Shell model calculations: An efficient new algorithm

We describe an efficient new algorithm which extends the range of feasible shell model calculations. This algorithm is applicable to single shell and multiple shell configurations, where two or more quantum numbers (e.g., L and S ) are required to label the states within each shell. The algorithm proceeds by factoring the shell model Hilbert space into a product of subspaces, one for each angular momentum. N ‐particle wave functions are built up recursively from N – 1 particle wave functions. Three kinds of N – 1‐ to N ‐particle coefficients are required to carry out the construction of N ‐particle electron (or fermion) states from N – 1 particle states. These are (1) coefficients of fractional parentage ( CFP s) within a single shell, (2) outerproduct isoscalar factors ( OISF s) within a single angular momentum subspace, and (3) innerproduct isoscalar factors ( IISF s) which describe how multishell states within the complementary angular momentum subspaces are combined to form totally antisymmetric wave functions. All three types of N – 1‐ to N ‐particle coefficients are generated recursively using a single powerful and efficient matrix diagonalization algorithm. Matrix elements of single particle creation and annihilation operators are expressed in terms of single particle CFP s, OISF s, and IISF s. We also describe an efficient algorithm for computing matrix elements of products of creation and anihilation operators by inserting and summing over complete sets of intermediate states. This is the Feynman‐like sum over path overlaps procedure. Timing benchmarks are presented comparing the new Drexel University shell model ( DUSM ) code with a state of the art shell model code.