved by means of an array of quantized vortices, each carrying a quantum of vorticity... 

Nuclear magnetic resonance spectroscopy is a form of absorption spectroscopy and concerns radio frequency (rf)-induced transitions between quantized energy states of nuclei that have been oriented by magnetic fields. Several nonmathemati-cal introductions to NMR are recommended to supplement the material here [1-9]. For greater mathematical depth, a number of excellent texts are available [10-26]. 

The presence of magnetic moments /lia, b, of nuclei A,B,... in a molecule are responsible for the two observables of the NMR experiment that are most frequently utilized in chemical applications. They are physically observed in form of quantized energy differences AE that can be measured very precisely. These two observables are the nuclear shielding tensor cr for nucleus A and the so-called indirect reduced coupling tensor KAB for a pair of nuclei A,B. Both crA and Kab are second-rank tensors that are defined via the phenomenological Hamiltonians... 

In terms of quantum mechanics, a system with zero energy is impossible. A quantum system must possess a minimum energy of Ev. This postulate is due to the irrepressible zero-point motion imposed on microscopic systems by the uncertainty principle and by quantization. Thus, the classical concept of nuclei in space and associated motion is replaced by the concept of a nuclear or vibrational... 

The key properties of nuclei that allow them to be probed by NMR are nuclear magnetism and nuclear spin. Quantum mechanics dictates that the angular momentum of any system is quantized and can take only the values ... 

A related RF technique to NMR is nuclear quad-rupole resonance (NQR). In NQR, transitions between nuclear quadrupole levels of nuclei in a solid material are induced by the applied radiation. The electric field gradients in the solid orient the quad-rupolar nuclei I>1/2) and give rise to quantized energy levels that yield transitions in the MHz range. FT-NQR spectroscopy measures these splittings and the relaxation times by free induction decay or various pulse echo experiments. FT-NQR spectroscopy provides information about the local environment around the quadrupolar nucleus in a crystal. 

When the lineshape is known, the Ti time can be estimated by calculating the seeond moment of a resonance line however the ordinary proeedure of the calculation (Al tshuler and Kozyrev 1972) must be modified in such a manner as to take into account the seatter of quantization axis orientations for different nuelear spins. Let us write down the Zeeman Hamiltonian of nuclei with the resonance frequency coq in the form... 

One noticeable exception is molecular spectroscopy, more specifically infrared spectroscopy, where, almost by definition, quantization of the vibrational states cannot be neglected since it concerns the measurement of the transitions between the quantized vibrational states [15]. Due to its importance in chemistry, for instance for the detection of functional groups in organic chemistry, infrared spectroscopy is one of the very few domains where the students in both physics and chemistry experience the application of a full-quantum mechanical treatment for both the electrons and the nuclei in a molecular system. However, there is growing evidence that a significant number of various chemical reactions are impacted by strong quantum-mechanical effects involving nuclei [16]. 

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