Question

Two identical particles with spin $s$. What is the spin of its corresponding “center-of-mass” and “relative” particles?

Answer 1

Two-electron atoms. Consider the scattering of two identical particles of spin s charge e and mass m. The motion of the two particles can be factorized into an overall motion described by of the center of masscoordinate R and a relative motion described by therelative distance r between the two particles.

Answer 2

$<marquee><b> Let us start with Spin Classification. One essential parameter for classification of particles is their "spin" or intrinsic angular momentum. Half-integer spin fermions are constrained by the Pauli exclusion principle whereas integer spin bosons are not. The electron is a fermion with electron spin 1/2. Experimental evidence like the hydrogen fine structure and the Stern-Gerlach experiment suggest that an electron has an intrinsic angular momentum, independent of its orbital angular momentum. These experiments suggest just two possible states for this angular momentum, and following the pattern of quantized angular momentum, this requires an angular momentum quantum number of 1/2 The wavefunction which describes a collection of fermions must be antisymmetric with respect to the exchange of identical particles, while the wavefunction for a collection of bosons is symmetric. The fact that electrons are fermions is foundational to the buildup of the periodic table of the elements since there can be only one electron for each state in an atom (only one electron for each possible set of quantum numbers). The fermion nature of electrons also governs the behavior of electrons in a metal where at low temperatures all the low energy states are filled up to a level called the Fermi energy. This filling of states is described by Fermi-Dirac statistics. According to our manuscript “A Grand Unification Theory” the interinsjc 1/2 Spin of the fermion particles is due to our postulation that the strings of energy making up their waves have either left handed or right handed helicities while the bosonic force carriers have are made of strings of energy with both heicities, hence their intiger spin.$