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...

Understanding and predicting the formation of shell structure from nuclear forces is a central challenge for nuclear physics. While the magic numbers N = 2, 8, 20 are generally well understood, N = 28 is the first standard magic number that is not reproduced in microscopic theories with twonucleon forces. In this Letter, we show that three-nucleon forces give rise to repulsive interactions between two valence neutrons that are key to explain 48 Ca as a magic nucleus, with a high 2 + excitation energy and a concentrated magnetic dipole transition strength. The repulsive threenucleon mechanism improves the agreement with experimental binding energies. 21.60.Cs, 27.40.+z In nuclei certain configurations of protons and neutrons (nucleons) are observed to be particularly wellbound. These closed-shell or "magic" nuclei form the basis of the nuclear shell model (exact diagonalizations in spaces based on the observed shell structure [1]), which provides a key computational method in nuclear physics. Exploring the formation of shell structure and how these magic configurations evolve with nucleon number towards the drip lines is a frontier in the physics of nuclei, and a microscopic understanding from nuclear forces presents a major challenge for theory.The theoretical shortcomings in predicting shell structure are particularly evident in the calcium isotopes. While microscopic calculations with well-established twonucleon (NN) forces reproduce the standard magic numbers N = 2, 8, 20, one of the most striking failures is that they do not predict 48 Ca as a doubly-magic nucleus when neutrons are added to 40 Ca [1,2], making N = 28 the first standard magic number not reproduced in microscopic NN theories. As a result, phenomenological forces have been adjusted to yield a doubly-magic 48 Ca [3,4], and it has been argued these phenomenological adjustments may be largely due to neglected three-nucleon (3N) forces [5]. Recently, we have shown that 3N forces play a decisive role for the oxygen anomaly and can explain why 24 O is the heaviest oxygen isotope [6]. In this Letter, we present the first study of the impact of 3N forces on medium-mass nuclei. Our results demonstrate that oneand two-body contributions from 3N forces to valence neutrons, as well as extended valence spaces, are essential to understand shell structure in the calcium isotopes and N = 28 as a magic number based on nuclear forces. Three-nucleon forces were introduced in the pioneering work of Fujita and Miyazawa (FM) [7] and arise because nucleons are finite-mass composite particles that can also be excited by interacting with other particles. The longrange part of 3N forces is dominated by the FM 3N mechanism, where one nucleon virtually excites a second nucleon to the ∆(1232 MeV) resonance, which is de-excited by interacting with a third nucleon. Additional longrange and shorter-range 3N interactions are included naturally in chiral effective field theory (EFT) [8], which provides a systematic expansion for nuclear forces. The importance of chiral 3N fo...

The neutrino-nucleus reaction cross sections of 4 He and 12 C are evaluated using new shell model Hamiltonians. Branching ratios of various decay channels are calculated to evaluate the yields of Li, Be, and B produced through the -process in supernova explosions. The new cross sections enhance the yields of

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