A new single particle Λ− nucleus potential is considered for the study of the Λ−particle energies in hypernuclei. This potential belongs to the class of potentials for which the formalism of the s−power series expansions of the Hypervirial Theorems technique is applicable. The numbers d_k (k = 0, 1, 2, 3, 4) related to the derivatives of the potential form factor f , determining the potential shape, are obtained and therefore the approximate analytic expression of the energy level Enl (including third-order terms in the small parameter s). Preliminary numerical results are also given and a discussion is made.

An investigation is carried out to consider a renormalized HVT approach in the context of s-power series expansions for the energy eigenvalues of a particle moving non-relativistically in a central potential well belonging to the class

An analysis is carried out mainly of the ground state binding energies of the Λ-particle in hypernuclei with values of the core mass number AC between 15 and 207 (included) using, as far as possible, recent experimental data.Τhe renormalized (non- relativistic) quantum mechanical hypervirial theorem (RHVT) technique is employed in the form of s- power series expansions and a Gauss single particle potential for the motion of a Λ- particle in hypernuclei is used. Not exact analytic solution is known for the Schrödinger eigenvalue problem in this case. Thus, the approximate analytic expressions (AAE) for the energy eigenvalues which are obtained with the RHVT approach and are quite useful as long as the involved dimensionless parameter s is sufficiently small, are compared only with the numerical solution. The potential parameters are determined by a least-squares fit in the framework of the rigid core model for the hypernuclei. A discussion is also made regarding the determination of the renormalization parameter χ.

An investigation is carried out to consider a renormalized quantum mechanical HVT approach in the context of s-power series expansions for the Schrödinger energy eigenvalues of a particle moving in a central potential well belonging to a fairly wide class of potential wells. This approach is designed and applied in detail to estimate energies of a Λ in hypernuclei. The determination of the renormalization parameter is also discussed.Keywords: Hypernuclei; quantum mechanical HVT approach; central potentials in Schrödinger eigenvalue problems; approximate analytic expressions for Schrödinger energy eigenvalues.PACS Number(s): 21.80.+a, 03.65.Ge

A preliminary account is given of an effort undertaken to allow for the effective mass of the Λ-particle in a phenomenological analysis of existing experimental data for the (ground state) energy of the Λ : EΛ in hypernuclei. The non - relativistic treatment is adopted to describe the motion of the Λ - particle, by considering a central potential well V (r), formed by the nuclear "host" medium of the Λ in the hypernucleus. The Λ - effective mass in the medium is taken to be an r-dependent effective mass mΛ(r) representing approximately some non-local effects in a way suggested in the past. Certain preliminary numerical results are obtained and discussed.