Projectile energy dependence

The cross-section curve a(E) gives the dependence of the nuclear cross-section on the projectile energy, E. The measured energy spectra of emitted particles or the excitation curve N(Eq) wiU depend on the depth profile N(x) of the analyzed isotope and on the cross-section curve (t(E(x)), where E(x) gives the energy of the projectiles at a depth x. Evaluation of the depth profile N (x) from measured energy spectra or excitation curves often requires a tedious evaluation procedure if the cross-section curve has a complex structure. It is simplified for two special types of behavior of the cross-section curve ... 

Gun propellants are designed to provide large quantities of gas which is used to propel projectiles at high kinetic energies. The velocity of the projectile is dependent on the rate at which the gas is produced, which in turn is dependent on the amount of chemical energy released, and the efficiency of the gun tj as shown in Equation 8.1. 

As an example of the energy dependence of the total cross section for positron-atom scattering, a schematic of the data for helium atoms is shown in Figure 2.1, together with the corresponding data for electrons. It is seen that [Pg.41]

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

The first hints that the energy dependence of a + near E was different for positrons and electrons came from the results of Fromme et al. (1986, 1988) for helium and molecular hydrogen, which revealed that energy dependence than <7+(e ) and that the former falls below the latter very close to E. This type of behaviour is consistent with the expected Wannier laws for the two projectiles, though the energy width of the positron beam and other instrumental effects (see section 4.3 for a discussion of the operation of the ion extractor in this experiment) meant that the measurements were insufficiently precise for a value of the exponent to be extracted. 

Impact parameter dependence of the projectile energy loss... 

Fig. 6. The impact-parameter dependence of energy loss in collision of hydrogen and carbon ions with gold atom at a projectile energy E = 0.5 MeV/a.u. For comparison the first-order perturbation results (the doted curves) and that for equivalent negative projectiles (the dashed curves) are also shown.

For one collision partner at rest prior to the collision, the kinematics are depicted in Fig. 2. The exact amounts of transferred momentum and energy depend on the details of the collision, for example, impact parameter b and scattering angle 6. In the laboratory system, the energies E] and E2 of the projectile and the target atom, respectively, after the collision are given as... 

It is a function of the projectile energy Eq and also depends on collision parameters like projectile mass m, target atom mass m2, projectile and target nuclear charge Z e and Z2C, where e is the elementary charge, and the angle of ion incidence... 

The reaction cross-section depends on the projectile energy as shown in Figure 14.2. The curves obtained for the partial reaction cross-section as a function of projectile energy are known as excitation functions or excitation curves. 

The stripping process energy dependence. The peculiar excitation functions of deuteron reactions were discovered soon after the first use of deuterons as projectiles in nuclear reactions. Lawrence, McMillan, and Thornton, found, by activation methods, that the rate at which the cross section of the d, p) reaction increased with energy was lower than that expected from the usual formula for penetration of charged particles. For Cu they found measurable activities for energies as low as 2 Mev. These results suggested that the mechanism of the... 

The fusion cross section (Tfus depends on the projectile energy Ep, the height of the fusion barrier E, and the angular momentum I of the system. The survival probability of the compound nucleus is determined by the excitation energy E, which yields the number of evaporated neutrons x For each step of neutron evaporation there is a strong competition between neutron evaporation and fission given by the ratio of neutron to fission width IEf. 

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