By Robert Jackson

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C 25, 2072 (1982) 12. R. B. Khadkikar effects Phys. Rev. Lett. 7 calculate the needed B(E2), B(M 1), Q(J) and µ(J) values involving the eigenstates. In addition, as described in Chapters 4 and 5, one can use the DSM wavefunctions to calculate GT strengths, double beta decay nuclear transition matrix elements and so on. In principle it is also possible to include three-body terms in the Hamiltonian and perform DSM calculations. Appendix A gives the equations needed for including three-body interactions.

The dominant component of these levels is the 2p-2h configuration (r3)10 (g9/2 )2 . 3 Conclusions DSM has been quite successful in describing the collective bands of 68 Ge using a realistic effective interaction. The levels of the ground band up to J = 4+ have the dominant configuration (r3)12 . The wave function of the 6+ state shows a mixture of the configurations (r3)12 and (r3)10 (g9/2 )2 . The following conclusions can be drawn regarding the structure of the three 8+ states: (i) The proton aligned 8+ state is very high in energy and plays no role in the structure of the lowest three 8+ states; (ii) the first 8+ level is a neutron aligned level having the dominant structure (r3)10 (g9/2 )2 ; (iii) the 8+ 2 is also two neutron aligned state but it has significant mixture from (r3)12 configuration and the 8+ 3 has complex structure.

48) Note that b is the oscillator length parameter. Extending Eq. (2n′ + 2l′ + 1)!! n′ ! 49) ′ (−2)k+k nk nk′ [(l + l′ + 2k + 2k ′ + λ + 1)/2]! (λ + 12 )! − l+l′ +2k+2k′ ,λ 2 2 2 + 32 , q 4b . In the above equation, 1 F1 (α, γ, z) is a hyper-geometric function. 2 Matrix elements of M1 transition operator The magnetic dipole (M 1) operator to lowest order is, 3 1 4π 2 M1 = k (1 + τ k ) (gl l(k) + gs s(k)) + (1 − τ k )gs′ s(k) . 50) The summation is over all the nucleons; τ k = 1 for protons and −1 for neutrons.