Effect of the Tensor Force on the Level Structure of Li^{6} and Li^{7}
Abstract
The splittings of the ^{3}S_{1} and ^{1}S_{0} states of Li^{6} and the P doublet states of Li^{7} by the tensor force are calculated by a variational method which includes the effect of configuration interaction. Other forces which would contribute to the splitting, such as spindependent central forces or vector spinorbit forces, are not considered. The method of calculation is based on the use of a variational function of the form ψ=ψ_{0}+λt'ψ_{0}, where t' is essentially the tensor force, treated as a perturbation on a central force oscillator wave function, ψ_{0}. The effect of the tensor force is shown to be equivalent to a mixture of ordinary and spinexchange central forces plus a vector type spinorbit force of rather complicated structure. Using a HuMassey Gaussian shape tensor potential, an Sstate splitting of 1.4 Mev is found for Li^{6} and an inverted Pdoublet splitting of 380 kev is found for Li^{7}. A Yukawa shape potential would give similar results. In view of the approximations made in the analysis, these results are in reasonable agreement with the experimental splittings of 3.5 Mev and 480 kev for Li^{6} and Li^{7} respectively. The tensor force is found to contribute about 12 Mev to the binding energy of these nuclei and to introduce a 6 percent admixture of excited states into the ground state. The importance of configuration interaction is shown by a secondorder perturbation calculation neglecting configuration interaction which gives entirely different resultsa negligible Sstate splitting for Li^{6} and a normal P doublet structure for Li^{7}. The effect of the tensor force on the Pdoublet separation in Be^{7} and the F doublet separation in Li^{7} is discussed briefly.
 Publication:

Physical Review
 Pub Date:
 January 1956
 DOI:
 10.1103/PhysRev.101.258
 Bibcode:
 1956PhRv..101..258F