Orthogonal Classification of Alpha-Particle Wave Functions

A four-nucleon wave function has four parts: spin (S), isospin (T), angular-momentum (L), and internal (I), combined into a totally antisymmetric function. The nonrelativistic α-particle ground state is described by 32 independent internal functions. Cohen, using an overcomplete set of 34 internal functions, has previously classified the α-particle ground state into three ¹S₀, eight ³P₀, and six ⁵D₀ states, not all mutually orthogonal (or even independent). With the help of the concept of S independence, the present paper describes a grouping of the 32 independent internal functions into an orthogonal and complete set of three ¹S₀, six ³P₀, and five ⁵D₀ states.