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...

The possible existence of deeply bound nuclear K states is investigated theoretically for few-body systems. The nuclear ground states of a K Ϫ in 3 He, 4 He, and 8 Be are predicted to be discrete states with binding energies of 108, 86, and 113 MeV and widths of 20, 34, and 38 MeV, respectively. The smallness of the widths arises from their energy-level locations below the ⌺ emission threshold. It is found that a substantial contraction of the surrounding nucleus is induced due to the strong attraction of the Iϭ0 K N pair, thus forming an unusually dense nuclear medium. Formation of the Tϭ0 K Ϫ 3 HeϩK 0 3 H state in the 4 He ͑stopped K Ϫ , n) reaction is proposed, with a calculated branching ratio of about 2%.

The limit of neutron-rich nuclei, the neutron drip line, evolves regularly from light to medium-mass nuclei except for a striking anomaly in the oxygen isotopes. This anomaly is not reproduced in shell-model calculations derived from microscopic two-nucleon forces. Here, we present the first microscopic explanation of the oxygen anomaly based on three-nucleon forces that have been established in few-body systems. This leads to repulsive contributions to the interactions among excess neutrons that change the location of the neutron drip line from (28)O to the experimentally observed (24)O. Since the mechanism is robust and general, our findings impact the prediction of the most neutron-rich nuclei and the synthesis of heavy elements in neutron-rich environments.

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