From 996a03d5ab90d5a13af442afe7e9fab5421a3aa7 Mon Sep 17 00:00:00 2001
From: Paul Romano <paul.k.romano@gmail.com>
Date: Sat, 25 Oct 2014 16:37:30 -0400
Subject: [PATCH 1/2] Add new evaporation spectrum sampling method outlined in
 LA-UR-14-27694. Still need documentation.

---
 src/physics.F90 | 17 ++++++++++-------
 1 file changed, 10 insertions(+), 7 deletions(-)

diff --git a/src/physics.F90 b/src/physics.F90
index 8fa0575cd..d136d7306 100644
--- a/src/physics.F90
+++ b/src/physics.F90
@@ -797,7 +797,7 @@ contains
         sampling_scheme = 'cxs'
       end if
 
-    ! otherwise, use free gas model  
+    ! otherwise, use free gas model
     else
       if (E >= FREE_GAS_THRESHOLD * kT .and. awr > ONE) then
         v_target = ZERO
@@ -859,7 +859,7 @@ contains
       m = (nuc % elastic_0K(i_E_up + 1) - xs_up) &
        & / (nuc % energy_0K(i_E_up + 1) - nuc % energy_0K(i_E_up))
       xs_up = xs_up + m * (E_up - nuc % energy_0K(i_E_up))
-      
+
       ! get max 0K xs value over range of practical relative energies
       xs_max = max(xs_low, &
         & maxval(nuc % elastic_0K(i_E_low + 1 : i_E_up - 1)), xs_up)
@@ -972,7 +972,7 @@ contains
     case default
       call fatal_error("Not a recognized resonance scattering treatment!")
     end select
-    
+
   end subroutine sample_target_velocity
 
 !===============================================================================
@@ -1835,14 +1835,15 @@ contains
       lc = 2 + 2*NR + 2*NE
       U = edist % data(lc + 1)
 
+      y = (E_in - U)/T
+      v = 1 - exp(-y)
+
       ! sample outgoing energy based on evaporation spectrum probability
       ! density function
       n_sample = 0
       do
-        r1 = prn()
-        r2 = prn()
-        E_out = -T * log(r1*r2)
-        if (E_out <= E_in - U) exit
+        x = -log((1 - v*prn())*(1 - v*prn()))
+        if (x <= y) exit
 
         ! check for large number of rejections
         n_sample = n_sample + 1
@@ -1852,6 +1853,8 @@ contains
         end if
       end do
 
+      E_out = x*T
+
     case (11)
       ! =======================================================================
       ! ENERGY-DEPENDENT WATT SPECTRUM

From 332970ea2e03d2512e75575c9939b50b8d576f31 Mon Sep 17 00:00:00 2001
From: Paul Romano <paul.k.romano@gmail.com>
Date: Tue, 28 Oct 2014 21:53:39 -0400
Subject: [PATCH 2/2] Update documentation for evaporation spectrum.

---
 docs/source/methods/physics.rst | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/docs/source/methods/physics.rst b/docs/source/methods/physics.rst
index 54dc91345..db6cfd89e 100644
--- a/docs/source/methods/physics.rst
+++ b/docs/source/methods/physics.rst
@@ -682,17 +682,20 @@ nuclear temperature, which is a function of the incoming energy of the
 neutron. The ACE format contains a list of nuclear temperatures versus incoming
 energies. The nuclear temperature is interpolated between neighboring incoming
 energies using a specified interpolation law. Once the temperature :math:`T` is
-determined, we then calculate a candidate outgoing energy based on rule C45 in
-the `Monte Carlo Sampler`_:
+determined, we then calculate a candidate outgoing energy based on the algorithm
+given in LA-UR-14-27694_:
 
 .. math::
     :label: evaporation-E
 
-    E' = -T \log (\xi_1 \xi_2)
+    E' = -T \log ((1 - g\xi_1)(1 - g\xi_2))
 
-where :math:`\xi_1, \xi_2` are random numbers sampled on the unit
-interval. The outgoing energy is only accepted according to a specified
-restriction energy as in equation :eq:`maxwell-restriction`.
+where :math:`g = 1 - e^{-w}`, :math:`w = (E - U)/T`, :math:`U` is the
+restriction energy, and :math:`\xi_1, \xi_2` are random numbers sampled on the
+unit interval. The outgoing energy is only accepted according to the restriction
+energy as in equation :eq:`maxwell-restriction`. This algorithm has a much
+higher rejection efficiency than the standard technique, i.e. rule C45 in the
+`Monte Carlo Sampler`_.
 
 ACE Law 11 - Energy-Dependent Watt Spectrum
 +++++++++++++++++++++++++++++++++++++++++++
@@ -1591,6 +1594,8 @@ References
 
 .. _Monte Carlo Sampler: https://laws.lanl.gov/vhosts/mcnp.lanl.gov/pdf_files/la-9721_3rdmcsampler.pdf
 
+.. _LA-UR-14-27694: http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-14-27694
+
 .. _MC21: http://www.osti.gov/bridge/servlets/purl/903083-HT5p1o/903083.pdf
 
 .. _Sutton and Brown: http://www.osti.gov/bridge/product.biblio.jsp?osti_id=307911