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paper/paper.md

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 Atoms and molecules are examples of quantum level systems in which the allowed energy states take on discrete values.  These states, which are eigenstates of the system's Hamiltonian, are *levels*, which are characterized by the energy relative to the lowest energy level (the "ground state") and by their *multiplicity* if a set of states has exactly the same energy, in which case the states are *degenerate* (for example, see [@griffiths_introduction_2018]).  Interaction with the external world allows a quantum level system to transition between one level and another.  The rate of transition between levels depends on the details of the levels and the nature of the interaction between the system and the external world.  In an ensemble of quantum level systems in contact with the external world at a given temperature (a "heat bath"), there will be a probability of a given system existing in a particular level.  Level probabilities will evolve with time, but, as long as the heat bath changes slowly compared to transition times between levels, the ensemble can achieve an equilibrium characterized by the temperature of the heat bath.  
 
-The Python package ``lvlspy'' stores generic quantum level system data, particularly level energies, multiplicities, and spontaneous transition rates, and includes built-in functions that calculate induced transition rates from detailed balance, rate matrices, and equilibrium probabilites.  Optional properties may be added to any species, level, or spontaneous transition rate, and API routines allow the user to input the relevant data from XML with a well-defined schema.  The source code for ``lvlspy`` has been archived to Zenodo at the linked DOI[@jaad_tannous_2023_8193379].
+The Python package ``lvlspy`` stores generic quantum level system data, particularly level energies, multiplicities, and spontaneous transition rates, and includes built-in functions that calculate induced transition rates from detailed balance, rate matrices, and equilibrium probabilites.  Optional properties may be added to any species, level, or spontaneous transition rate, and API routines allow the user to input the relevant data from XML with a well-defined schema.  The source code for ``lvlspy`` has been archived to Zenodo at the linked DOI[@jaad_tannous_2023_8193379].
 
 # Statement of Need
 
@@ -41,13 +41,13 @@ These examples point to the need for a straightforward software package that is
 
 The code has four essential classes:
 
-    - **Level**: This class stores the energy and multiplicity of a given level.  The class has methods to retrieve or update the level energy or multiplicity and to compute the level Boltzmann factor in thermal equilibrium.  The energy is stored in *keV* by default, but the user may specify *ev*, *MeV*, or *GeV* with the optional *units* keyword when storing or retrieving the level energy.
+- **Level**: This class stores the energy and multiplicity of a given level.  The class has methods to retrieve or update the level energy or multiplicity and to compute the level Boltzmann factor in thermal equilibrium.  The energy is stored in *keV* by default, but the user may specify *ev*, *MeV*, or *GeV* with the optional *units* keyword when storing or retrieving the level energy.
 
-    - **Transition**: A spontaneous transition occurs as an *upper* (higher-energy) level spontaneously decays to a *lower* (lower-energy) level through the release of energy.  This class stores the upper, lower, and Einstein *A* (spontaneous transition rate) for a transition.  Class methods allow the user to retrieve data about the transition, to update the Einstein *A* coefficient, to compute the Einstein *B* coefficients, and, at thermal equilibrium at temperature *T*, to compute the rates of transitions between the levels.
+- **Transition**: A spontaneous transition occurs as an *upper* (higher-energy) level spontaneously decays to a *lower* (lower-energy) level through the release of energy.  This class stores the upper, lower, and Einstein *A* (spontaneous transition rate) for a transition.  Class methods allow the user to retrieve data about the transition, to update the Einstein *A* coefficient, to compute the Einstein *B* coefficients, and, at thermal equilibrium at temperature *T*, to compute the rates of transitions between the levels.
 
-    - **Species**: For ``lvlspy``, a species is any item (especially, a nucleus, an atom, or a molecule) that has a discrete spectrum of levels and transitions between those levels.  This class stores levels and transitions for such an item and has methods to add and remove levels and transitions, retrieve the levels and transitions, to level probabilities in thermal equilibrium, and, in thermal equilibrium, to compute the rate matrix that governs the time-evolution of level probabilities.
+- **Species**: For ``lvlspy``, a species is any item (especially, a nucleus, an atom, or a molecule) that has a discrete spectrum of levels and transitions between those levels.  This class stores levels and transitions for such an item and has methods to add and remove levels and transitions, retrieve the levels and transitions, to level probabilities in thermal equilibrium, and, in thermal equilibrium, to compute the rate matrix that governs the time-evolution of level probabilities.
 
-    - **SpColl**: This class stores a collection of species and has methods to add and remove species, get the collection as a dictionary, and to update data from and write data to XML.
+- **SpColl**: This class stores a collection of species and has methods to add and remove species, get the collection as a dictionary, and to update data from and write data to XML.
 
 The code also has a base **Properties** class that stores optional properties in a dictionary.  The class has methods to update and retrieve properties. Each of the four essential classes inherits the Properties class, so the user may add properties to and retrieve properties from each of Level, Transition, Species, or SpColl instance, as desired.