Sohd angle

The strength of a photon—molecule interaction is deterrnined by the frequency-dependent cross section 0 (v), expressed in cm for absorption and related to a(y) in equation 1 or by the differential cross section (k5(y) jin units of cm /sr for scattering (14). The latter specifies the likelihood that active species scatter some portion of the incident laser fluence (photons /cm ) into a viewing soHd angle, AQ, measured in steradians (Fig. 1). The cross sections can be expressed as in equation 5 ... 

This simulation can be achieved in terms of a source—sink relationship. Rather than use the gas concentration around the test object as a target parameter, the test object can be surrounded by a sink of ca 2-7T soHd angle. The solar panel is then maintained at its maximum operating temperature and irradiated by appropriate fluxes, such as those of photons. Molecules leaving the solar panel strike the sink and are not likely to come back to the panel. If some molecules return to the panel, proper instmmentation can determine this return as well as their departure rates from the panel as a function of location. The system may be considered in terms of sets of probabiUties associated with rates of change on surfaces and in bulk materials. 

Theoiy permits the approximation of the maximum size of a bubble that can adhere to a submerged horizontal surface if the contact angle between bubble and sohd (angle formed by solid-hquid and liquid-gas interfaces) is known [Wark, ]. Phys. Chem.,. 37, 623 (1933) Jakob, Mech. Eng., 58, 643 (1936)]. Because the bubbles that actually rise from a surface are always considerably smaller than those so calculated and inasmuch as the contact angle is seldom known, the theoiy is not direc tly useful. 

Photon fluence rate ( ) The rate of photon fluence. Four times the ratio of the photon flow, volume element containing the point under consideration divided by the surface of that sphere, Sk. (f,f Lpdm, simphfied expression F = 4 constant over the sohd angle considered). The SI unit is m s. ... 

Spherical radiance Same as radiant exitance, M. It is the integration of the radiant power, P, leaving a source over the sohd angle and over the whole wavelength range. The SI unit is W m . ... 

Static lenses accepting electrons from a higher soHd angle [5, 6], By using a molecular beam directed towards a surface, relatively high local pressures (up to 10" mbar) can be achieved in front of a sample, while the base pressure of the analyzer chamber is stiU in the mbar range. Such experiments are carried... 

In QENS experimenis, one measures the double-differential cross-section, d cr/ df2 dE, which represents the number of neutrons scattered into the sohd angle df2 with energy in the range dE. The amphtude of the scattered wave varies between nuclei (because of different isotopes or spins), so that averages have to be performed for each element. The total cross-section per scatterer is obtained by integrating over energies and sohd angles... 

The distance between the sample on the reflector surface and the detector can be made small, thus the soHd angle for detection is large. 

The need to correct can be better understood considering that the total sohd angle variation along the usefiil radius is 20 % while the expeaed energy resolution of the instrument is 2 % at 120 KeV... 

The look up table is defined in such a way that the difference m sohd angle between two adjacent areolas is less then 1%[2]... 

Collision termc ksJ j f x,m ) pa m m )dm. It represents the source of photons in the phase space volume dxdm in relation to photons with propagation direction m that are scattered at x in the direction m (see Fig. 8D). c ksj[x,m )dxdm is the rate at which photons within dxdm are scattered, andpsi m m ) is the probabifity density for their scattering direction to be [Pg.27]

L (x,(w) at location x, in the direction flux density due to photons with direction (O crossing the surface normal to (O at location x (per unit of the sohd angle io3 and per unit of the frequency interval Av). To hnk the intensity and the distribution function, we will consider the radiant energy 5Q that crosses the surface dS (perpendicular to m) in the direction O) during At ... 

A modification of this method (O Keeffe, 1979) calcuiates a weighted CN, where the contribution of each tece of the domeUn is weighted in proportion to the soHd angle subtended by that face at the centre WON = SSn/S = 4n/Si where is the largest solid angle. 

Knowledge of the visible reflectance of underlying land and ocean surfaces is necessary for calculating the diffuse radiation field. The reflectance and transmittance depend upon both the angles of incidence and reflection or transmission. For an angular beam of radiation with radiance within a cone of sohd angle dco around... 

If we multiply the Boltzmann equation by SI and then integrate over all sohd angles we find that... 

Normally, one assumes that the differential reaction cross-section does not depend on the azimuthal angle. Hence, one takes advantage of the axial symmetry of the collision and works with differential cross-sections integrated over . Thus, one uses the element of sohd angle dm = 27t sin 0 dO ... 

Step 2. After irradiation and appropriate radioactive decay of the sample and standards, these are measured on either a well-t3q)e or a coaxial large volume Ge(Li) y-ray detector system coupled to a PC-based y-spectroscopy system (explained in Sect. 6.3.4) to find out the energies of the y-rays in the observed spectrum (and hence the corresponding isotopes of the elements present in the sample). The distance of the sample fi om the detector (and hence the sohd angle) is adjusted depending on the coimt rate which should be about 100-500 counts per second. 

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