Abstract
Recent Λ3H lifetime measurements in relativistic heavy ion collision experiments have yielded values shorter by (30±8)% than the free Λ lifetime τΛ, thereby questioning the naive expectation τ(HΛ3)≈τΛ for a weakly bound Λ hyperon. Here we apply the closure approximation introduced by Dalitz and coworkers to evaluate the Λ3H lifetime, using Λ3H wavefunctions generated by solving three-body Faddeev equations. Our result, disregarding pion final-state interaction (FSI), is τ(HΛ3)=(0.90±0.01)τΛ. In contrast to previous works, pion FSI is found attractive, reducing further τ(HΛ3) to τ(HΛ3)=(0.81±0.02)τΛ. We also evaluate for the first time τ(nΛ3), finding it considerably longer than τΛ, contrary to the shorter lifetime values suggested by the GSI HypHI experiment for this controversial hypernucleus.
Highlights
Recent 3ΛH lifetime measurements in relativistic heavy ion collision experiments have yielded values shorter by (30±8)% than the free Λ lifetime τΛ, thereby questioning the naive expectation that τ (3ΛH) ≈ τΛ for a weakly bound Λ hyperon
We comment briefly on the calculations in Refs. [15, 16]: (i) Rayet and Dalitz (RD) [15], using a closure approximation to sum over the final nuclear states reached in the 3ΛH weak decay, reduced the 3ΛH lifetime calculation to the evaluation of a 3ΛH exchange matrix element defined in Sect. 2 below
Evaluating the pion final-state interaction (FSI) in the three-body 3ΛH decays to p + d + π− and n + d + π0 final states is more involved than done above for the two-body decay modes because the nuclear bound state wavefunction ψN has to be replaced by continuum nucleon wavefunctions
Summary
Λ hyperon is bound to a deuteron core by merely BΛ(3ΛH)=0.13±0.05 MeV, presents in the absence of two-body ΛN bound states the lightest bound and one of the most fundamental hypernuclear systems [1]. (i) Rayet and Dalitz (RD) [15], using a closure approximation to sum over the final nuclear states reached in the 3ΛH weak decay, reduced the 3ΛH lifetime calculation to the evaluation of a 3ΛH exchange matrix element defined in Sect. With a suitable choice of the closure energy, and including a questionable 1.3% repulsive pion FSI decay-rate contribution (see below), they obtained τ (3ΛH) ≈ 0.95 τΛ. In a genuinely ab-initio calculation used a wavefunction obtained by solving three-body Faddeev equations with NN and Y N Nijmegen soft-core potentials to evaluate all three π− decay channels: 3He + π−, d + p + π− and p + p + n + π−. We study here τ (3ΛH) within a closure-approximation calculation in which the associated exchange matrix element is evaluated with wavefunctions obtained by solving 3ΛH three-body Faddeev equations. Our estimate suggests a value of τ (3Λn) considerably longer than τΛ, in strong disagreement with the shorter lifetime reported in Ref. [23]
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