!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!!!!!!!!!!!!!!!!!!!   Welcome to NuLib   !!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!                      !!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

DISCLAIMER:
-----------

Please note that the routines provided here come with absolutely no
warranty and we are unable to guarantee that we will be able to
provide support or help if you run into problems integrating them with
your simulation code. If you decide to use the provided routines in
published work, it is YOUR responsibility to check their physical
correctness and consistency.

If you have any questions or have discovered a bug in our routines,
please e-mail us at evan.oconnor@astro.su.se or open an issue.

COPYRIGHT:
----------

While NuLib is open source, its copyright is held by Evan O'Connor and
Christian Ott. In the absence of suitable open scientific software
licenses, we release this version of NuLib to the community under the
Creative Commons attribution-noncommercial-share alike license:

http://creativecommons.org/licenses/by-nc-sa/3.0/us

Essentially, you may use NuLib, but must make reference to our work,
must not use NuLib for commercial purposes, and any code including or
using our routines or part of them may be made publically available,
and if so, only under the same license.

Introduction:
-------------

The goal of NuLib is to provide a basic standard set of neutrino
matter interaction routines that can be readily incorporated in
radiation-hydrodynamics codes for physics benchmarking.

NuLib v1.0 includes the basic neutrino emissivities and absorption
opacities (including pair processes) as well as neutrino-nucleon,
eutrino-nucleus elastic scattering processes and neutrino-electron
inelastic scattering.  Other inelastic processes will also be
including in future versions.

If anyone would like to contribute to the development of NuLib please
let me know, I'm hosting this on GitHub with this in mind. I am
currently developing a neutrino transport code that will make use of
all these interactions, that being said it is not finished and since
I've never done such a task, it may well be the case that methodlogies
of coding these interactions will change slightly (and have not been
fully tested) If you have advice on this front please fill me in, I am
more than happy to make NuLib as accessible as it needs to be to allow
others to benefit from it.

NuLib, in its current form, is used by me to make tables of neutrino
emissivities, opacities (scattering and absorption), and scattering
kernels.  It is not yet optimized for on-the-fly calculations of
quantities.  In fact, the routines are coded in such a way as to be as
clear and accurate as possble, with little or no regard for
computational speed.  For example, the weak magnitism correction for
scattering processes is small but many terms long, I do the full
calculation.  In the future I hope NuLib will have routines capable of
on the fly calculations, I expect this is necessary if one whats fully
differential cross sections (in energy and angle, as a function of
energy).

NuLib v1.0 Neutrino Interactions.
---------------------------------

Emissivities:
-------------

1. electron-positron annhilation to \nu - \bar{\nu}. This is currently
done two ways.  Both follow Bruenn 1985 and while the first one uses
Burrows, Reddy, Thompson(2006) as well. The first way is a bit of a
kludge.  It calculates the emission assuming no final state blocking
and gets an opacity via Kirchhoff's law.  It is not an appropiate use
of the law, but it generally gives single neutrino interaction rates
that make sense for he-lepon neutrinos.  It doesn't work so well for
electron-type neutrinos, but these rates are not expected to be
dominant for electron-type neutrinos.  The second way is more involved
for the user and the correct way.  NuLib can calculate both the
production (via e+e- annihilation) and annihilation (via \nu-\bar{\nu}
annihilation) kernels (i.e. as a function of the energy of both
neutrinos).  The user must then make use of these appropiately.  The
default option is 1, for heavy-lepton neutrinos only.

2. Nucleon-Nucleon Bremsstrahlung, this is an approximation used in
Burrows Reddy, and Thompson (2006) [BRT06].  A full calculation of
this reaction would be great! The default is to use this only for
heavy-lepton neutrinos.

Scattering Opacities:
---------------------

For the scattering opacities, I list only the base interactions, the
neutrino type plays a role in the calculations, see the code for a
full description of the interaction.  The cross sections all come from
BRT06 with appropiate corrections (e.g. weak magnetism [has a logical
flag to turn off if desired])


1. neutrino scattering on neutrons

2. neutrino scattering on protons

3. neutrino scattering on heavy nuclei (this includes lots of
corrections, see BRT06 and the code for details)

4. neutrino scattering on electrons (elastic, Thomspon, T. PhD)

5. neutrino scattering on alphas

Absorption Opacities:
---------------------

1. \nu_e absorption neutrons: This currently includes a stimulated
absorption term as described in BRT06, final
state electron blocking and also final state proton blocking.  Weak
magnitism, phase space and recoil corrections [optional via flag] are
applied via Horowitz (2002).

2. \bar{\nu}_e absorption protons: This currently includes a
stimulated absorption term as described in Burrows, Reddy, and
Thompson, final state positorn blocking and also final state neutron
blocking.  Weak magnitism, phase space and recoil corrections
[optional via flag] are applied via Horowitz (2002).

3. \nu_e absorption on heavy nuclei: This follows the simple treatment
of Bruenn 85 (among others), placing cuts on the cross section based
on the average A and average Z of the nucleus.  Much better treatment
is desired and someday will be implemented.

Neutrino-Electron Inelastic Scattering Kernels:
-----------------------------------------------

For a temperature and electron chemical potential, NuLib calculates
the first two terms in a Legendre expansion of the scattering kernels
for neutrinos on electrons.  We essentially follow Bruenn 1985 and
references there in.


Electron-Capture Rates on Nuclei:
---------------------------------

Chris Sullivan and Evan O'Connor et al. have implemented a new module
for microphysical electron-capture rates on nuclei in NuLib. It utilizes the
formalism discussed in:
------------------------------------------------------------------------------------
| Sullivan, C., O'Connor, E., Zegers, R. G. T., Grubb, T., & Austin, S. M. (2015). |
| The Sensitivity of Core-Collapse Supernovae to Nuclear Electron Capture.         |
| http://arxiv.org/abs/1508.07348                                                  |
| Contact: Chris Sullivan <sullivan@nscl.msu.edu>                                  |
------------------------------------------------------------------------------------
The primary calculation is electron-neutrino type emissivities from
electron captures on medium-heavy nuclei. These calculations rely on
a library ofelectron-capture rate tables that have been compiled and
are availableas a part of the weak_rates module (set in the parameters
file). In addition, number densities (abundances) and nuclear masses
are needed for a large set of nuclei. These are calculated via Matthias
Hempel's NSE mass distributions discussed below. To include emissivities
and opcaities for this interaction, set the corresponding flag in
requested_interactions.inc, as well as WEAK_RATES=1 in make.inc. If
these routines are utilized in a work, cite the above paper as well the
following publications from which the weak-rate tables derive:
--------------------------------------------------------------------------------
| Fuller, G. M., Fowler, W. A., & Newman, M. J. (1982).                        |
| Stellar weak interaction rates for intermediate-mass nuclei.                 |
| II - A = 21 to A = 60. The Astrophysical Journal, 252, 715.                  |
| http://doi.org/10.1086/159597                                                |
--------------------------------------------------------------------------------
| Oda, T., Hino, M., Muto, K., Takahara, M., & Sato, K. (1994).                |
| Rate Tables for the Weak Processes of sd-Shell Nuclei in Stellar Matter.     |
| Atomic Data and Nuclear Data Tables, 56(2), 231-403.                         |
| http://doi.org/10.1006/adnd.1994.1007                                        |
--------------------------------------------------------------------------------
| Langanke, K., & Mart\'{i}nez-Pinedo, G. (2000).                              |
| Shell-model calculations of stellar weak interaction rates:                  |
| II. Weak rates for nuclei in the mass range in supernovae environments.      |
| Nuclear Physics A, 673(1-4), 481-508.                                        |
| http://doi.org/10.1016/S0375-9474(00)00131-7                                 |
--------------------------------------------------------------------------------
| Langanke, K., & Mart\'{i}nez-Pinedo, G. (2003).                              |
| Electron capture rates on nuclei and implications for stellar core collapse. |
| Physical Review Letters 90, 241102.                                          |
| http://prl.aps.org/abstract/PRL/v90/i24/e241102                              |
--------------------------------------------------------------------------------

Tables are available from: https://groups.nscl.msu.edu/charge_exchange/weakrates.html

Sample Executables:
-------------------

make_table_example: by default this makes a horribly under resolved
10x10x10x24 (rho,temp,ye,energy) + (10x10x24*24)
(temp,eta,energy_in,energy_out) NuLib table in h5 format. The
calculations takes abut 1 minute to generate.  The table boundaries,
and number of data points are changable in the make_table_example.F90
file.  To get enough accuracy in the interpolation I expect at least
10 points per decade in rho, 20 in temperature and 1 for every 0.01 or
0.02 in ye.  This makes a table ~1GB in size with 24 energy bins.  The
energy spacing is changable in nulib.F90, right now it is a 4MeV bin,
then a logarithmic spacing starting at 1MeV going to ~300MeV, this may
not be the best choice, if you have a better suggestion, let me know,
or code up a routine to generate good energy spacing and send a pull
request (?).

You must specify an equation of state, NuLib is set up to read in the
EOS tables on stellarcollapse.org, the filename is set in
make_table_example.F90.  For each EOS you must set the reference mass,
this is used to convert the density into a number density for the
scattering and absorption cross sections.

The main routine that make_table_example.F90 calls is
single_point_return_all.  This routine takes as input all of the
equation of state variables and returns the emissivity, absorption
opacity and scattering opacity for all neutrino species and energies.
You also must specify the neutrino scheme, this is what sets the
number of species. Here the comments regarding the different neutrino
scheme currently available in NuLib, again if you have a request let
me know, I want to make this as useful as possible.

! many people use different number of species, this is the possible
! summing scheme NuLib can currently do
!
! mytable_neutrino_scheme = 1 (three output species)
! species #1: electron neutrino             #2 electron antineutrino
!         #3: muon+tau neutrino+antineutrino
!
! neutrino_scheme = 2 (four output species)
! species #1: electron neutrino             #2 electron antineutrino
!         #3: muon+tau neutrino             #4 mu and tau antineutrino
!
! neutrino_scheme = 3 (six output species)
! species #1: electron neutrino             #2 electron antineutrino
!         #3: muon neutrino                 #4 mu antineutrino
!         #5: tau neutrino                  #6 tau antineutrino

single_point_return_all appies Kirchoff's law to the emissivities and
absorption cross sections.  This adds an contribution to the
emissivity from the absorption cross section (and vice-versa).  This
is explained in BRT06 and explicitly showed in the
single_point_return_all routine. There is a similar routine for the
inelastic scattering kernels, single_Ipoint_return_all.  This routine
only calculates half of the terms, we use symmetry laws to calculate
the other half.

point_example: this program shows examples of how to call the NuLib
routines for a single point. Again, the energy spacing is changable in
nulib.F90, right now it is a 4MeV bin, then a logarithmic spacing
starting at 1MeV going to ~300MeV, this may not be the best choice, if
you have a better suggestion, let me know, or code up a routine to
generate good energy spacing and send a pull request (?). You must
specify an equation of state, NuLib is set up to read in the EOS
tables on stellarcollapse.org, the filename is set in
point_example.F90.  For each EOS you must set the reference mass, this
is used to convert the density into a number density for the
scattering and absorption cross sections.

Unlike single_point_return_all, the individual calls to emissivity
(e.g. return_emissivity_spectra_given_neutrino_scheme) or the cross
section routines
(e.g. return_absorption_opacity_spectra_given_neutrino_scheme) do not
apply Kirchoff's law.

nulibtable_driver: This routine is a driver routine for reading in a
NuLib table and using a trilinear interpolation (log rho, log temp,
ye) routine to interpolate the emissivities and cross sections to any
rho,temp,ye. This is extermely useful for transport simulations and
prevents on the fly calculations of the neutrino interaction terms.
It does not currently interpolate in energy, this would be a useful
feature to add, it would require slightly adjusting the units of the
emissivities, in addition to writing a 4th order interpolator.  There
are several routines available in nulibtable.F90 for accessing the
table.  The large number of variables can lead to long times spent in
interpolating. I've tried to optimize this but more could be done I'm
sure.

nulibtable_driver also reads in inelastic kernels and ep-annihilation
kernels.  two types of symmetries are applied to ensure detailed
balence for the inelastic electron scattering.  For the
ep-annihilation, only one symmetry is used, the other, crosses
neutrino species and it is left to the user if they would like to take
advantage of it.

Installation.
-------------

If you are reading this then you are halfway there.  You must set the
F90 and F90FLAGS compiler variables in the make.inc file in this
directory to point to your Fortran compiler.  Also, you must have HDF5
compiled with the _same_ compiler.  This usually means downloading the
source from http://www.hdfgroup.org/HDF5/release/obtain5.html,
configuring with your version of:

./configure --enable-fortran FC=ifort --prefix=/Users/evanoc/opt/hdf5-current-ifort12

and then

make
make install

the HDF5DIR variable in make.inc would then be set to /Users/evanoc/opt/hdf5-current-ifort12

After this, a simple make should create three executables in the main
directory, a brief explanation of these is in the section
`executables' above.

Extras
------

There is support in NuLib for using Matthias Hempel's NSE mass
distributions available from
https://astro.physik.unibas.ch/en/people/matthias-hempel/equations-of-state/
(for example, sfho_frdm_comp.zip). To enable these
use must download his code and tables from his website, place them in
the directory src/extra_code_and_tables/ and enable the preprocessor
flag NUCLEI_HEMPEL.  We use the SFHo table as an example in the code,
you can change this by editting nuclei_distribution_helpers.F90
directly.  Please see this file for more details.

A few small changes must be made to xxxx_xxxx_composition_module.f
as provided by M. Hempel if the weak_rates module (electron-capture
rates). Primarily a public (non-private) copy of the loaded nuclear
masses must be exposed. e.g. for the SFHo EOS, one must add the
following to the source file:
---------------------------------------------------
| double precision, dimension(kmax) :: sfho_mass  |
|---------------------- & ------------------------|
| sfho_mass = mass                                |
---------------------------------------------------
The first should go in the module declaration (for example line 85). 
The second should go in the 'compdata_readin' subroutine after the 
mass variable has been read in (for example line 102).

We also found that an updated path is needed for the
composition binary included with the module (or a symbolic link
from the run directory).