.. currentmodule:: mrsimulator.method.lib .. _stvas_ref: Satellite-transition variable-angle spinning (ST-VAS) """"""""""""""""""""""""""""""""""""""""""""""""""""" The following classes are used when simulating a satellite-transition variable-angle spinning spectrum which correlates the frequencies from the satellite transitions to the central transition frequencies. The :math:p and :math:d pathways for the ST-VAS methods are .. math:: p: &0 \rightarrow -1 \rightarrow -1 \\ d: &0 \rightarrow \pm d_0 \rightarrow 0 where :math:d_0 = m_f^2 - m_i^2 for transition :math:|m_i\rangle \rightarrow |m_f\rangle. The value of :math:n depends on the spin quantum number, :math:I, and is listed in :numref:tb_stvas. **Affine mapping** The resulting spectrum is sheared and scaled, such that the frequencies along indirect dimension are given as .. math:: \langle \Omega\rangle_\text{ST-VAS} = \frac{1}{1+\kappa}\Omega_{m, m-1} + \frac{\kappa}{1+\kappa}\Omega_{1/2, -1/2}. Here, :math:\langle \Omega\rangle_\text{ST-VAS} is the average frequency along the indirect dimension, :math:\Omega_{m, m-1} and :math:\Omega_{1/2, -1/2} are the frequency contributions from the :math:|m\rangle \rightarrow |m-1\rangle satellite transition and the central transition, respectively, and :math:\kappa is the shear factor. The values of the shear factor for various satellite transitions are listed in :numref:tb_stvas. .. cssclass:: table-bordered .. _tb_stvas: .. list-table:: The table lists the satellite transitions associated with the spin :math:I, and the corresponding shear factor, :math:\kappa, used in affine mapping of the ST-VAS methods. :widths: 20 40 20 20 :header-rows: 1 * - Spin - Satellite transitions - :math:d_0 - :math:\kappa * - 3/2 - :math:\left(\frac{3}{2} \rightarrow \frac{1}{2}\right), :math:\left(-\frac{1}{2} \rightarrow -\frac{3}{2}\right) - :math:2 - 24/27 * - 5/2 - :math:\left(-\frac{3}{2} \rightarrow -\frac{1}{2}\right), :math:\left(\frac{1}{2} \rightarrow \frac{3}{2}\right) - :math:2 - 21/72 * - 5/2 - :math:\left(\frac{5}{2} \rightarrow \frac{3}{2}\right), :math:\left(-\frac{3}{2} \rightarrow -\frac{5}{2}\right) - :math:4 - 132/72 * - 7/2 - :math:\left(-\frac{3}{2} \rightarrow -\frac{1}{2}\right), :math:\left(\frac{1}{2} \rightarrow \frac{3}{2}\right) - :math:2 - 84/135 * - 7/2 - :math:\left(-\frac{5}{2} \rightarrow -\frac{3}{2}\right), :math:\left(\frac{3}{2} \rightarrow \frac{5}{2}\right) - :math:4 - 69/135 * - 9/2 - :math:\left(-\frac{3}{2} \rightarrow -\frac{1}{2}\right), :math:\left(\frac{1}{2} \rightarrow \frac{3}{2}\right) - :math:2 - 165/216 * - 9/2 - :math:\left(-\frac{5}{2} \rightarrow -\frac{3}{2}\right), :math:\left(\frac{3}{2} \rightarrow \frac{5}{2}\right) - :math:4 - 12/216 .. _st1_vas_ref: Inner satellite variable-angle spinning method '''''''''''''''''''''''''''''''''''''''''''''' .. autoclass:: ST1_VAS :show-inheritance: :members: :inherited-members: BaseModel .. _st2_vas_ref: Second to inner satellite variable-angle spinning method '''''''''''''''''''''''''''''''''''''''''''''''''''''''' .. autoclass:: ST2_VAS :show-inheritance: :members: :inherited-members: BaseModel