Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double $\Lambda$ Hypernuclei and the Nuclear Medium Effective
  $\Lambda\Lambda$ Interaction   We fit the $^1 S_0 \Lambda\Lambda$ interaction in the nuclear medium to the
masses of the experimentally known double-$\Lambda$ hypernuclei:
$^{\phantom{6}6}_{\Lambda\Lambda}$He, $^{10}_{\Lambda\Lambda}$Be and
$^{13}_{\Lambda\Lambda}$B. We derive this effective interaction from OBE
J\"ulich $\Lambda\Lambda$-type potentials and using both Hartree-Fock and
variational approaches. We find that the inclusion of $\Lambda\Lambda$
correlations in the variational scheme leads to significant differences and a
better understanding of the dynamical features of the system. We investigate
the sensitivity of the binding energies and the mesonic decay widths of the
above double-$\Lambda$ hypernuclei to the $\omega \Lambda\Lambda $ coupling and
the form factor at the $\sigma \Lambda\Lambda$ vertex.
  We also use this effective interaction to predict binding energies and pionic
decay widths of heavier double-$\Lambda$ hypernuclei, not discovered yet.
Finally, we discard the existence of $^1 S_0$ $\Lambda\Lambda$ bound states
provided the $\Lambda\Lambda-\Xi N$ coupling can be neglected.

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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin