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In addition, there are two new relationship types between use and misuse cases [Alexander]:

for both Pee and Pee elastic scattering. If this were the case, then, in contrast to (12.64), we would have

(5.64)

A threaten relationship from a misuse to a use case indicates that the misuse case exploits one or more vulnerabilities within the use case. A mitigate relationship from a use to a misuse case indicates that the use case prevents, thwarts, detects, or otherwise responds to the misuse case.



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where X == (i Iii !) and we have assumed that (! If I !) = (i Irl i) = 0 (which is often the case for symmetry reasons). The atomic Hamiltonian also simplifies in this case. Setting the zero of energy halfway between the two atomic levels for convenience, the atomic Hamiltonian becomes (5.65) where w is the frequency of the atomic transition between I i) and I!). When adopting the two-level atom approximation, one often represents the atomic operators by Pauli matrices. These matTices are defined by





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The most striking difference between the two angular distributions, (12.59) and (12.62), is that Pee scattering vanishes for cos () = 1, whereas Pee scattering does not. With our definition of (), see Fig. 12.9, this correspor1ds to backward scattering of the beam particle. We could have anticipated these results from the helicity arguments we used to interpret previous calculations. The by now familiar pictures are shown in Fig. 12.10. Backward Pee scattering is forbidden by angular momentum conservation. In fact, the process Pee -+ Pee proceeds entirely in a J = 1 state with net helicity + 1; that is, only one of the three helicity states is allowed. This is the origin of the factor t in (12.64). With our definition of (), the allowed amplitude is proportional to ll (()) = !(1 - cos ()), see (6.39), in agreement with result (12.61).

The regular relationship types extend, include, generalize, and use can also be used between misuse cases and between misuse cases and misusers [SO00]. Table 15.10 shows the available node and relationship types in misuse case diagrams.

a == I !)(i I, ax==a+a t ,

(5.66) (5.67) (5.68) (5.69)

526 15

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Elastic vee- and jiee- scattering can also proceed via a weak neutral current interaction (see Fig. 12.11) which interferes with the charged current interaction (Fig. 12.8a). This is discussed in Section 13.5. However, high-energy neutrino beams are predominantly v" (or jilL)' and so the most accessible (charged current) purely leptonic scattering process is

ay == ia - ia t ,

FROM/TO Actors Use cases ACTORS generalize USE CASES use generalize extend include Misusers Misuse cases threaten generalize use generalize extend include MISUSERS MISUSE CASES

LET MATTER BE!

(12.65)

Pauli matrices are very convenient to use in calculations because they have commutators that resemble vector multiplication of Cartesian vectors:

The figure on page 527 shows the Non-repudiation of origin component of the Common Criteria for IT Security Evaluation [ISO15408] as a misuse case diagram. In this diagram, the topmost use case represents a regular functional requirement, that is, that the proposed system must be able to transmit information from an originator to a recipient. The transmission commits the originator to further action, for example providing payment later. The diagram also shows a misuse case that represents a security threat to the transmission function, that is, that the originator can later deny having provided the information, and thereby renege on their commitment. Below the misuse case is another use case, which represents a corresponding security requirement, that is, that the system must be able to prove the identity of the originator of the transmitted information. In the figure, use cases thereby represent both regular functional requirements and security requirements, but they are shown with the same icons because they both represent required system behaviour. See figure on page 527.

(5.70)

260 8

(i.e., inverse muon decay). Here, there is no neutral current contribution, and so the cross section is given just by (12.59).

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