Cross-sectional area of the projectil

Injury to people due to fragments usually occurs either because of penetration by small fragments or blunt trauma by large fragments. Baker et al. (1983) review skin penetration and suggest that it is a funaion o(AfM where. 4 is the cross-sectional area of the projectile along its trajectory zndM is the mass of the projectile. Injury from blunt projectiles is a function of the fragment mass and velocity. Very limited information is available for this effect. 

Pair is the density of air, Ap is the cross-sectional area of the projectile, Co is an empirical drag coefficient, and u is the relative velocity of the projectile with respect to tiiat of the wind w. 

The energy produced by a unit volume, defined as the energy density , is an important property for both propellants and explosives. For rocket and gun propulsions, the aerodynamic drag during flight in the atmosphere increases as the cross-sectional area of these projectiles increases. The reduction in cross-sectional area is... 

Consider the situation (Fig. 10.4) where a beam of projectile nuclei of intensity < >0 particles/second is incident upon a thin foil of target nuclei with the result that the beam is attenuated by reactions in the foil such that the transmitted intensity is < j particles/second. We can ask what fraction of the incident particles disappear from the beam, that is, react, in passing through the foil. Let us assume the beam intersects an area A on the foil. We can then assert that the fraction of beam particles that is blocked (reacts) is the fraction of the area A that is covered by target nuclei. If the foil contains N atoms /cm2, then the area a that is covered by nuclei is LI (atoms/ cm2) x a (cm2) x (the effective area subtended by one atom) (cm2/atom). This latter term, the effective area subtended by one atom, is called the cross section, a, for the reaction under study. Then the fraction of the area A that is blocked is a/A or LI (atoms/cm2)a(cm2/atom). If we say the number of projectile nuclei absorbed per unit time is A< >, then we have... 

The ionization cross section can be written, in terms of the projectile energy, as a product of the ionization probability and the area deflned by the impact parameter b, as. 

For heavy projectiles, the area around the target nucleus, where deflection effects take place, is small compared to the geometrical area presented for excitation or ionization of the electron the Bohr radius for the K-shell of an antiproton is mjntp)(aQ)Zj. But at energies low compared to the potentials in the vicinity of the nucleus these deflection effects are important enough to show up, not just in cross sections differential in the impact parameter, but also in total cross sections. The reason is that at projectile speeds slow compared to the circulating electrons excitation and ionization takes place at small impact parameters. 

To describe quantitatively the interactions of bombarding particles with atomic nuclei the concept of cross section was introduced. In this sense the term "cross section" is a measure of the probability of occurrence of a given process under certain conditions. To illustrate the concept of nuclear cross section, it can be visualized as the cross-sectional (or target) area presented by a nucleus to an incident neutron. If we further visualize the nucleus as a sphere of radius r cm, and think of the neutrons as point projectiles, then the target area or cross section o of each nucleus is a = 7T r cm. This simple picture illustrates only one type of cross section, the geometrical, and considers only collisions of neutrons with target nuclei. But it serves to derive a formula for cross section that can be extended to any kind of interaction of neutrons with atomic nuclei. Today, there are experimental values for many kinds of cross sections (absorption, scattering, activation, etc.) for different materials, and several types of each (microscopic, macroscopic, atomic, nuclear, differential). 

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

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