In many applications one has to deal with functions that depend on two directions. A convenient basis for function expansion is provided by bipolar harmonics that are given by an irreducible tensor product of the spherical functions with different arguments. The basis of biharmonic functions is overcomplete for a fixed total angular momentum and for arbitrary internal angular momenta. Bipolar harmonics with a small rank of total momentum often enter the final results while the ranks of the internal tensors can run over a wide (or infinite) range. But it is possible to decompose the bipolar harmonic using the smallest set of internal orbital momenta for a fixed total momentum. Here, the new method is applied for calculations of decomposition coefficients at low values of total angular momenta and arbitrary values of internal momenta. Basis functions from the minimal set are modified in two respects: 1. Expansion coefficients include total dependence on the angle between two directions and basis functions are independent from this angle. 2. New basis is orthogonal and normalized to the absolute value of unity. These tensors form the normalized orthogonal basis from the minimal set of bipolar harmonics. The basis and expansion coefficients are presented explicitly for total orbital momentum $L\le 3$.

Close

PrevNext

View figure in article

• Few-body systems
• Nuclear reactions