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  • doc/guide/pd/polydispersity.rst

    rd712a0f r29afc50  
    2020  P(q) = \text{scale} \langle F^* F \rangle / V + \text{background} 
    2121 
    22 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an  
    23 average over the size distribution $f(x; \bar x, \sigma)$, giving 
    24  
    25 .. math:: 
    26  
    27   P(q) = \frac{\text{scale}}{V} \int_\mathbb{R}  
    28   f(x; \bar x, \sigma) F^2(q, x)\, dx + \text{background} 
     22where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an 
     23average over the size distribution. 
    2924 
    3025Each distribution is characterized by a center value $\bar x$ or 
     
    4641with larger values of $N_\sigma$ required for heavier tailed distributions. 
    4742The scattering in general falls rapidly with $qr$ so the usual assumption 
    48 that $f(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)f(r - 3\sigma_r)$ 
     43that $G(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)G(r - 3\sigma_r)$ 
    4944will not contribute much to the average may not hold when particles are large. 
    5045This, too, will require increasing $N_\sigma$. 
     
    6863 
    6964Additional distributions are under consideration. 
    70  
    71 .. note:: In 2009 IUPAC decided to introduce the new term 'dispersity' to replace  
    72            the term 'polydispersity' (see `Pure Appl. Chem., (2009), 81(2),  
    73            351-353 <http://media.iupac.org/publications/pac/2009/pdf/8102x0351.pdf>`_  
    74            in order to make the terminology describing distributions of properties  
    75            unambiguous. Throughout the SasView documentation we continue to use the  
    76            term polydispersity because one of the consequences of the IUPAC change is  
    77            that orientational polydispersity would not meet their new criteria (which  
    78            requires dispersity to be dimensionless). 
    7965 
    8066Suggested Applications 
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