Levels of Ar 41 experimentally observed up to excitation energy of 4.5 MeV are considered. Using experimental data from neighboring nuclei the positions of 40 odd-parity states are calculated in the framework of the shell model. Good agreement is obtained for the low-lying levels. Approximate treatment of the dm 2 fv2 2 pm and dzn 2 f 7 n 2 pm configurations in addition to the dm 2 fin* ground configuration gives a semiquantitative account of all odd parity 3/2 and 1/2 levels up to 4.5 MeV. Many odd-parity levels with J>3/2 which were not yet found experimentally are predicted to be in this region.were actually observed. 1 We shall confine our treatment only to the odd parity states. There is much information on 1/7/2" configurations in this region 5,6 as well as on the ^3/2-/7/2 interaction. We shall try to extend previous calculations to the more complicated case of Ar 41 .We shall use throughout the //-coupling shell model assuming two body effective interactions between nucleons. Rather than use an arbitrary phenomenological potential we shall use matrix elements for the effective interaction as determined from neighboring nuclei. 7 In particular, the matrix elements of the ^3/2-/7/2 interaction will be taken from the level schemes of K 40 and CI 38 where excellent agreement has been obtained between theory and experiment.
II. STRUCTURE OF THE ENERGY MATRIX IN THE SHELL MODELA possible complete set of wave functions in the ^3/2 2 /7/2 3 configuration is the following. We can take an antisymmetric state of the protons with a definite spin J Py an antisymmetric state of the neutrons with definite spin J n and couple J p and J n to a total /. In antisymmetric states, J p can be either 0 or 2 and J n can be 3/2, 5/2, 7/2, 9/2, 11/2, 15/2. In these states, dzji{J p )f7/2 3 (Jn)J, the mutual interaction energy of the protons, V(dz /2 2 J P ) is diagonal as well as that of the neutrons, F(/7/2 3 /n)-The actual values of these interaction energies will be taken from neighboring nuclei in which these configurations appear. The kinetic energy as well as the interaction of the dz/2 protons and / 7 /2 neutrons with the closed shells have the same value in all states of a given configuration. Since we are considering only level spacings, these energies will thus be omitted. However, the proton-neutron interaction has, in addition to diagonal elements, nonvanishing nondiagonal elements between states with 5 1. Talmi, in