Probing three-nucleon-force effects via (p,2p) reactions

Abstract

We propose to use proton knockout reactions (p,2p) from a deeply bound orbit as a new probe into threenucleon-force (3NF) effects. The remarkable advantage of using (p,2p) reaction is that we can choose an appropriate kinematical condition to probe the 3NF effects. We analyze (p,2p) reactions on a 40 Ca target within the framework of distorted-wave impulse approximation with a g-matrix interaction based on chiral two-and three-nucleon forces. The chiral 3NF effects significantly change the peak height of the triple differential cross section of (p,2p) reaction. We also clarify the correspondence between the (p,2p) cross sections and the inmedium pp cross sections. PACS numbers: 21.30.Fe, 24.10.Eq, Three-nucleon forces (3NFs) are one of the essential elements which dictate a variety of the dynamics in few-nucleon systems, finite nuclei, and nuclear matter. Without 3NFs, even the saturation property of nuclei can not be explained, and equation-of-state of neutron star is unrealistic [1]. For nuclear structure calculations, the 3NF gives the last piece to reproduce binding energies of light nuclei [2]. For nucleondeuteron elastic scattering, 3NF effects are clearly observed in cross sections at middle and large angles, in which the twonucleon force (2NF) is relatively small [3], and are also detected in spin observables [4]. In heavier systems, 3NF effects may be represented by the density-dependence of the nucleon-nucleon (NN) effective interaction (the g-matrix interaction) [5,6]. Very recently, nucleus-nucleus elastic scattering is investigated as a probe of 3NF effects at high density [7]. 3NF effects reduce the cross sections at large scattering angles significantly, where higher than normal density is produced in the overlapping area between the projectile and target densities.Besides three-nucleon correlations via ordinary NN interaction, 3NFs may arise from intermediate excitations of nonnucleonic degrees of freedom, typically an isobar ∆. A pioneering work for two-pion exchange 3NFs by Fujita and Miyazawa [8] was followed by various phenomenological models, such as Tucson-Melbourne [9] and Urbana [10] models, which have been used frequently to investigate the roles of 3NF effects in nuclear systems. In the last two decades, the theoretical description of 3NF has progressed considerably by chiral effective field theory (Ch-EFT) [11][12][13], in place of phenomenological 3NFs. Ch-EFT enables us to organize two-, three-, and many-body forces consistently and systematically. The chiral interactions are applied to microscopic calculations of few-nucleon scattering [14], finite nuclei [15,16], and nuclear matter [17][18][19]. Furthermore, the g-matrix interaction including the chiral 3NF contributions has been constructed and applied to describe many-body reactions [20][21][22].In this Letter, we investigate chiral 3NF effects in nuclear many-body reactions, in particular, the proton knockout reaction (p,2p). This reaction is suitable for studying effective nucleon-nucleon interactions since (p,2p) reactions at ...

Reexamination of microscopic optical potentials based on multiple scattering theory

“…In addition to the conventional nucleon-nucleon interactions, modern interactions including three-body-force (3BF) effects have been developed [12][13][14][15]. Those interactions are also used to investigate the 3BF effects for nucleus-nucleus scattering [16,17] and proton knockout reactions [18]; the 3BF effects are found not to be essential for nucleon-nucleus elastic scattering. Furthermore, great efforts have been done to derive optical potentials by ab initio approach, though it is still restricted to reaction systems containing a very limited number of nucleons [19].…”

Three-nucleon force contribution in the distorted-wave theory of (d,p) reactions

“…Finally, when most of the present calculations were finished, Minomo et al published their investigation of 3N effects in (p,2p) reactions at high energies within the distorted-wave impulse approximation [25]. They came to the conclusion that the 3N contribution is small in most cases apart from some of those with special kinematic conditions for knockout of protons from deeply bound orbits.…”

Microscopic effective reaction theory for direct nuclear reactions

“…We do not find a significant 3NF effect on these observables because the proton elastic scattering probes mainly the surface region of the target nucleus in which the density is low and the 3NF is expected to be small. On the other hand, we see a somewhat large 3NF effect on nucleus-nucleus elastic and inelastic scattering cross sections [24,25]. For details, see the references above as well as the proceedings paper for CNR*15 by K. Minomo and his collaborators.…”