Nuclear Spin and the Pauli Principle

The deuterium (D or H) contained in CD3 has nuclear spin 7=1 and belongs to the class of bosons (particles with integer value of spin) [88]. The Pauli principle... 

The hydrogen nucleus is classified as a Eermi particle with nuclear spin I = 1/2. Because of Pauli exclusion principle, hydrogen molecule is classified into two species, ortho and para. Erom the symmetry analysis of the wave functions, para-hydrogen is defined to have even rotational quantum number J with a singlet nuclear spin function, and ortho-hydrogen is defined to have odd J with a triplet nuclear spin function. The interconversion between para and ortho species is extremely slow without the existence of external magnetic perturbation. 

The treatment of atoms with more than one electron (polyelectronic atoms) requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number (the spin quantum number) which specifies the intrinsic energy of the electron in any orbital. The restriction on numbers of atomic orbitals and the number of electrons that they can contain leads to a discussion of the Pauli exclusion principle, Hund s rules and the aufbau principle. All these considerations are necessary to allow the construction of the modern form of the periodic classification of the elements. 

M. E. KeUman The idea by Prof. Quack of using molecular experiments to test fundamental symmetries is very interesting. In connection with the Na3 pseudorotation experiments we heard about yesterday, have you considered testing permutation symmetry of identical particles, that is, the Pauli principle and nuclear spin statistics ... 

M. Quack The violation of the principle of nuclear spin symmetry conservation [1] could be seen in a similar scheme as I discussed for parity, but, in contrast to parity violation, it can also be seen by more standard spectroscopic techniques (and has been seen repeatedly). On the other hand, one might also look for violations of the Pauli principle, which in fact we have done [2]. However, it seems unlikely to find such a violation (and nothing of that kind has ever been found), although in principle one must allow even for such a phenomenon. 

The overall symmetry of a given level must be antisymmetric with respect to the permutation P 2 of the two H nuclei to satisfy the Pauli principle. The + and -parity combinations defined by equation (8.202) are antisymmetric and symmetric respectively with respect to P 2 (because the electronic wavefunction has u character, see equation (8.251)). Since the ortho and para nuclear spin states are symmetric and antisymmetric respectively, we see that the + parity states combine with the ortho... 

Here, only the deuteron spin projections (z-components) of the nuclear spin fuction ( i) are given in the expression for simplicity. These three anti-symmetric nuclear spin functions belong to B irreducible representation in the C2 symmetry (point group) of CHD2 and are only allowed to couple with the rotational function ( r) at the lowest level of 7 = 0 (even) by the Pauli principle. 

Due to the Pauli principle, only n-p pairs can have their spins aligned and otherwise have the same quantum numbers. These pairs are referred to as short-range correlated (SRC) pairs and their presence strongly affects the properties of cold, dense nuclear matter, such as that found in neutron stars. This nucleon-nucleon interaction is also required to explain the fact that the n-p spin triplet is bound (i.e., the deuteron) while the n-n and p-p, required singlets, are not. Consideration of n-p interactions is also essential to understand the evolution of the phenomenological spin-orbit interaction as a function of n/p asymmetry (Otsuka 2005), one of the most discussed topics in nuclear structure research today. 

We like to hint at an interesting phenomenon related to the relative intensities of rotational lines in the spectra of homonuclear molecules. Because of the central symmetry of the molecules, the nuclear spin / of the atoms influences the population of rotational levels with even and odd quantum numbers differently, because of the Pauli principle. In general, one finds that the ratio between the statistical weights of the rotational levels, and thus the line intensity as well, with even/odd quantum numbers is... 

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