Chiral symmetry and three-nucleon forces

Abstract

After a brief review of the role three-nucleon forces play in the few-nucleon systems, the chiral-perturbation-theory approach to these forces is discussed. Construction of the (nominal) leading-and subleading-order Born terms and pion-rescattering graphs contributing to two-pion-exchange three-nucleon forces is reviewed, and comparisons are made of the types of such forces that are used today. It is demonstrated that the short-range c-term of the Tucson-Melbourne force is unnatural in terms of power counting and should be dropped. The class of two-pion-exchange three-nucleon forces then becomes rather uniform.

Local three-nucleon interaction from chiral effective field theory

“…We note that the local two-pion-exchange terms appear also in the Tucson-Melbourne NNN interaction [20]. The analogous terms to c 1 , c 3 and c 4 are present in particular in the TM ′ interaction [21,22]. The TM ′ parameters are denoted by a ′ , b and d with the relation to the above c 1 , c 3 and c 4 given by…”

“…An interaction local in coordinate space may be more convenient for some methods. In fact, most of the NNN interactions used in few-body calculations, such as the Tucson-Melbourne (TM ′ ) [21,22], Urbana IX (UIX) [19] or Illinois 2 (IL2) [26], are local in coordinate space. The two alternatively regulated contact interactions lead to different three-nucleon matrix elements.…”

“…At the same time, it is known that details of the NNN interaction are important for nuclear structure applications. For example, the Urbana IX [19] and the Tucson-Melbourne [20,21,22] NNN interactions perform differently in mid-p-shell nuclei [16,23,24] although their differences appear to be minor. In the Green's function Monte Carlo (GFMC) calculations with the AV18 NN potential [25], the best results for p-shell nuclei up to A = 10 are found using the Illinois NNN interaction that augments the Urbana IX by a two-pion term from the Tucson-Melbourne NNN interaction and by three-pion terms that in the χEFT appear beyond the N 3 LO [26,27].…”

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

“…Stimulated by [29] we studied the binding energy of 3 A study of pion range -short range 3NF terms is underway [30] where are predicted by chiral perturbation theory.…”

“…Chiral perturbation theory has been successfully applied in the πN system [24,25] and it is already playing an important role in its application to the NN system as well [26][27][28] In [29] it recommended that the pion range -short range part of the c-term of the TM 2π-exchange 3NF should be dropped, based on arguments from chiral perturbation theory. In doing this the pion range -short range part of the c-term remains, which is of the same type than the a-term.…”