Two particles interacting via a contact interaction on $S^2$

Abstract

We consider two particles interacting via a contact interaction that are constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary precision and for arbitrary angular momentum. We show how the non-inertial frame leads to non-trivial solutions for different angular momenta. Our results represent an extension of the finite-volume Lüscher formulas but now to a non-trivial geometry. We apply our results to predict the spectrum of select two-nucleon halo nuclei and compare with experimental results.

24 pages, 6 figures

References in corpus (4)

• First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li
• Halo nuclei 6He and 8He with the Coulomb-Sturmian basis
• Ground state energy of the interacting Bose gas in two dimensions: an explicit construction
• Universal Properties of Weakly Bound Two-Neutron Halo Nuclei