Deuteron nuclear spin functions

For the rotational 7=1 (odd) level of CHD2 the Pauli principle requires the following six possible deuteron nuclear spin functions with A irreducible representation (total symmetry) [75] ... 

Now consider D2. The nuclear spin of a deuteron is 1, and we can have 7=0, 1, or 2. The T— 2 and r=0 nuclear spin functions are symmetric and the T— 1 functions are antisymmetric (Problem 4.24). The ground electronic state must be 2+ (as in H2), and the nuclei are bosons. Hence the 7=0 and T=2 spin functions go with the 7=0,2,4,... rotational levels. Cooling D2 to low temperature in the presence of a paramagnetic catalyst gives molecules with 7=0 and T=0 and 2. Warming this gas in the absence of catalyst gives 7 = 0,2,4,... molecules this modification of D2 is called ortho deuterium. (The convention is to use ortho for the modification with symmetric nuclear spin functions.)... 

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. 

The difference in electric dipole moment (0.007 72 D) between the proton and deuteron species is discussed by Muenter and Klemperer [87] and attributed to the difference in zero-point amplitude averaged over the same dipole moment function. If the difference is purely vibrational in origin, the dipole moment of the vibrationless molecule is calculated to be 1.7965 D, which compares with a theoretical value of 1.942 D obtained from Hartree Fock calculations by Huo [94], The nuclear spin-rotation constants of non-rigid diatomic molecules have been discussed theoretically by Hindermann and Cornwell [95]. 

The ortho-para ratio is determined by the statistical calculation of the availability of states given by the partition function. Calculated ortho-para equilibria for H2, D2, and T2 are shown in Figure 6 at the temperature range from 0 to 300K. When the two nuclear spins are parallel, the resultant nuclear spin quantum number is 1 (i.e. 1/2 -E 1 /2) and the state is threefold degenerate. When the two spins are opposed, however, the resultant nuclear spin is zero and the state is nondegenerate. Therefore para-H2 has the lower energy and this state is favored at lower temperatures. The equilibrium concentration of H2 approaches three parts ortho to one part para at room temperature. As the nuclear spin quantum number of the deuteron is 1 rather than 1/2 for the proton (see Table 1), the D2 system is described by Bose-Einstein... 

Figure 4- SE signal as a function of the phase difference between the incident and scattered beams. The upper part of the figure shows the principle difference, in the case of deuterons and protons, between the scattering from a nucleus with and without nuclear spin. The lower part shows the NSE signals obtained in both cases—the count rate is plotted against the current of the phase correction coil. Acob und vdincoh ore the echo amplitudes for coherent and incoherent scattering, No is the average count rate outside the echo, N+ and iV are the maximal and minimal count rates with the ir/2-flippers on, and Nap and iVdown are the count rates of spin-up (rr-flipper off) and spin-down (ir-flipper on) measurements made with the nl2-flippers off.

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. 

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