Double-Λ hypernuclei and the nuclear medium effective ΛΛ interaction

Abstract

We fit the 1 S 0 ΛΛ interaction in the nuclear medium to the masses of the experimentally known double−Λ hypernuclei: 6 ΛΛ He, 10 ΛΛ Be and 13 ΛΛ B. We derive this effective interaction from OBE Jülich ΛΛ-type potentials and using both HartreeFock and variational approaches. We find that the inclusion of ΛΛ 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−Λ hypernuclei to the ωΛΛ coupling and the form factor at the σΛΛ vertex. We also use this effective interaction to predict binding energies and pionic decay widths of heavier double−Λ hypernuclei, not discovered yet. Finally, we discard the existence of 1 S 0 ΛΛ bound states provided the ΛΛ − ΞN coupling can be neglected.

ΛΛbond energy from the Nijmegen potentials

“…From the resulting ⌳⌳ binding energies, a quite large ⌳⌳ bond energy of around 4 to 5 MeV emerged, contrary to expectations from SU(3) [5]. A series of theoretical works, based either on phenomenological S =−2 baryon-baryon interactions or realistic ones, have studied the properties of double-⌳ hypernuclei for more than 30 years [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Diquark-diquark correlations in theS01ΛΛpotential

“…Approaches to the ΛΛ interaction potential have been pursued at the baryon and quark levels. At the baryon level phenomenological (in the sense of reproducing some indirect experimental information) meson-exchange (σ and ω) potentials have been constructed [5][6][7]. At the quark level, gluon dominant (only one-gluon exchange between quarks), pure chiral (only meson exchanges between quarks) and chiral constituent quark (gluon plus meson exchanges) models have been used [8].…”

Pionic decay of Λ hypernuclei in a continuum shell model

“…The Λ wave function in the initial hypernucleus, R (Λ) , is obtained from a WS potential [33] to account for the mean Λ-nuclear core interaction, with parameters compiled in Table 1. The nucleon dynamics will be studied in detail in Sect.…”

“…To improve the existing calculations [33,37] would require a correct treatment of the ΛΛ pair inside of the nuclear medium. Thus, the recent work of Ref.…”