Evolution of Nuclear Shells due to the Tensor Force

Abstract

The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments. DOI: 10.1103/PhysRevLett.95.232502 PACS numbers: 21.60.ÿn, 21.10.ÿk, 21.30.Fe, 21.65.+f Shell structure characterizes finite quantum many-body systems. Atomic electrons confined by the Coulomb potential are subject to a well-known shell structure. For nuclei, since Mayer and Jensen [1], the shell structure has played a major role in clarifying nuclear structure. Recently, much progress has been made in the structure of exotic nuclei, which have rather extreme ratios of proton number (Z) to neutron number (N). Naturally, what new features can be found in their shell structure is of great and general interest.Along these lines, in this Letter, we present the variation of the nuclear shell structure due to the tensor force. The nucleon-nucleon (NN) interaction is originally due to meson exchange processes as predicted by Yukawa [2], and its tensor-force part is one of the most distinct manifestations of this meson exchange origin. As we shall show, the tensor force does indeed change the shell structure in a unique and robust way throughout the nuclear chart. The tensor force has been discussed over many decades. Its contribution to the spin-orbit splitting has been discussed, for instance, by Arima and Terasawa in terms of the second-order perturbation [3]. The importance of the tensor force for the nuclear binding energy has been demonstrated, for instance, by Pudliner et al. [4]. We shall show, in this Letter, how single-particle levels are changed systematically by the tensor force in the first order. The tensor force itself has certainly been included in various numerical calculations as one of the channels of the realistic nuclear force. Its first-order effect was discussed in individual cases, e.g., for 15 C and 16 O in [5]. In other early attempts, a possible tensor-force effect on the reduction of the spinorbit splitting was discussed in [6] with an example in the Os-Pb region [7]. The purpose of this Letter is, however, to present, for the first time, an analytic relation and a robust general feature, as well as concrete examples in close relation to experiments.The change of the shell structure, or the shell evolution, may have different origins. We focus upon the shell evolution due to the tensor force in this Letter. It is well known that the one-pion exchange process is the major origin of the tensor force, which is written aswhere~1 ;2 s 1;2 denotes the isospin (spin) of nucleons 1 and 2, K means the coupling of two operators in the brackets to an angular momentum (or rank) K, Y denotes the spherical harmonics for the Euler a...

Coupling of the proton-hole and neutron-particle states in the neutron-rich48K isotope

“…[7]. This systematic trend is similar to that observed in the Ca isotopes and has been explained in terms of the interactions between the nucleons in the selected proton and neutron orbitals located near the Fermi surface [2]. For the N = 29, 48 K isotope, which is the subject of this report, the predominant proton-hole excitations are coupled to the single valence neutron in the lowest available orbital; i.e., the νp 3/2 state.…”

“…In particular, neutron-rich nuclei with nucleon numbers close to the magic ones have become a testing ground for models of exotic systems (see, e.g., [1,2]). One area of special interest concerns the isotopes around doubly-magic 48 Ca.…”

Chiral three-nucleon forces and the evolution of correlations along the oxygen isotopic chain

“…In general, we find values evenly spread between 70% and 90% of the independent particle model. The smaller values of SFs are obtained at low separation energies and involve transitions to/from 14,22,24 O. These isotopes present reduced particle-hole neutron gaps and therefore allow for stronger correlations at the Fermi surface.…”

“…(14), the matrix D couples single particle states to more complex intermediate configurations, while K and C are their unperturbed energies and interaction matrices. For the closed subshell isotopes we exploit the third order algebraic diagrammatic construction [ADC(3)] scheme, which is the best compromise between computational efforts and accuracy.…”

Physics Program at the RIBF with MINOS

“…These shell modifications have mostly been characterised through systematic studies of low-lying states of unstable nuclei (see examples in [25,26]). A comprehensive picture of the shell evolution as a function of neutron and proton number is not yet reached even though an appreciable number of theoretical works has been performed and several microscopic mechanisms related to fundamental aspects of the nucleonnucleon interaction are currently discussed candidates to be at the origin of shell evolution [27][28][29][30][31].…”