Information on the Size and Other Quantities of Λ-Orbitals in Hypernuclei From Experimental Λ-Energies

Abstract

An approach is proposed on the basis of which the experimentally known two lower energy eigenvalues of a Λ-particle, assumed to be bound in a hypernucleus by a central potential (from a fairly wide class of them), are able to provide in certain cases rather direct information on estimates of other useful quantities, such as the r.m.s. radii of the Λ orbitals, kinetic energies, etc.

The HVT Technique and the "Uncertainty" Relation for Central

“…These potentials are in their turn, more realistic than the well-known harmonic oscillator potential, which because of its considerable analytic advantages has been very popular in Nuclear Physics problems for purposes of rough estimates. The use of the HVT technique has shown that potentials of the class considered can be useful in a number of cases for these purposes 18,19]. To guarantee rather small values of s one should consider, however, hypernuclei with fairly large mass numbers.…”

The Role of Λ-Effective Mass in a Phenomenological Analysis of the Λ-Energy in Hypernuclei

“…In the present approach, as in ref. [9], the non-relativistic motion of the Ain the hypernucleus is governed by the radial Schrödinger equation in which the Λ-nucleus potential well V is assumed to be a local central potential of the form…”

“…In a recent paper [9] an approach was proposed on the basis of which the experimentally known two lower energy eigenvalues of the Λ-bound in a hypernucleus by a simple central potential, from a fairly wide class of them, are able to provide in certain cases rather direct information on other useful physical quantities, namely on the mean-square radii of the Λ-orbitals and the kinetic and potential energies of the Λ. Such an approach although of sim plified nature has the attractive feature that approximate analytic expressions for the physical quantities of interest can be derived under certain conditions.…”

A new Λ- nucleus potential for the Λ- particle energies in hypernuclei

“…We also note that this − s power series method was used in recent years in treating a variety of problems in which a small parameter s (see below) can be defined. We mention, in particular, the study of the saturation property of the Bertlmann and Martin [17,18] inequalities [19], the information on the size of − Λ orbitals in hypernuclei from the experimental − Λ energies [20], the approximate analytic evaluation of the Heisenberg uncertainty product [21] etc.…”