Lect23_[Compatibility_Mode]

Lect23_[Compatibility_Mode] - Physics 344 Foundations of 21...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Carefully review chapter 23 in your Physics 272 textbook, Matter & Interactions Volume II, 2 nd edition. ecitation Recap Question 1: The following particle decay does not occur. Which conservation law would be violated if it did? Recitation Recap A) 4-momentum conservation B) charge conservation K p n − + → + Λ C) electron-lepton number conservation D) meson number conservation E) baryon number conservation Answer: Assuming that the K- has sufficient kinetic energy when it strikes the proton, 4-momentum conservation can be satisfied. p n − → + Λ charge -1 + 1 = 0 + 0 OK aryon # 0 + 1 ≠ 1 + 1 violated K p n + → + Λ baryon # 0 + 1 ≠ 1 + 1 violated A photon collides with an electron that is initially at rest. What is the threshold photon energy for this particle production reaction? e e e e γ − − + − + → + + In terms of the photon energy we need to determine the system’s 4-momentum vector has lab-frame components. Actually, this is the system’s initial omentum vector but it does not change since sys E m E P ⇒ + ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ¡ 4-momentum vector, but it does not change since we assume the system is isolated from its surroundings. lab ⎢ ⎥ ⎣ ⎦ t threshold the kinetic energy of the three final- tate particles will be as At threshold, the kinetic energy of the three final state particles will be as small as possible. Note that it cannot be zero in the lab frame because the system’s momentum must be conserved. is smallest when the system’s internal kinetic 3 m ⎡ ⎤ It is smallest when the system s internal kinetic energy is zero. This means that the system’s kinetic energy is zero in its center-of-momentum frame. So, the components of the system’s sys ofM P ⇒ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ¡ 4-momentum vector in that frame are CofM ⎣ ⎦ Our two expressions for the system’s E m + ⎡ ⎤ 4-momentum in terms of the initial and final state variables give components in two different inertial coordinate frames. 2 2 ( ) sys sys sys b E P P P E m E ⇒ ⇒ ⇒ ⎢ ⎥ ⎢ ⎥ ⇒ ⋅ = + − ⎢ ⎥ ⎢ ⎥ ⎦ ¡ Nevertheless, we can use each to obtain expressions representing the frame-independent magnitude of the lab ⎣ ⎦ 3 m ⎡ ⎤ ⎥ system’s 4-momentum in terms of the initial and final state variables that we can equate and use to determine the reshold photon energy 2 9 sys sys sys CofM P P P m ⇒ ⇒ ⇒ ⎢ ⎥ ⎢ ⎥ ⇒ ⋅ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ¡ threshold photon energy....
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University.

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Lect23_[Compatibility_Mode] - Physics 344 Foundations of 21...

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