Model tests of cluster separability in relativistic quantum mechanics

A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster separability, whereby symmetries and conservation laws that hold for a system of particles also hold for isolated subsystems. Cluster separability can be restored by means of a recursive construction using unitary transformations, but implementation is difficult in practice, and the quantitative extent to which the Bakamjian-Thomas approach violates cluster separability has never been tested. This paper provides such a test by means of a model of a scalar probe in a three-particle system for which (1) it is simple enough that there is a straightforward solution that satisfies Poincar\'e invariance and cluster separability, and (2) one can also apply the Bakamjian-Thomas approach. The difference between these calculations provides a measure of the size of the corrections from the Sokolov construction that are needed to restore cluster properties. Our estimates suggest that, in models based on nucleon degrees of freedom, the corrections that restore cluster properties are too small to effect calculations of observables.Comment: 13 pages, 15 figure

Periods of activity cycles in late-type stars

The mean magnetic field dynamo theory is utilized to obtain the qualitative dependence of the period of activity on the angular velocity of rotation for stars with sufficiently extensive convective shells. The dependence of the cycle period on the spectral class is also discussed

Phase Transitions in liquid Helium 3

The phase transitions of liquid Helium 3 are described by truncations of an exact nonperturbative renormalization group equation. The location of the first order transition lines and the jump in the order parameter are computed quantitatively. At the triple point we find indications for partially universal behaviour. We suggest experiments that could help to determine the effective interactions between fermion pairs.Comment: 4 pages, 6 figures, LaTe

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that the equivalence holds for models that satisfy cluster separability. The generalized Bakamjian Thomas construction is used in most applications, even though it only satisfies cluster properties for systems of less than four particles. Different forms of dynamics are related by unitary transformations that remove interactions from some infinitesimal generators and introduce them to other generators. These unitary transformation must be interaction dependent, because they can be applied to a non-interacting generator and produce an interacting generator. This suggests that these transformations can generate complex many-body forces when used in many-body problems. It turns out that this is not the case. In all cases of interest the result of applying the unitary scattering equivalence results in representations that have simple relations, even though the unitary transformations are dynamical. This applies to many-body models as well as models with particle production. In all cases no new many-body operators are generated by the unitary scattering equivalences relating the different forms of dynamics. This makes it clear that the various calculations used in applications that emphasize one form of the dynamics over another are equivalent. Furthermore, explicit representations of the equivalent dynamical models in any form of dynamics are easily constructed. Where differences do appear is when electromagnetic probes are treated in the one-photon exchange approximation. This approximation is different in each of Dirac's forms of dynamics.Comment: 6 pages, no figure

Theoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropolone

Theoretical models of hydrogen bonding and proton transfer in the ground (S0) and lowest excited ππ∗ singlet (S1) states of tropolone are developed in terms of the localized OH...O fragment model and ab initio three‐dimensional potential energy surfaces (PESs). The PESs for proton transfer in the S0 and S1 states are calculated using ab initio SCF and CIS methods, respectively, with a 6–31G basis set which includes polarization functions on the atoms involved in the internal H bond. The Schrödinger equation for nuclear vibrations is solved numerically using adiabatic separation of the variables. The calculated values for the S0 state (geometry, relaxed barrier height, vibrational frequencies, tunnel splittings and H/D isotope effects) agree fairly well with available experimental and theoretical data. The calculated data for the S1 state reproduce the principal experimental trends, established for S1←S0 excitation in tropolone, but are less successful with other features of the dynamics of the excited state, e.g., the comparatively large value of vibrationless level tunnel splitting and its irregular increase with O...O excitation in S1. In order to overcome these discrepancies, a model 2‐D PES is constructed by fitting an analytical approximation of the CIS calculation to the experimental vibrationless level tunnel splitting and O...O stretch frequency of tropolone–OH. It is found that the specifics of the proton transfer in the S1 state are determined by a relatively low barrier (only one doublet of the OH stretch lies under the barrier peak). Bending vibrations play a minor role in modulation of the proton transfer barrier, so correct description of tunnel splitting of the proton stretch levels in both electronic states can be obtained in terms of the two‐dimensional stretching model, which includes O...O and O–H stretching vibration coordinates only. © 1994 American Institute of Physics

Hyperfine Level Splitting for Hydrogen-Like Ions due to Rotation-Spin Coupling

The theoretical aspects of spin-rotation coupling are presented. The approach is based on the general covariance principle. It is shown that the gyrogravitational ratio of the bare spin-1/2 and the spin-1 particles is equal unity. That is why spin couples with rotation as an ordinary angular momentum. This result is the rigorous substantiation of the cranking model. To observe the phenomenon, the experiment with hydrogen-like ions in a storage ring is suggested. It is found that the splitting of the $1 ^2!S_{1/2}, F=1/2$ hyperfine state of the $^{140}{\rm Pr}^{58+}$ and $^{142}{\rm Pm}^{60+}$ ions circulating in the storage ring ESR in Darmstadt along a helical trajectory is about 4.5 MHz. We argue that such splitting can be experimentally determined by means of the ionic interferometry.Comment: 6 pages, final versio