<i>Ab initio</i> calculation of charge-symmetry breaking in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:math> and 8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Λ</mml:mi></mml:math> hypernuclei
Hoai Le, J. Haidenbauer, Ulf-G. Meißner, A. Nogga
Abstract
The $\mathrm{\ensuremath{\Lambda}}$ separation energies of the isospin triplet $_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{He}, _{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{Li}^{*}, _{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{Be}$, and the $T=1/2$ doublet $_{\mathrm{\ensuremath{\Lambda}}}^{8}\mathrm{Li}, _{\mathrm{\ensuremath{\Lambda}}}^{8}\mathrm{Be}$ are investigated within the no-core shell model. Calculations are performed based on a hyperon-nucleon potential derived from chiral effective field theory at next-to-leading order. The potential includes the leading charge-symmetry breaking (CSB) interaction in the $\mathrm{\ensuremath{\Lambda}}N$ channel, whose strength has been fixed to the experimentally known difference of the $\mathrm{\ensuremath{\Lambda}}$ separation energies of the mirror hypernuclei $_{\mathrm{\ensuremath{\Lambda}}}^{4}\mathrm{He}$ and $_{\mathrm{\ensuremath{\Lambda}}}^{4}\mathrm{H}$. It turns out that the CSB predicted for the $A=7$ systems is small and agrees with the splittings deduced from the empirical binding energies within the experimental uncertainty. In the case of the $A=8$ doublet, the computed CSB is somewhat larger than the available experimental value.