qspec.doppler_el_d1  (  f ,  alpha ,  u ,  q ,  m ,  v0 = 0.0 ,  return_frame = 'atom' ,  relativistic = True  )[source]

The first derivative $\frac{\partial f^\prime}{\partial U} = \frac{\partial f^\prime}{\partial v}\frac{\partial v}{\partial U}$. Implemented as doppler_d1(f, v, alpha, return_frame) * v_el_d1(u, q, m, v0, relativistic).

Parameters:

farray_like

The frequency $f$ of light (arb. units).

alphaarray_like

The angle $\alpha$ between the velocity- and the light-vector in the laboratory frame (rad).

uarray_like

The electric potential difference $U$ added to the kinetic energy of a body with velocity v0 (V).

qarray_like

The electric charge $q$ of the body (e).

marray_like

The mass $m$ of the body (u).

v0array_like

The initial velocity $v_0$ of the body (m/s).

return_framestr

The coordinate system for which the frequency is returned. Can be either 'atom' or 'lab'.

relativisticbool

The calculation is performed either relativistically (True) or classically (False). The default is True.

Returns:

df_dUndarray

The first derivative $\partial f^\prime / \partial U$ of the Doppler-shifted frequency $f^\prime$ with respect to u in either the rest frame of the atom or the laboratory frame ([f] / V).

Raises:

ValueError

return_frame must be either 'atom' or 'lab'.