A semi-empirical formula is presented which gives a semi-quantitative account of the excitation energies in Λ-hypernuclear excitation spectra. Many elaborate studies made were numerical, but our studies yield an analytical expression. Different three-dimensional harmonic oscillators for the Λ- and the neutron-hole reproduce the observed energy spacings fairly well. However, it would be misleading that the oscillators give the wave functions of the corresponding states also. In the light of harmonic excitations, we briefly discuss some phenomenological and microscopic Λ-hypernuclear calculations.

We have obtained an expression for the oscillator frequency in inverse powers of the nuclear mass number, by equating the spacing of the outermost levels of a square well, found to be nearly constant to the oscillator spacing for which the spacings are also constant. The formulae for the oscillator frequency obtained here are compared with similar formulae obtained by other authors. A reasonable qualitative agreement is found to exist between our formulae ofħω_A andħω_N and those given in the standard literature, obtained mainly from size considerations. Our derivation is based only on the assumption that a particle-nucleus potential exists. Any reference to particle-hole states is made purely for a rough comparison of our parameters, otherwise nothing hinges on that description.

Semi-empirical formulae for ground state Λ-binding energy of heavy hypernuclei, in inverse powers of the mass number, using the mass distribution in the folding model, under fairly reasonable assumptions about the range of the Λ-nucleon force are obtained in more than one plausible way. However, they are found to give nearly identical results. A reasonable estimate of the Λ well-depth is obtained from a chi-square fit of the available ground state Λ-binding energy data of medium and heavy nuclei.

Starting with a Λ-nucleus potential, we have obtained a semi-empirical formula, which gives a fairly satisfactory account of the ground state Λ-binding energy of light hypernuclei, if the very light nuclei are ignored.

Here, we make an indirect phenomenological study of the possible presence of a CSB component in the λN interaction in medium and heavy hypernuclei using a semi-empirical formula for the difference in the ground stateB_λ of hypernuclear isobars. We find that light hypernuclei are better suited than heavier hypernuclei for such information.