Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Two and three nucleon induced photon absorption

We have investigated the mechanisms leading to two and three body photon absorption in nuclei. At photon energies around the pion production threshold we obtain a fraction of three body absorption of less than 10% of the total, contradicting previous theoretical claims that it dominates the absorption process. The strength of the three body channel grows smoothly with the photon energy reaching a maximum of about 60% of the total direct absorption at energies of the photon around 400 MeV.

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

Nonmesonic weak decay of the hypertriton

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3N scattering states, which are rigorous solutions of three-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion exchange together with heavier meson exchanges for the ¿N¿NN transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free ¿ decay rate. Integrated as well as differential decay rates are given. The p- and n-induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.

Correlations in hot asymmetric nuclear matter

Bulk and single-particle properties of hot hyperonic matter are studied within the Brueckner-Hartree-Fock approximation extended to finite temperature. The bare interaction in the nucleon sector is the Argonne V18 potential supplemented with an effective three-body force to reproduce the saturating properties of nuclear matter. The modern Nijmegen NSC97e potential is employed for the hyperon-nucleon and hyperon-hyperon interactions. The effect of temperature on the in-medium effective interaction is found to be, in general, very small and the single-particle potentials differ by at most 25% for temperatures in the range from 0 to 60 MeV. The bulk properties of infinite matter of baryons, either nuclear isospin symmetric or a Beta-stable composition that includes a nonzero fraction of hyperons, are obtained. It is found that the presence of hyperons can modify the thermodynamical properties of the system in a non-negligible way.

Bulk and single-particle properties of hyperonic matter at finite temperature

Bulk and single-particle properties of hot hyperonic matter are studied within the Brueckner-Hartree-Fock approximation extended to finite temperature. The bare interaction in the nucleon sector is the Argonne V18 potential supplemented with an effective three-body force to reproduce the saturating properties of nuclear matter. The modern Nijmegen NSC97e potential is employed for the hyperon-nucleon and hyperon-hyperon interactions. The effect of temperature on the in-medium effective interaction is found to be, in general, very small and the single-particle potentials differ by at most 25% for temperatures in the range from 0 to 60 MeV. The bulk properties of infinite matter of baryons, either nuclear isospin symmetric or a Beta-stable composition that includes a nonzero fraction of hyperons, are obtained. It is found that the presence of hyperons can modify the thermodynamical properties of the system in a non-negligible way.

Critical review of K- ppn bound states

We make a thorough study of the process of three-body kaon absorption in nuclei, in connection with a recent FINUDA experiment which claims the existence of a deeply bound kaonic state from the observation of a peak in the Lambdad invariant mass distribution following K- absorption on 6Li. We show that the peak is naturally explained in terms of K- absorption from three nucleons leaving the rest as spectators. We can also reproduce all the other observables measured in the same experiment and used to support the hypothesis of the deeply bound kaon state. Our study also reveals interesting aspects of kaon absorption in nuclei, a process that must be understood in order to make progress in the search for K- deeply bound states in nuclei.

Study of B0(s)→K0Sh+h′− decays with first observation of B0s→K0SK±π∓ and B0s→K0Sπ+π

A search for charmless three-body decays of B 0 and B0s mesons with a K0S meson in the final state is performed using the pp collision data, corresponding to an integrated luminosity of 1.0 fb−1, collected at a centre-of-mass energy of 7 TeV recorded by the LHCb experiment. Branching fractions of the B0(s)→K0Sh+h′− decay modes (h (′) = π, K), relative to the well measured B0→K0Sπ+π− decay, are obtained. First observation of the decay modes B0s→K0SK±π∓ and B0s→K0Sπ+π− and confirmation of the decay B0→K0SK±π∓ are reported. The following relative branching fraction measurements or limits are obtained $ B(B0→K0SK±π∓)B(B0→K0Sπ+π−)=0.128±0.017(stat.)±0.009(syst.),B(B0→K0SK+K−)B(B0→K0Sπ+π−)=0.385±0.031(stat.)±0.023(syst.),B(B0s→K0Sπ+π−)B(B0→K0Sπ+π−)=0.29±0.06(stat.)±0.03(syst.)±0.02(fs/fd),B(B0s→K0SK±π∓)B(B0→K0Sπ+π−)=1.48±0.12(stat.)±0.08(syst.)±0.12(fs/fd)B(B0s→K0SK+K−)B(B0→K0Sπ+π−)∈[0.004;0.068]at90%CL.

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.