Properties of finite nuclei are evaluated with two-nucleon (NN) and three-nucleon (NNN) interactions derived within chiral effective field theory. The nuclear Hamiltonian is fixed by properties of the A=2 system, except for two low-energy constants (LECs) that parametrize the short range NNN interaction, which we constrain with the A=3 binding energies. We investigate the sensitivity of 4He, 6Li, 10,11B, and 12,13C properties to the variation of the constrained LECs. We identify observables that are sensitive to this variation and find preferred values that give the best overall description. We demonstrate that the NNN interaction terms significantly improve the binding energies and spectra of mid-p-shell nuclei not just with the preferred choice of the LECs but even within a wide range of the constrained LECs. We find that a very high quality description of these nuclei requires further improvements to the chiral Hamiltonian.

The complete exact solution of the T 1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with nondegenerate single-particle levels and including isospin symmetry-breaking terms. The power of the method is illustrated with a numerical calculation for 64 Ge for a pf g 9=2 model space which is out of reach of modern shell-model codes. DOI: 10.1103/PhysRevLett.96.072503 PACS numbers: 21.60.Fw, 03.65.ÿw, 27.50.+e, 74.20.Rp Exactly solvable models (ESM) provide important insights into the structure of many-body quantum systems. The two main advantages of ESMs are: (1) they can describe in an analytical or exact numerical way a wide variety of elementary phenomena. (2) They can be and have been used as a testing ground for various many-body approaches.A particular class of ESMs, extensively used in nuclear physics, are the dynamical-symmetry models. In this case the Hamiltonian can be expressed in terms of Casimir operators of a chain of nested algebras. An example often used to introduce nuclear superconductivity [see, e.g., Ref.[1] ] is the rank-1 (Lie) algebra SU(2). Examples of dynamical-symmetry models associated with a rank-2 algebra are Elliott's SU(3) model of nuclear deformation [2] and the SO(5) model of T 1 isovector pairing between neutrons and protons [3] which has found many applications in nuclei [see, e.g., Ref. [4] ].The concept of quantum integrability, closely linked with exact solvability, goes beyond the limits of the dynamical-symmetry approach. A quantum system is integrable if there exist as many commuting Hermitian operators (integrals of motion) as quantum degrees of freedom [5]. The set of Casimir operators of a chain of nested algebras satisfies this condition.Dynamical-symmetry models are usually defined for degenerate single-particle levels. Lifting this degeneracy breaks the dynamical symmetry but may still preserve integrability. The pairing model with nondegenerate single-particle levels, of which an exact solution was found by Richardson in the 1960s [6], represents an example of an ESM with such characteristics. Recently, more general exactly solvable pairing models, both for fermions and for bosons, called Richardson-Gaudin (RG) models, have been proposed [7,8].The RG pairing models are based on rank-1 algebras: SU(2) for fermions and SU(1,1) for bosons. In this Letter we carry out the first step in extending the RG models to higher-rank algebras by considering a RG model based on the rank-2 algebra SO(5). The model Hamiltonian describes a two-component system consisting of neutrons and protons interacting through an isovector (T 1) pairing force and distributed over nondegenerate orbits. This neutron-proton (np) pairing Hamiltonian with nondegenerate orbits has been studied by Richardson [9] who proposed an exact solution. However, it was shown subsequently that Richardson's solution is incorrect for more than two nucleon pairs [10] by explicitly solving the case of three-nucleon pairs. Independently, Links et al. derived an ex...

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We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on 24 Mg. The correct binding energy (within 2% of the full-space result) as well as lowenergy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space.The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.

The Scale Invariant Vacuum (SIV) theory rests on the basic hypothesis that the macroscopic empty space is scale invariant. This hypothesis is applied in the context of the Integrable Weyl Geometry, where it leads to considerable simplifications in the scale covariant cosmological equations. After an initial explosion and a phase of braking, the cosmological models show a continuous acceleration of the expansion. Several observational tests of the SIV cosmology are performed: on the relation between H 0 and the age of the Universe, on the m − z diagram for SNIa data and its extension to z = 7 with quasars and GRBs, and on the H ( z ) vs. z relation. All comparisons show a very good agreement between SIV predictions and observations. Predictions for the future observations of the redshift drifts are also given. In the weak field approximation, the equation of motion contains, in addition to the classical Newtonian term, an acceleration term (usually very small) depending on the velocity. The two-body problem is studied, showing a slow expansion of the classical conics. The new equation has been applied to clusters of galaxies, to rotating galaxies (some proximities with Modifies Newtonian Dynamics, MOND, are noticed), to the velocity dispersion vs. the age of the stars in the Milky Way, and to the growth of the density fluctuations in the Universe. We point out the similarity of the mechanical effects of the SIV hypothesis in cosmology and in the Newtonian approximation. In both cases, it results in an additional acceleration in the direction of motions. In cosmology, these effects are currently interpreted in terms of the dark energy hypothesis, while in the Newtonian approximation they are accounted for in terms of the dark matter (DM) hypothesis. These hypotheses appear no longer necessary in the SIV context.

A Nilsson mean-field plus extended pairing interaction Hamiltonian with many-pair interaction terms is proposed. Eigenvalues of the extended pairing model are easy to obtain. Our investigation shows that one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the three- and higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the (154-171)Yb isotopes shows that the extended pairing model is applicable to well deformed nuclei.

Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.