Effects of the isotensor potential in nuclear excitation carrying isospin

We discuss some isospin effects in nuclear strength distributions. We deal with the distribution, in energy, of the states of fixed isospin by considering essentially the centroid energies. In particular, we discuss the way in which the centroid energies for an excitation carrying a unit of isospin (isovector excitation) on a target $T$, split among the various available isospin channels. In these processes we may excite various $T+1\mathrm{}$, $T$, and $T-1\mathrm{}$ states. The energy separation between these three components is expressed both in terms of properties of the target state and of the interaction between the excitation and the target, and also in terms of measurable quantities; a method is given of analyzing data by means of target and interaction parameters. An important result has emerged from our analysis: The isospin geometry involved in these processes suggests parametrizing the theory with isoscalar, isovector, and isotensor effective potentials. Dipole (particle-hole) excitations and isovector excitations produced by adding or taking away two nucleons are carefully analyzed along these lines. A phenomenological lower limit for the isotensor potential significant in size and systematic, is found in the case of the dipole excitation. It is shown that an isotensor energy emerges naturally from a schematic model approach to the problem. Finally, we prove that the isotensor effective potential is basically a two-body potential and arises from second order effects when the interaction between the nucleons (nucleon holes) carrying the unit of isospin and the target is treated perturbatively.