General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N*(J) ↔ Nπ-transitions (N*(J) is thenucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N* contributions to the s-channel amplitudes correspond to J = JπN only ( JπN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤ JπN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S31, P31( JπN = 1/2) and P33, D33(JπN = 3/2), but our approach – to P33 and D33 only. The comparison of these results with the data of the partial wave analysis on the S31-amplitude in the ∆(1232)-region shows the better agreement for the present approach.

Superintegrability of (2n + 1)-body choreographies, n = 1,2,3,…,∞ on the algebraic lemniscate by Bernoulli (inverse problem of classical mechanics)

For one 3-body and two 5-body planar choreographies on the same algebraic lemniscate by Bernoulli we found explicitly a maximal possible set of (particular) Liouville integrals, 7 and 15, respectively, (including the total angular momentum), which Poisson commute with the corresponding Hamiltonian along the trajectory. Thus, these choreographies are particularly maximally superintegrable. It is conjectured that the total number of (particular) Liouville integrals is maximal possible for any odd number of bodies [Formula: see text] moving choreographically (without collisions) along given algebraic lemniscate, thus, the corresponding trajectory is particularly, maximally superintegrable. Some of these Liouville integrals are presented explicitly. The limit [Formula: see text] is studied: it is predicted that one-dimensional liquid with nearest-neighbor interactions occurs, it moves along algebraic lemniscate and it is characterized by infinitely many constants of motion.

Oscillatory persistent currents in quantum rings

The density functional theory is used to study persistent currents in two-dimensional quantum rings containing several electrons. We find a series of magic numbers for the total angular momentum of electrons in the strong magnetic field and show that changes in the angular momentum of electrons lead to persistent current oscillations. We suggest an empirical expression for the period of persistent current in quantum rings and examine the effect of Coulomb interaction on the properties of persistent currents.

Ридберговские состояния радикала ОН

We study Rydberg states of radical in adiabatic (rotational Born–Oppenheimer) approximation as well as in the inverse limit. The needed value, d = 0.833, of the OH+cation’s dipole moment was calculated using the RCCSD(T)/aug-cc-pV5Zmethod. Our calculations show that a dipole moment of this magnitude influence weakly on the energies of the Rydberg states. The exception are the states originating from s-states in the central-symmetric field, which are influenced significantly by the cation dipole moment. In the inverse Born–Oppenheimer limit, we study in detail the dependence of the Rydberg spectrum upon the total angular momentum, J, of the molecule. This dependence substantially differs from the well-known dependence, ∼J(J + 1), of the rotating top energy on its total momentum.