789 research outputs found
On the theory of beta-radioactivity IV : The polarization of beta-rays emitted by aligned nuclei in allowed transitions
The consequences of alignment of nuclei, which show allowed Ă-transitions, are investigated. A general formula is derived for the transition probability of an allowed β-transition, in which the direction of emission of electron and neutrino, the polarization of the electron and the orientation of the nuclear spin are taken into account. The calculations have been made for a Hamiltonian for the β-interaction, which is an arbitrary "mixture" of the five invariants of the Dirac theory. The influence of the nuclear charge has, however, been neglected. From this formula the following results are immediately obtained:
The angular distribution of the β-radiation remains spherically symmetric if the nuclei are aligned, so that the alignment cannot be detected in this way.
The emitted β-radiation is polarized and the degree of polarization follows from the general formula. If we take the special case that the interaction Hamiltonian is of the tensor or the axial vector type and if the β-rays are emitted perpendicular to the direction of the nuclear spin of completely aligned nuclei with nuclear spin ji, the degree of polarization is given by: a) 1/Eif ji = jf + 1, b) 1/E(ji + 1), if ji = jf,c)ji/E(ji + 1), if ji = ji - 1. (E is the relativistic energy of the electrons, E â 1 for small kinetic energies; jf gives the spin of the final nucleus)
On the theory of beta-radioactivity III : The influence of electric and magnetic fields on polarized electron beams
The influence of electric and magnetic fields on the spin orientation (polarization) of electrons in a beam is calculated according to the Pauli spin theory and the Dirac theory. For the cases, where the field is perpendicular or parallel to a polarized electron beam, the following results are found.
Transverse electric field. In the non-relativistic approximation the spin orientation remains constant in space, even if the beam is deflected; the relativistic formula gives for the ratio of the rotation of the spin orientation and the angle of deflection of the beam: Ekin/E (ratio of kinetic energy and total energy, i.e., including the rest mass).
Transverse magnetic field. The spin orientation does not change in relation to the direction of propagation.
Longitudinal electric field. Though the beam is accelerated (or retarded) the spin orientation remains constant in space.
Longitudinal magnetic field. The spin orientation rotates about the direction of propagation.
It is shown that longitudinal polarization of electron beams (spins parallel or antiparallel to the direction of propagation) can be observed by means of an electric deflection of the beam and a scattering experiment in succession
A general theorem on the transition probabilities of a quantum mechanical system with spatial degeneracy
In the general case of a quantum mechanical system with a Hamiltonian that is invariant for rotations spatial degeneracy will exist. So the initial state must be characterized except by the energy also by e.g. the magnetic quantum number. Both for emission of light and electrons plus neutrinos (Ă-radioactivity) of a quantum mechanical system the following theorem is important: the total transition probability from an initial level with some definite magnetic quantum number mi to every possible final level belonging to one energy does not depend on mi. A simple proof is given for this theorem that embraces the case of forbidden transitions, which case is not covered by the usual proof. In the proof a Gibbs ensemble of quantum mechanical systems is used; the necessary and sufficient conditions for the rotational invariance of such an ensemble are give
Non-equilibrium thermodynamics and liquid helium II
The thermodynamics of irreversible processes, based on the O n s a g e r reciprocal relations, is applied to a system consisting of a mixture of two substances, of which one can go over into the other. The mixture is enclosed in two communicating reservoirs at different temperatures T and T + ÎT. The situations, in which systems arrive, when one, two or more differences between the values of state parameters in the two reservoirs are kept fixed, are called âstationary states of first, second etc. orderâ. For the stationary state of the first order with fixed ?T the corresponding pressure difference ?P is calculated. This gives the thermomolecular pressure effect
ÎP/ÎT = âQ*/v T = (h â U*)/v T,
where h and v. are the mean specific enthalpy and volume. This equation shows the connection with the mechano-caloric effect Q*, since application of the O n s a g e r relations shows that Q* is the âheat of transferâ i.e. the heat supplied per unit of time from the surroundings to the reservoir at temperature T, when one unit of mass is transferred from one reservoir to the other in the stationary state of the second order with fixed ÎP and ÎT = 0 (uniform temperature). Similarly U* is the âenergy of transferâ. The influence of ÎT on the relative separation (thermal effusion) and the âchemical affinityâ of the two components is also calculated. The heat conduction can be split into an âabnormalâ part due to the coupling of diffusion and chemical reaction between the components and a ânormalâ part also present when no reaction takes place.
The results can be applied to liquid helium II, considered in the two-fluid theory as a mixture of ânormalâ (1) and âsuperfluidâ (2) atoms, capable of the âchemical reactionâ 1 â 2. When it is supposed that chemical equilibrium is immediately established and that only superfluid atoms can pass through a sufficiently narrow capillary, the above mentioned equation leads . to G o r t e r's formula
v ÎP/ÎT = Ď1 âs/âĎ1,
where Ď1 is the fraction of normal atoms and s the mean specific entropy of the mixture. Under the same circumstances only the ânormalâ part of the heat conduction subsists
Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation
A generalized approach to the quantization of a large class of maps on a
torus, i.e. quantization via the von Neumann Equation, is described and a
number of issues related to the quantization of model systems are discussed.
The approach yields well behaved mixed quantum states for tori for which the
corresponding Schrodinger equation has no solutions, as well as an extended
spectrum for tori where the Schrodinger equation can be solved.
Quantum-classical correspondence is demonstrated for the class of mappings
considered, with the Wigner-Weyl density going to the correct
classical limit. An application to the cat map yields, in a direct manner,
nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the
correspondence limit.Comment: 36 pages, RevTex preprint forma
Monitoringplan Deltaprogramma Waddengebied : advies voor het toekostbestendig maken van het monitoringsysteem voor waterveilidheid in het Waddengebied
Het Waddengebied krijgt de komende eeuw te maken met klimaatverandering. Naarmate de zeespiegel verder stijgt, vraagt het intergetijdengebied van de Waddenzee meer zand en onttrekt dat naar verwachting aan de buitendeltaâs en de eilandkusten. Het is dan de vraag of het meegroeivermogen van het gebied voldoende is om de zeespiegelstijging bij te houden
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