Cross section, differential

The differential fc-quark production cross-section is measured as a function of muon transverse momentum and pseudorapidity. The flavor composition is determined by performing a fit in each analysis bin. The binning is chosen such that the number of events in every bin is sufficient for a stable fit and at the same time a maximum purity is achieved. The purity V is defined as the fraction of selected reconstructed events in each bin that have the respective generated quantity in the same bin and is calculated based on the MC simulation  

Here NrJf is the number of reconstructed MC events with muon transverse momentum (or pseudorapidity) in bin i. The reconstrutced muons are matched to generated muons (based on Ai ) in order to determine N fJ Sgen i.e. the number of events with both reconstructed and generated muon transverse momentum (pseudorapidity) in bin i. The purity takes into account bin-to-bin migration caused by resolution effects and contributions from fake muons in ( -events. 

The templates for the fraction fit are determined individually for each bin. While the distributions are similar in all bins of muon pseudorapidity, a shift to higher 

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Pack R T 1978 Anisotropic potentials and the damping of rainbow and diffraction oscillations in differential cross-sections Chem. Phys. Lett. 55 197... 

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... 

The measurable quantity in a three dimensional scattering experiment is the differential cross section da (9)/dQ. This is defined as... 

This differential cross section may be integrated over scattering angles to define an integral cross section a as follows ... 

The total differential cross-section (equation (B1,3,A11 + equation (B1,3,A211 is then... 

The differential cross section for inelastic collisions exciting the nth state of the target then takes the fomi... 

In this expression, factors that describe the incident and scattered projectile are separated from the square modulus of an integral that describes the role of the target in detemiining the differential cross section. The temi preceding the... 

The Bom approximation for the differential cross section provides the basis for the interpretation of many experimental observations. The discussion is often couched in temis of the generalized oscillator strength. 

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... 

The differential cross section da.j-/ dj for — /transitions from any one of the g-initial states is defined as [dR-j-/ / gjj, the transition frequency per unit incident current. Since current is the number of particles... 

The basic relationship satisfied by the differential cross sections for the forward and reverse /transitions is... 

Since this agrees with the first Bom differential cross section for (in)elastic scattering, Femii s Rule 2 is therefore valid to first order in the interaction F. 

For ion-point dipole D interactions, only A J = +1 transitions are allowed. For ion-point quadnipole Q interactions only A J = 0, +2 transitions are allowed. The Bom differential cross sections for j transitions are... 

The transition matrix T(b)f is therefore the probability of scattering particles with impact parameter b. B2.2.6.4 DIFFERENTIAL CROSS SECTIONS... 

Wlien expanded as a series of Legendre polynomials /Jj (cos 0), tire differential cross section has the following form... 

For pure S-wave scattering, the difFerential cross section (DCS) is isotropic. For pure P-wave scattering, tlie DCS is symmetric about 0 = n/2, where it vanishes the DCS rises to equal maxima at 0 = 0, ti. For combined S- and P-wave scattering, the DCS is asynnnetric with forward-backward asynnnetry. 

The differential cross section for scattering of both the projectile and target particles into direction 0 is... 

For femhons with half-mtegral spin s, the statistical weights are = s/(2s + 1) and = (.s + l)/(2.s + 1). The differential cross section for fennion-fennion scattering is then... 

Symmetry oscillations therefore appear in die differential cross sections for femiion-femiion and boson-boson scattering. They originate from the interference between imscattered mcident particles in the forward (0 = 0) direction and backward scattered particles (0 = 7t, 0). A general differential cross section for scattering... 

The corresponding differential cross sections f will therefore exliibit interference oscillations. The integral cross sections are... 

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

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