Importance of multipole moment

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    One of the examples I found was about numerical calculations using the so-called “Fast multipole method”. This technique, introduced by Leslie Greengard and Vladimir Rokhlin Jr, is used to solve multi-body problems when long range forces are present. This is done by expanding the Green’s function of the system as a multipole expansion. Computationally, the quickness stems from a set of values which do not need to be stored. This reduces the required memory and computation time.

    Another is Mössbauer spectroscopy where, in specific conditions, it is possible to measure the nuclear electric quadrupole and magnetic dipole moments.

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