A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

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118 conclusions been tested and found to have only a relatively poor performance. More massive external shielding and SiPM produced by different manufacturesis are under discussion. The observed increase in dark count rate can introduce an additional complication: Low light level detection does not require large dynamic range SiPMs. Consequently the number of pixels in the detector matrix can be kept relatively small what would result in an appropriate high PDE due to the resulting large fill factor. On the other hand spontaneous pixel activation is stimulated on irradiated SiPM giving rise to a reduced effective number of active pixels due to the time needed to charge the intrinsic capacitor trough the quenching resistor (dead time). Dynamic range is reduced as a consequence in irradiated SiPM and this effect has to be taken into account to choose the optimum number of APDs for applications in high radiation environments.
T H E O R E T I C A L B A C K G R O U N D a.1 overview Observations always involve theory. — Edwin Hubble In this appendix, we will derive in detail the general structure of the differential cross-section for the reaction e(p, e ′ K + )Y analyzed in this thesis. Our aim is providing a complete, unified and pedagogical reference within the text itself, where the constrains imposed by the known electromagnetic interaction on the cross-section can be clearly understood. The derivation is mostly based on references [7, 92, 93, 94, 95, 96, 97, 98, 99, 100] conveniently adapted for our particular case. Starting from a simple example in non relativistic multichannel scattering theory, the concept of transition charge density is introduced. Relativistic electron scattering off the proton is then studied by considering the dynamics of its spinorial wave function in the external electromagnetic field produced by the evolving hadronic system, effectively described by a transition current density. Following Bjorken and Drell, Green functions are introduced inspired by Huygens principle and used to derive the integral equation satisfied by the electron field. The scattering amplitude is then immediately obtained by a simple projection of the electron wave function at t = +∞ onto the plane wave representing a possible final state. It is argued that if the interaction is weak, the state of the outgoing electron can be sufficiently well described by its initial wave function in the integral equation for the scattering amplitude (what defines the Born approximation). The result has the suggestive structure of two transition currents hocked together, the well known electron current and the structurally rich hadronic current. The squaring of this amplitude is written in terms of the contraction of the leptonic and hadronic tensors: The first one, fully determined by the electron kinematics and the second one, codifying the dynamics of the reaction channel. Gauge invariance is used to establish some constrains on the components of these tensors. The general form of the cross-section, resulting from the remaining terms in the contraction, is then explicitly written by expressing the components of the leptonic tensor as functions of the electron variables and exploiting Lorentz covariance of the hadronic tensor to extract the azimuthal angle dependency. A natural separation in terms of virtual photon flux and virtual photoproduction cross-section is obtained by comparing electro and 119 A
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M E A S U R E M E N T O F T H E U N
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A B S T R A C T The new stage of th
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C O N T E N T S i kaon electroprodu
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Part I K A O N E L E C T R O P R O
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4 introduction Lorentz invariance.
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6 introduction appear in the K + Λ
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8 introduction there was almost no
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10 introduction This allows us to w
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12 introduction K ¡p γ ∗ Λ(Σ
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14 introduction means of the isobar
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16 introduction amount of resonance
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18 introduction photo and electropr
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20 introduction 1.6 previous experi
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22 introduction Figure 9: Total cro
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E X P E R I M E N TA L S E T U P A
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2.3 target 27 Figure 11: Schematic
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2.4 kaos spectrometer 2.4 kaos spec
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M MWPC L F 2.4 kaos spectrometer 31
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Table 3: Spectrometers properties 2
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2.4 kaos spectrometer 35 Figure 16:
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2.4.5.1 Read out electronics 2.4 ka
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2.4 kaos spectrometer 39 channels.
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2.5 kaos single arm trigger 41 64MB
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2.6 spectrometer b 43 Figure 23: Sc
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2.7 coincidence setting 45 to be im
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2.8 data acquisition and analysis s
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2.9 kinematical setting 49 (GeV/c)
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52 detection efficiencies and data
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A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

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