qspec.lambda_r  (  r ,  r_d ,  r_ref ,  r_ref_d ,  dr = None ,  dr_d = None ,  v2 = 1.0 ,  v2_ref = 1.0 ,  v4 = 1.0 ,  v4_ref = 1.0 ,  v6 = 1.0 ,  v6_ref = 1.0 ,  c2c1 = 1.0 ,  c3c1 = 1.0  )[source]

The differential nuclear charge radius series up to $\mathcal{O}(r^6)$ between two isotopes and its uncertainty calculated from the Barrett radii, elastic electron scattering form factors and the Seltzer coefficients $$\begin{aligned} \Lambda &= \delta\!\langle r^2\rangle + \frac{C_2}{C_1}\delta\!\langle r^4\rangle + \frac{C_3}{C_1}\delta\!\langle r^6\rangle\\[2ex] \Delta\Lambda &= \sqrt{\Delta\delta\!\langle r^2\rangle^2 + \left(\frac{C_2}{C_1}\Delta\delta\!\langle r^4\rangle\right)^2 + \left(\frac{C_3}{C_1}\Delta\delta\!\langle r^6\rangle\right)^2} \end{aligned}$$ The moments of the differential nuclear charge radii and their uncertainties are calculated with the functions delta_r2, delta_r4 and delta_r6.

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.

v4array_like

The shape factor $V_4$ of the first isotope.

v4_refarray_like

The shape factor $V_{4,\mathrm{ref}}$ of the second isotope.

v6array_like

The shape factor $V_6$ of the first isotope.

v6_refarray_like

The shape factor $V_{6,\mathrm{ref}}$ of the second isotope.

c2c1array_like

Seltzer's coefficient for the quartic moment $C_2 / C_1$ ([1 / r**2]).

c3c1array_like

Seltzer's coefficient for the sextic moment $C_3 / C_1$ ([1 / r**4]).

Returns:

out(ndarray, ndarray)

The difference of the nuclear charge radius series between two isotopes $\Lambda$ and its uncertainty $\Delta\Lambda$ ([r**2]).