epsproc.geomFunc.lfblmGeom module

epsproc.geomFunc.lfblmGeom.lfblmXprod(matEin, QNs=None, EPRX=None, p=[0], BLMtable=None, lambdaTerm=None, RX=None, eulerAngs=None, thres=0.01, thresDims='Eke', selDims={'Type': 'L', 'it': 1}, sumDims=['mu', 'mup', 'l', 'lp', 'm', 'mp'], sumDimsPol=['P', 'R', 'Rp', 'p'], symSum=True, SFflag=True, squeeze=False, phaseConvention='S', dlistMatE=['lp', 'l', 'L', 'mp', 'm', 'M'], dlistP=['p1', 'p2', 'L', 'mup', 'mu', 'M'], normFactors=[0.3333333333333333, 0.2])[source]

Implement \(\beta_{LM}\) calculation as product of (Clebsch-Gordan coeff) tensors.

Formalism as per Cross section and asymmetry parameter calculation for sulfur 1s photoionization of SF6, A. P. P. Natalense and R. R. Lucchese, J. Chem. Phys. 111, 5344 (1999), http://dx.doi.org/10.1063/1.479794

\[\begin{split}\begin{eqnarray} \beta_{\mathbf{k}}^{L,V} & = & \frac{3}{5}\frac{1}{\sum_{p\mu lhv}|I_{\mathbf{k},\hat{n}}^{(L,V)}|^{2}}\sum_{\stackrel{p\mu lhvmm_{v}}{p'\mu'l'h'v'm'm'_{v}}}(-1)^{m'-m_{v}}I_{\mathbf{k},\hat{n}}^{(L,V)} \\ & \times & \left(I_{\mathbf{k},\hat{n}}^{(L,V)}\right)^{*}b_{lhm}^{p\mu}b_{l'h'm'}^{p'\mu'*}b_{1vm_{v}}^{p_{v}\mu_{v}}b_{1v'm'_{v}}^{p'_{v}\mu'_{v}*} \\ & \times & [(2l+1)(2l'+1)]^{1/2}(1100|20)(l'l00|20) \\ & \times & (11-m'_{v}m_{v}|2M')(l'l-m'm|2-M') \end{eqnarray}\end{split}\]

Where each component is defined by fns. in :py:module:`epsproc.geomFunc.geomCalc` module.

22/06/20 In progress - code crudely adapted from mf/af cases, rather messy. Dev code:

http://localhost:8888/lab/tree/dev/ePSproc/geometric_method_dev_Betas_090320.ipynb D:codeePSprocpython_devePSproc_MFBLM_Numba_dev_tests_120220.PY http://localhost:8888/notebooks/epsproc/tests/LF_AF_verification_tests_190620_fullCG.ipynb


Parameters:phaseConvention (optional, str, default = 'S') – Set phase conventions with epsproc.geomCalc.setPhaseConventions(). To use preset phase conventions, pass existing dictionary.
normFactors : optional, list of int or float, default = [1/3, 1/5]
Additional normalization factor to match ePS defns. Should be mu and m degeneracy factor? Always 1/3 for B0 term, 1/5 for B2 term? Or 1/(2L+1) term?