### Author Topic: Spin 1 quadrupolar powder patterns  (Read 3693 times)

#### MalcolmHLevitt

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##### Spin 1 quadrupolar powder patterns
« on: December 20, 2012, 02:36:34 PM »
This notebook (which uses v2.5.5) shows how to calculate spin-1 powder patterns, including biaxiality (often referred to as "asymmetry").

#### 1K

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##### Re: Spin 1 quadrupolar powder patterns
« Reply #1 on: January 10, 2013, 12:28:29 PM »
It seems like there is only opT["I",{2,0}]  in your Hamiltonian:

HQ[\[CapitalOmega]_]:=Simplify@ExpToTrig[\[Omega]Q*{-\[Eta]Q/Sqrt[6],0,1,0,-\[Eta]Q/Sqrt[6]}.WignerD[2,{{0}}][\[CapitalOmega]]*opT[I,{2,0}]/Sqrt[6]];

Shouldn't opT["I",{2,0}] be a matrix of {opT["I", {2, -2}], opT["I", {2, -1}], opT["I", {2, 0}], opT["I", {2, 1}], opT["I", {2, 2}]}? This is so that the components of the Wigner matrix will multiply by their respective tensor operators.

1K

#### MalcolmHLevitt

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##### Re: Spin 1 quadrupolar powder patterns
« Reply #2 on: January 11, 2013, 05:13:55 PM »
Hi 1K, no, this is not correct. In the secular limit (interaction with static field much larger than the quadrupolar Hamiltonian) then the m !=0 components of the spin operators are suppressed. See pages 185 and 190 of SpinDynamics 2nd edition. The presence of biaxiality (eta!=0) has nothing to do with this. In the example notebook, biaxiality is simulated by including m!=0 components of the spatial part of the interaction (not the spin part).

You're correct that the zero-field form of the quadrupolar interaction would include all combinations of spin and space tensor components (see page 614). However, in high magnetic field, the interaction with the main field suppresses the influence of the T2-1, T2-2, T21 and T22 terms. If these were included, the simulation concerns zero-field NMR of quadrupolar nuclei (also known as NQR).