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Address @paulromano comments

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amandalund 2019-03-07 09:09:01 -07:00
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18
docs/source/methods/photon_physics.rst
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@ -775,7 +775,7 @@ formula can be used to find the collision stopping power of the material:
:label: material-collision-stopping-power
S_{\text{col}}(T) = \frac{2 \pi r_e^2 m_e c^2}{\beta^2} N_A \frac{Z}{A_M}
[\ln(T^2/I^2) + ln(1 + \tau/2) + F(\tau) - \delta_F(T)],
[\ln(T^2/I^2) + \ln(1 + \tau/2) + F(\tau) - \delta_F(T)],
where :math:`N_A` is Avogadro's number, :math:`A_M` is the molar mass,
:math:`\tau = T/m_e`, and :math:`F(\tau)` depends on the particle type. For
@ -797,7 +797,7 @@ while for positrons
The density effect correction :math:`\delta_F` takes into account the reduction
of the collision stopping power due to the polarization of the material the
charged particle is passing through by the electric field of the particle.
It can be evaluated using the method described by [Sternheimer]_, where the
It can be evaluated using the method described by Sternheimer_, where the
equation for :math:`\delta_F` is
.. math::
@ -821,14 +821,14 @@ where :math:`\bar{v}_i` is defined as
.. math::
:label: density-effect-nubar
\bar{\nu}_i = \nu_i \rho / \nu_p.
\bar{\nu}_i = h\nu_i \rho / h\nu_p.
The plasma energy :math:`h\nu_p` of the medium is given by
.. math::
:label: plasma-frequency
h\nu_p = \sqrt{(hc)^2/\pi r_e \rho_m N_A Z / A},
h\nu_p = \sqrt{\frac{(hc)^2 r_e \rho_m N_A Z}{\pi A}},
where :math:`A` is the atomic weight and :math:`\rho_m` is the density of the
material. In :eq:`density-effect-nubar`, :math:`h\nu_i` is the oscillator
@ -840,8 +840,8 @@ defined as
.. math::
:label: density-effect-li
l_i &= (\bar{v}_i^2 + 2/3f_i)^{1/2} ~~~~&\text{for}~~ \bar{v}_i > 0 \\
l_n &= f_n^{1/2} ~~~~&\text{for}~~ \bar{v}_n = 0,
l_i &= (\bar{\nu}_i^2 + 2/3f_i)^{1/2} ~~~~&\text{for}~~ \bar{\nu}_i > 0 \\
l_n &= f_n^{1/2} ~~~~&\text{for}~~ \bar{\nu}_n = 0,
where the second case applies to conduction electrons. For a conductor,
:math:`f_n` is given by :math:`n_c/Z`, where :math:`n_c` is the effective
@ -1047,8 +1047,4 @@ emitted photon.
.. _Salvat: http://www.oecd-nea.org/globalsearch/download.php?doc=77434
.. _Sternheimer: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.26.6067
.. [Sternheimer] R. M. Sternheimer, S.M.Seltzer, and M.J.Berger, *Density
effect for the ionization loss of charged particles in various substances*,
Phys. Rev. B, 26, 6067–6076 (1982).
.. _Sternheimer: https://doi.org/10.1103/PhysRevB.26.6067