Effect of three-body ΛNN long-range potential in nuclear matter

doi:10.1016/0550-3213(67)90007-7

Nuclear Physics B

Volume 3, Issue 4, 1 November 1967, Pages 380-386

https://doi.org/10.1016/0550-3213(67)90007-7 Get rights and content

Abstract

The effect of the two-pion-exchange ΛNN force on the binding of a Λ in nuclear matter is considered using perturbation theory. It is pointed out that the contribution of the dominant noncentral part of the ΛNN potential to B_Λ is extremely sensitive to nucleon-nucleon (NN) correlation. The long-range part of the ΛNN force (for ΛN distances > 0.6 fm) gives a repulsive contribution of a few MeV, but this number can not be predicted unless the NN correlation function is accurately known.

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ΣΛ Conversion in <inf>Λ</inf>3H and in other S-shell hypernuclei
1973, Nuclear Physics, Section A
The binding energy of the Λ-particle in the $J = 12 and 32$ states of _Λ³H and the doublet and quartet Λ-d scattering lengths are calculated with a separable ΛN-ΣN potential matrix, fitted to experimental data in ΛN and ΣN channels. The dependence of the results on ΛΣ coupling is explained in terms of a perturbative treatment of ΛΣ coupling. This perturbative treatment is also applied in a qualitative discussion of the effects of ΛΣ conversion in the J = 0 and 1 states of _Λ⁴H-_Λ⁴He and in the $J = 12$ state of _Λ⁵He. The importance of three-body ΛNN forces caused by ΣΛ coupling is stressed.
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The binding-energy data of the s-shell hypernuclei and the low-enery Λp scattering data are analysed in terms of a simple model which employs both a Λ-nucleon (ΛN) and a Λ-nucleon-nucleon (ΛNN) potential. The ΛN potential is chosen to be central, with a hard core of radius 0.45 fm and an intrinsic range of 2.0 fm, and to have a charge-symmetry-breaking component. Two types of ΛNN potential are considered in this investigation, one being a phenomenological central potential and the other being the strongly non-central potential obtained by Bhaduri, Loiseau and Nogami using a two-pion-exchange mechanism. The ΛN potential fitted to the B_Λ values for _Λ³H, _Λ⁴H and _Λ⁴H and _Λ⁴He and to the Λp scattering data (total cross sections and forward-backward asymmetries) has a rather small degree of spin dependence and a strength in odd-parity states which is only 20–70% of that in even-parity states. This potential gives overbinding for _Λ⁵He by more than 2 MeV. The effect on this overbinding problem of introducing a ΛNN potential into the analysis is carefully examined. It is shown that a repulsive central ΛNN potential does reduce the calculated value for B_Λ(_Λ⁵He) but that this is only by a negligible amount, for general reasons which are discussed. For the non-central ΛNN potential, it is found that a proper account of nucleon-nucleon correlations in the hypernuclear wave functions can modify its effect greatly, to an extent depending on the cut-off radius d adopted in this potential. For small values of d(0.45 to 0.7 fm), this non-central ΛNN potential actually increases the overbinding; for $d⪆0.7 fm$ , it does give net repulsion but the reduction found in B_Λ(_Λ⁵He) is far too small to yield agreement between the calculated and experimental values.
A microscopic approach to Λ9Be
1972, Nuclear Physics, Section B
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^∗: Supported by the National Research Council of Canada.

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Nuclear Physics B

Abstract

References (10)

Nucl. Phys.

Phys. Rev.

Nucl. Phys.

Nuclear Interaction of the Hyperon

Phys. Rev.

Cited by (19)

Two-meson exchange hyperonic three-body forces and consequences for neutron stars

Reaction matrix calculation of <sup>4</sup>He including Δ degrees of freedom

ΣΛ Conversion in <inf>Λ</inf><sup>3</sup>H and in other S-shell hypernuclei

Phenomenological study of s-shell hypernuclei with ΛN and ΛNN potentials

A microscopic approach to Λ<sup>9</sup>Be

Nucleon-nucleon correlation and two-pion-exchange three-body force in nuclear matter