Solids angle

Integrating over all solid angles and using equation (Al.fi.lSf and equation (A 1.6.1 O ) we find... 

For themial light, the iiumber of transitions per second induced by stimulated emission integrated over solid angles, is equal to The total emission, which is the sum of the stimulated and spontaneous emission, may be obtained by letting A A + 1 in the expression for stimulated emission, giving... 

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

Here/(9,(p, i ) is the probability distribution of finding a molecule oriented at (0,cp, li) within an element dQ of solid angle with the molecular orientation defined in tenus of the usual Euler angles (figure B 1.5.10). 

The cross section for scattering into the differential solid angle dD centred in the direction (9,(l)), is proportional to the square of the scattering amplitude ... 

Let the rate of the event under study be R. It will be proportional to the cross section for the process under study, a, the incident electron current, Iq, the target density, n, the length of the target viewed by the detectors,, the solid angles subtended by the detectors, Aoi and A012 the efficiency of the detectors, and... 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

In TOF-SARS [9], a low-keV, monoenergetic, mass-selected, pulsed noble gas ion beam is focused onto a sample surface. The velocity distributions of scattered and recoiled particles are measured by standard TOF methods. A chaimel electron multiplier is used to detect fast (>800 eV) neutrals and ions. This type of detector has a small acceptance solid angle. A fixed angle is used between the pulsed ion beam and detector directions with respect to the sample as shown in figure Bl.23.4. The sample has to be rotated to measure ion scattering... 

Figure Bl.24.3. Layout of a scattering experiment. Only primary particles that are scattered within the solid angle O spaimed by the solid state detector are counted.

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... 

Number of lesl particles scattered by one field dfy(i i jf. particle into unit solid angle per unit time dS2 Current of incident beam... 

In the Lab frame, the projectile is scattered by 0 and the target, originally at rest, recoils tlirough angle 9g. The number of particles scattered into each solid angle in each frame remains the same, the relative speed v is now and j- = N v in each frame. Hence... 

A number of experimental and physical realities cloud this rosy picture. Inevitably many emitted photons are lost due to the finite solid angle over which the fluorescence is collected, losses at the various filters, lenses, windows, and other... 

Solid angle steradian sr The solid angle which, having its vertex in... 

Solid angle over which lumi- F(P,DF) Standard Gibbs energy of ac- ag ... 

Solid angle over which radi- Standard hydrogen electrode SHE... 

The energy that is radiated spreads out over a solid angle and is therefore proportional to r". We saw in Sec. 10.2 that this energy is proportional to hence E varies with r . ... 

Brightness. This is defined as the power emitted per unit area of the output mirror per unit solid angle and is extremely high compared with that of a conventional source. The reason for this is that, although the power may be only modest, as in, for example, a 0.5 mW helium-neon gas laser, the solid angle over which it is distributed is very small. 

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