The c -Term of the Tucson-Melbourne Three-Body Force: To Be or Not to Be

Abstract

In Faddeev calculations of 3 H we study the dependence of the binding energy on the three nucleon force. We adopt the 2π-exchange Tucson-Melbourne three-nucleon force and investigate phenomenologically the dependence on the strength of the individual three-body force operators (a-, b-, c-and dterms). While the a-term provides a tiny contribution the b-and d-terms are important to gain the experimental binding energy. We find two solutions for the c-term, one around the value used in the Tucson-Melbourne model and a new one close to zero, which supports the recent recommendation of chiral perturbation theory that the short-range c-term should be dropped.

Isospin dependence of the three-nucleon force

“…(3.27) is numerically smaller in size than the corresponding subleading charge-symmetry-conserving contribution in eq. (3.33) as well, although the reason is now completely #11 In [38] contributions of various pieces of the Tucson-Melbourne 3NF to the 3 H are considered. While the so-called a-term (it corresponds to the c1-term in the chiral 3NF) was found to provide only a tiny contribution, the b-(∝ c3) and d-terms (∝ c4) give about 250 .…”

“…The Lagrangian density defined in Eq. (38) gives rise to the following relevant terms in the nucleon rest-frame system:…”