Hadronic Effective Field Theory Applied to $\Lambda$-Hypernuclei

Abstract

In the present work, the approach of Furnstahl, Serot, and Tang (FST) is extended to the region of nonzero strangeness in application to single-particle states in single $\Lambda$-hypernuclei. To include $\Lambda$'s, an additional contribution to their effective lagrangian is systematically constructed within the framework of FST. The relativistic Hartree (Kohn-Sham) equations are solved numerically, and least-square fits to a series of experimental levels are preformed at various levels of truncation in the extended lagrangian. The ground-state properties of any $\Lambda$-hypernuclei are then predicted. In addition, ground-state $Lambda$-particle-nucleon-hole splittings are calculated where appropriate, and the apporach is calibrated against a calculation of the $s_{1/2}$-doublet splitting in the nucleus $^{32}_{15}P_{17}$.