Separation energies of light $$\varLambda $$ hypernuclei and their theoretical uncertainties
Hoai Le, J. Haidenbauer, Ulf-G. Meißner, A. Nogga
Abstract
Abstract Separation energies of light $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> hypernuclei ( $$A\le 5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> ) and their theoretical uncertainties are investigated. Few-body calculations are performed within the Faddeev-Yakubovsky scheme and the no-core shell model. Thereby, modern and up-to-date nucleon-nucleon, three-nucleon and hyperon-nucleon potentials derived within chiral effective field theory are employed. It is found that the numerical uncertainties of the few-body methods are well under control and an accuracy of around 1 keV for the hypertriton and of better than 20 keV for the separation energies of the $$^{\,4}_{\varLambda }\textrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow/> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mspace/> <mml:mn>4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mtext>He</mml:mtext> </mml:mrow> </mml:math> and $$^{\,5}_{\varLambda }\textrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow/> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mspace/> <mml:mn>5</mml:mn> </mml:mrow> </mml:msubsup> <mml:mtext>He</mml:mtext> </mml:mrow> </mml:math> hypernuclei can be achieved. Variations caused by differences in the nucleon-nucleon interaction are in the order of 10 keV for $$^{\,3}_{\varLambda }\textrm{H}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow/> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mspace/> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mtext>H</mml:mtext> </mml:mrow> </mml:math> and no more than 110 keV for $$A=4,\,5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> hypernuclei, when recent high-precision potentials up to fifth order in the chiral expansion are employed. The variations are smaller than the expected contributions from chiral hyperon-nucleon-nucleon forces which arise at the chiral order of state-of-the-art hyperon-nucleon potentials. Estimates for those three-body forces are deduced from a study of the truncation uncertainties in the chiral expansion.