symmetric form, leaving unaltered the interaction between two symmetrically coupled particles, this will affect only negligibly the binding energies of the highly symmetric H 3 and He 4 nuclei, 3 ' 6 but it produces a large change (arising of course exclusively from the antisymmetrically coupled pairs of particles) in the energy matrix of Be 9 . The simple (ls) 4 (2£) B term mentioned does not describe a bound state of Be 9 at all with the symmetric form of (1), and while this lends ^weight to the view 7 that the purely chargesymmetric interaction is not an admissible one either, it is not conclusive. To investigate more closely the binding predicted by this interaction for light nuclei, more states, mixed configurations, and wave functions made more flexible by the introduction of different oscillator-parameters into the different single-particle states must ibe considered. To this end formulas generalizing integrals of Elliott 5 and Talmi 8 have been developed.t[n calculations with many-parameter oscillator wave functions, for central, tensor, or spin-orbit terms, the radial integrals are always of the form o Jo r^Llr 2 L2ex p(~-^i r i 2 -p 2r2 2 )fk(ri,r 2 )ri 2 drir2 2 dr2;( 2) where L h L 2f k are integers of the same parity (Li, L 2 both s^&)> the v's arise as sums of the oscillator parameters, and the /fc's are defined by type distance-dependence, the V(r) in (3)
is of the form exp(-r/r c )/(r/r c ) for the central force and of the form exp(-r/r t )/(r/rt) zfor the tensor force. The It's can be most conveniently expressed in this case by single Hh functions, 9 which were used by Elliott, who also pointed out that the coefficient of the divergent tensor force term [i.e., (4) when 1 = 02 always vanishes in the complete matrix. 5 (This result is independent of the distance-dependence used.) For an interaction which is constant when OSr^ro, say, and of Yukawa type when r>ro, (4) can be expressed as a sum of Hh functions, and such an expression has been used in preliminary calculations with an interaction possessing a finite hard core.2 fk(r h r 2 )P k (cosa>) = V(r), [r 2 =ru 2 =ri 2 +r 2 2 -2nr 2 cosco], (3) with V(r) the distance-dependence, of the interaction (divided by r 2 , for tensor force terms 5 ). Then, on putting vi~