Rotational energy levels with nuclear spin/rotation interaction

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

The interaction of a molecular species with electromagnetic fields can cause transitions to occur among the available molecular energy levels (electronic, vibrational, rotational, and nuclear spin). Collisions among molecular species likewise can cause transitions to occur. Time-dependent perturbation theory and the methods of molecular dynamics can be employed to treat such transitions. 

The agreement between experiment and theory is now much better than before, the discrepancy having been reduced from 5.444 to 0.182 MHz, but it is still poor compared with the experimental accuracy which is quoted as 0.01 MHz. However, our theory is still approximate because the electron spin spin interaction mixes N = 2 with N = 4, which introduces more hyperfine matrix elements off-diagonal in both N and J. The nuclear spin-rotation term, equation (8.271), does not contribute to the first-order energy of the N = 0 level, and makes a negligible second-order contribution. We will not pursue this analysis any further, our aim having been to illustrate the complexity of the fitting process moreover this was achieved for 13 different vibrational levels. 

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