Cross-section calculations

The normalization γ ray in the (n,n'γ) ATLAS is the 847-keV 2+1 → 0+gs transition in 56Fe which has a relative intensity (RI) of 100 units. In the example below, we adopt a partial γ-ray production cross section (σγ) of 329.46 ± 37.55 mb for this transition. To extract cross sections relative to this value we add the following code to our SQL transactions:

      CREATE TEMP TABLE _Variables(
          Name TEXT PRIMARY KEY,
          FeCS FLOAT,
          FeRatio FLOAT,
	  d_FeCS FLOAT,
	  d_FeRatio FLOAT,
          RI FLOAT

      INSERT OR REPLACE INTO _Variables VALUES ('Constant', 329.46, 3.2946, 37.55, 0.3755, 100.0);

Here, FeCS=329.46 is σγ for the 56Fe transition, d_FeCS=37.55 is its associated uncertainty, RI=100.0 is the relative intensity of the 56Fe transition, FeRatio=3.2946 is the ratio σγ(56Fe)/RI(56Fe), and d_FeRatio=0.3755 is the uncertainty ratio. These variables can be adjusted to accommodate user-specified values. Several SQL scripts utilizing the above "global variables" temporary table are provided in the examples directory ~/BaghdadAtlas/sql_codes, e.g., getDyCs_Vars.sql which calculates partial cross sections and associated uncertainties for transitions in natural dysprosium. A similar script that does not use the temporary-table method above is also provided for comparison, getFeCS.sql which calculates partial cross sections and associated uncertainties for transitions in natural iron. Note that the extension library (Linux: libsqlitefunctions.so, Mac OS X: libsqlitefunctions.dylib) must be loaded into these transactions because nonstandard-sqlite3 functionality is being used. The appropriate library gets defined automatically during installation. The SQL scripts impacted during the installation process will therefore contain the following OS-dependent transactions:

	SELECT load_extension('../UDF/sqlite-amalgamation/libsqlitefunctions.so'); /* Linux library */
	SELECT load_extension('../UDF/sqlite-amalgamation/libsqlitefunctions.dylib'); /* Mac OS X library */

Alternatively, cross-section calculations may also be performed using the Jupyter Notebook. To illustrate this, a CrossSection class has been defined in one of the cells in the example notebook sql_queries_atlas.ipynb provided in ~/BaghdadAtlas/notebook_analysis. The class constants FeCS, FeRatio, d_FeCS, d_FeRatio, and RI are defined as above. The cross sections for natRe(n,n'γ), for example, are shown here. To calculate cross sections for a different nucleus change the atomic number (Z), chemical symbol (Chem_symb), and atomic mass (A) to that of the nucleus of interest in the corresponding cell.