Changeset 3ba2251 in sasmodels

Timestamp:

Jul 6, 2018 10:13:45 AM (6 years ago)

Author:

Torin Cooper-Bennun <torin.cooper-bennun@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

751da81

Parents:

05cd67f

Message:

added a note on rg meaning (thanks paul b)

File:

• sasmodels/models/guinier.py (modified) (1 diff)

sasmodels/models/guinier.py

@@ -18 +18 @@
 where the $q$ vector is defined as
 
-.. math:: q = \sqrt{q_x^2 + q_y^2}
+.. math:: q = \sqrt{q_x^2 + q_y^2}\,\.
 
-Note that $R_g^2$ may be negative, which happens when a form factor $P(Q)$ is
-increasing with $Q$ rather than decreasing. This can occur for core/shell
-particles, hollow particles, or for composite particles with domains of
-different SLDs in a solvent with an SLD close to the average match point.
-(Alternatively, this might be regarded as there being an internal inter-domain
-"structure factor" within a single particle which gives rise to a peak in the
-scattering).
+In scattering, the radius of gyration $R_g$ quantifies the objects's
+distribution of SLD (not mass density, as in mechanics) from the objects's
+centre of mass. It is defined by
+
+.. math:: R_g^2 = \sum_i^\text{all points}\rho_i\left(r_i-r_0\right)^2
+
+where $r_0$ denotes the object's centre of mass and $\rho_i$ is the SLD at a
+point $i$.
+
+Notice that $R_g^2$ may be negative (since SLD can be negative), which happens
+when a form factor $P(Q)$ is increasing with $Q$ rather than decreasing. This
+can occur for core/shell particles, hollow particles, or for composite
+particles with domains of different SLDs in a solvent with an SLD close to the
+average match point. (Alternatively, this might be regarded as there being an
+internal inter-domain "structure factor" within a single particle which gives
+rise to a peak in the scattering).
 
 To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative