- qspec.delta_r2 ( r , r_d , r_ref , r_ref_d , dr = None , dr_d = None , v2 = 1.0 , v2_ref = 1.0 )[source]
The difference of the mean square nuclear charge radius between two isotopes and its uncertainty calculated from the Barrett radii and elastic electron scattering form factors $$\begin{aligned} \delta\!\langle r^2\rangle &= \left(\frac{R}{V_2}\right)^2 - \left(\frac{R_\mathrm{ref}}{V_{2,\mathrm{ref}}}\right)^2\\[2ex] \Delta\delta\!\langle r^2\rangle &= \sqrt{\left(\frac{2 R\Delta R}{V_2^2}\right)^2 + \left(\frac{2 R_\mathrm{ref}\Delta R_\mathrm{ref}}{V_{2,\mathrm{ref}}^2}\right)^2}. \end{aligned}$$ If the uncertainty
dr_d
is specified, which is often much lower thanr_d
andr_ref_d
, an improved formula is used that gives smaller uncertainties $$\begin{aligned} \delta\!\langle r^2\rangle &= sd, \quad s \coloneqq \frac{1}{V_2}\left(\frac{R}{V_2} + \frac{R_\mathrm{ref}}{V_{2,\mathrm{ref}}}\right), \quad d \coloneqq \delta R + R_\mathrm{ref}\left(1 - \frac{V_2}{V_{2,\mathrm{ref}}}\right)\\[2ex] \Delta\delta\!\langle r^2\rangle &= \sqrt{\left(s\Delta\delta R\right)^2 + \left(\frac{d}{V_2^2}\Delta R\right)^2 + \left(\left[\frac{d}{V_2V_{2,\mathrm{ref}}} + s\left(1 - \frac{V_2}{V_{2,\mathrm{ref}}}\right)\right]\Delta R_\mathrm{ref}\right)^2}. \end{aligned}$$- Parameters:
-
- rarray_like
The Barrett radius $R$ of the first isotope (arb. units).
- r_darray_like
The uncertainty of the Barrett radius $\Delta R$ of the first isotope ([
r
]).- r_refarray_like
The Barrett radius $R_\mathrm{ref}$ of the second isotope ([
r
]).- r_ref_darray_like
The uncertainty of the Barrett radius $\Delta R_\mathrm{ref}$ of the second isotope ([
r
]).- drarray_like
The difference between the Barrett radii $\delta R = R - R_\mathrm{ref}$ of the first and second isotope ([
r
]).- dr_darray_like
The uncertainty of the difference between the Barrett radii $\Delta\delta R$ of the first and second isotope ([
r
]).- v2array_like
The shape factor $V_2$ of the first isotope.
- v2_refarray_like
The shape factor $V_{2,\mathrm{ref}}$ of the second isotope.
- Returns:
-
- (dr2, dr2_d)(ndarray, ndarray)
The difference of the mean-square nuclear charge radius between two isotopes $\delta\!\langle r^2\rangle$ and its uncertainty $\Delta\delta\!\langle r^2\rangle$ ([
r ** 2
]).