Mass Frame Research Articles

A spark chamber with low mass frame

Spark chamber plates of expanded polystyrene sandwiched between aluminium foils allow the construction of a “massless” chamber with 75 μm thick Melinex frames.

Collision energy dependence of angular distributions for vibrational excitation of H 2 by He

Angular distributions for the vibrational excitation of H 2 by He have been obtained assuming that H 2 is a rotationless anharmonic oscillator. A set of two coupled-channel scattering equations has been solved for all orbital angular momenta, for the n = 0 to n = 1 transition. Increasing the collision energies from twice to six times the first vibrational excitation energy changes intensities in the center of mass frame from backward peaked into forward peaked.

Coordinates and Democracy in the N-Body Problem

It is shown that the construction of ``democratic'' subgroups of O3N−3 in the N-body problem is greatly facilitated by the ``proper'' choice of relative vectors in the center of mass frame. The word ``proper'' is taken to mean that the set of (N − 1) relative vectors forms a basis for reduced representations of the corresponding democracy subgroup of SN. The imposition of this requirement easily leads us to the reduction chains O6⊃SU3⊃SO3rot and O9⊃SO31×SO32×SO33⊃SO3rot in the three- and four-body problems, respectively, and to O3N−3⊃SON−1×SO3rot in the N > 4 case.

Energy Levels and Lorentz Invariance

THE relativistic soundness of the quantum theoretical formula has been questioned by Synge1. In an interesting note, he derives instead the formula where m′ is the relativistic mass of the system (atom) in its initial state S′ in the initial rest frame (the centre of mass frame) and m is the lower energy state S of the system (mc2 being the proper energy in this state). The energies E′ and E are measured in the initial and final rest frame of the system. We do not in any way disagree with Synge, but wish to give a slightly different formulation of this question which, in a sense, preserves (1) by giving it an interpretation fully consistent with equation (2). This requires all the energies in equation (1) to be measured in the same frame.

Graphical Method of Illustrating Relativistic Conservation Laws

Graphical methods can be utilized to analyze relativistic free-particle interactions by representing the momentum of a free particle as a vector in two-dimensional momentum space. This vector is constrained to lie on the mass hyperbola for all inertial frames of reference. By employing the Lorentz invariance of the difference in the hyperbolic angles for any two vectors, one can analyze graphically free-particle interactions in the most convenient frame of reference. In particular two-particle interactions are studied in the laboratory and center of mass frames of reference.

Poles of the two-body Green function

The invariant contribution of a discrete intermediate state to the two-body field theoretic Green function is found and is shown, for the case of two interacting spinless particles of un­equal mass, to give rise to two distinct poles when the Green function in momentum space is expressed as an analytic function of the total two-body energy in the centre of mass frame. The general requirements of time reversal or parity invariance, or stability, are shown not to lead to any simplification that would allow the two poles to be combined into one in the invariant centre of mass energy squared complex plane.

Effect of Target Gas Temperature on the Scattering Cross Section

If a beam of particles is scattered by a gas or plasma, the differential scattering cross section that is observed experimentally may, in some cases, be altered a discernible amount by the random thermal motion of the target particles. To explore the feasibility of using this effect as a means of measuring high temperatures, or to correct for the temperature of the target in the event that the desired cross section must be measured at high temperatures, a theoretical study was made of the temperature dependence of the cross section. A general expression was obtained for the observed differential scattering cross section in the laboratory frame in terms of the differential cross section in the center-of- mass frame for the general case of arbitrary initial motion of the target. Detailed results for the temperature dependence are given for hardsphere scattering (which is also applicable to low-energy neutron scattering) and for Coulomb scattering, in the approximation in which the projectiles are light and rapidly moving, compared to the targets. For hard-sphere scattering the case of equal projectile and target mass is also considered. (auth)

Dispersion relations for photoproduction of mesons

The Feynman amplitude for the reaction γ + nucleon → → π + nucleon is simply related to a causal amplitude which satisfies dispersion relations. These are derived in the « natural » frame. The connection with the amplitudes in the centre of mass frame is discussed in detail.