Mass kinetic energy

Several reactivity trends are worth noting. Reactions that are rapid frequently stay rapid as the temperature or centre-of-mass kinetic energy of the reactants is varied. Slow exothenuic reactions almost always show behaviour such tliat... 

Energy—Capacity for doing work. "Potential energy" is the energy inherent in a mass because of its spatial relation to other masses. "Kinetic energy" is the energy possessed by a mass because of its motion (SI unit joules) ... 

Laboratory angular distributions of the scattered He(23S) intensity measured with the described apparatus at various center-of-mass kinetic energies are shown in Fig. 3, which is a reproduction of a figure in Brutschy et al.30... 

Figure 3. Newton diagrams for the two sets of measurements shown in Figs. 4 and 5. On left, He beam source is cooled to liquid-nitrogen temperature and ground-state helium beam is at room temperature, whereas beam temperatures are interchanged on right. This gives same center-of-mass kinetic energy but different laboratory energies for scattered atoms.

The kinetic energy has been divided into two contributions an internal kinetic energy (the first term) and an external center-of-mass kinetic energy Tc m., where... 

For the rigid system of particles we may use (8.66) and (8.65) to reformulate the expression for the centre-of-mass kinetic energy as... 

The threshold is the difference of the electron and positron affinities of the species A. Knowledge of the center-of-mass kinetic energy of the colliding species, and the measurement of that of the receding species yields the positron affinity. A competing reaction is Ps formation, but this produces a neutral product A that will not interfere. 

If ffij, Ei j, Epj, and Uj are the flow rates of mass, kinetic energy, potential energy, and internal energy for the th process stream, then the total rate at which energy is transported into or out of the system by this stream is... 

Once all the projectile impact parameter grid has been generated as described in Section 3.2. one obtains the projectile center of mass kinetic energy loss for each trajectory as... 

In (10) the V(tj) axe the usual grad operators expressed in the Cartesian components of tj and the first term represents the centre-of-mass kinetic energy and the eigenfunctions of this, the translation-free Hamiltonian are denoted (t). 

The Schrodinger equation for the system when the center of mass kinetic energy term has been eliminated can be expressed as... 

Chemiluminescence in the 450- to 360-nm range resulting from collisions of P" ions with H2 or D2 molecules (center-of-mass kinetic energies Ec.m. = 2.3 to 12.2 eV) was Identified with the A- X emission of PH+ and PD+ ions. A spectral analysis has been performed at the maximum cross section (Ecm. = 6.4 eV) by comparison with computer-simulated spectra which were based on the spectroscopic constants of [7, 9, 10] besides the already known 0- 1, 0 0, and 1- 0 bands, some new bands, 1- 1 for PH+ and 2 0, 1- 2, 0 2 for PD+, could be localized. Additional experiments were carried out to verify that the observed emission is indeed due to the chemiluminescent exchange reaction P ( P, D)+H2 PH-"(A 2A)+H and not to collisionally excited PH+ impurities in the P+ beam [11]. 

Kinetic Energy Measurements. The centre of mass kinetic energy release... 

Notice that two quantum numbers specify the exciton eigenstates, eqn (6.13) or eqn (6.16) the principle quantum number, n, and the (pseudo) momentum quantum number, K (or fUj). For every n there are a family of excitons with different centre-of-mass momenta, and hence different centre-of-mass kinetic energy. Odd and even values of n correspond to the relative wavefunction, tl>n r), being even or odd under a reversal of the relative coordinate, respectively. We refer to even and odd parity excitons as excitons whose relative wavefunction is even or odd imder a reversal of the relative coordinate. This does not mean that the overall parity of the eigenstate (eqn (6.12)), determined by both the centre-of-mass and relative wavefiictions, is even or odd. The number of nodes in the exciton wavefunction, V rt( ), is n— 1. Figure 6.2 illustrates the wavefunctions and energies of excitons in the effective-particle model. 

ION CENTER OF MASS KINETIC ENERGY, eV Fig. 12. Cross section for 0 formation from the reaction of excited (02 ) ions with Ne as a function of translational energy. 

This energy field caused the ions to separate according to their mass (kinetic energy = m r). Thus, the time of flight of ion in a specified drift space ( >) and a single accelerating region (a) was... 

The last term is the kinetic energy due to the mean translational motion. The term in N on the right side expresses the fact that the MD average of the center-of-mass kinetic energy is not... 

We now disregard the centre-of-mass kinetic energy which vanishes in the rest frame of the baryon. The Hamiltonian appears as the sum of two three-dimensional harmonic oscillators. We thus find the eigenvalues... 

Equations (3.12)-(3.14) specify the so-called full-folding form of the first-order optical potential. Note that the effective two-body energy, e, depends upon the struck nucleon initial energy,, as well as upon the integration variable P and the intermediate excited state rest energies of the projectile proton and target nucleon. The dependence on the center-of-mass kinetic energy in intermediate states... 

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