ar X iv : n uc l - th / 9 50 30 23 v 1 2 7 M ar 1 99 5 The three - baryon Λ NN potential

Using a three-baryon ΛNN potential having a spin-independent dispersive and a two-pion exchange components, realistic variational Monte Carlo calculations have been performed for the Λ-seperation energy for ΛHe. A relationship between strengths associated with both pieces of ΛNN force giving exact experimental Λ-seperation energy has been obtained which then combined with our previous study on 17 ΛO hypernucleus determines a unique and acceptable set of strength parameters for ΛNN potential. The ΛNN force is found important for the core polarization. PACS numbers: 21.80.+a,21.10.Dr,13.75.Ev,27.20.+n Typeset using REVTEX 1 The Cluster Monte Carlo(CMC) technique first used for nuclei [1] is recently generalised to 17 ΛO hypernucleus for a realistic microscopic calculations [2]. The same has been further extended to ΛHe in this work to study the A-dependence of the expectation value of ΛNN potential which is of great importance. In case of 17 ΛO, we find that the operatorial NN, NNN, ΛN and ΛNN correlations completely change the previously determined ΛNN potential using central correlations [3] and that a reasonable VΛNN results in a Λ-seperation energy(BΛ) consistent with the ”empirically” determined value i.e. -13 ±0.4 MeV. Also, ΛNN force generates a corresponding correlation which has been found playing a significant role in changing the density profile and energy of the core nucleus. This provokes a deep interest in determining the correct three-baryon ΛNNpotential. The ΛNN potential is written as a combination of a dispersive central force [3] (V D ΛNN) and a two-pion exchange force [4] (V 2π ΛNN) VΛNN = V D ΛNN + V 2π ΛNN . (1) We do not invoke a spin dependence in the V D ΛNN which is unimportant for spin-zero core hypernuclei. Thus, we use a phenomenological form V D NNΛ = W0T 2 π (r1Λ)T 2 π (r2Λ). (2) Indeed, we find a negligibly small value for spin-spin ΛN potential in 17 ΛO [2] and also herein for ΛHe. Tπ(r) is the OPE tensor potential Tπ = ( 1 + 3 x + 3 x2 ) e x ( 1− e 2 )2 (3) with x=μr, μ=0.7 fm is the pion mass, and the cut-off parameter c=2.0 fm. The V 2π ΛNN , consists of two parts, arising from sand pwave π−Λ potentials [4]. The former is strongly suppressed and that almost all contribution is coming from the latter one. We, thus, do not consider the s-wave channel and write the V 2π ΛNN as V 2π ΛNN = − ( Cp 6 ) (τ 1 · τ 2) {σ1 · σΛYπ(r1Λ) + S1ΛTπ(r1Λ),σ2.σΛYπ(r2Λ) + S2ΛTπ(r2Λ)} , (4) 2 The SiΛ is the tensor operator and Yπ(r) = e μr ( 1− e 2 ) . (5) The experimental BΛ value has been obtained theoretically by the relation BΛ = < ΨN |HN |ΨN > < ΨN |ΨN > − < Ψ|H|Ψ > < Ψ|Ψ > , (6) where, Ψ is the full wavefunction of the hypernucleus, ΨN is the ground state wavefunction of A-1 nucleons. The H and HN are the hamiltonians for the hypernucleus and its core, H = HN − h̄ 2mΛ ∇ 2 Λ + A−1