MY-ASSIGNMENTEXPERT™可以为您提供utoronto PHY357H1S Particle Physics电动力学课程的代写代考和辅导服务！
这是多伦多大学粒子物理课程的代写成功案例。
PHY357H1S课程简介
The subatomic particles; nuclei, baryons and mesons, quarks, leptons and bosons; the structure of nuclei and hadronic matter; symmetries and conservation laws; fundamental forces and interactions, electromagnetic, weak, and strong; a selection of other topics: CP violation, nuclear models, standard model, proton decay, supergravity, nuclear and particle astrophysics. This course is not a prerequisite for any PHY400-level course.Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of a microsecond. They occur after collisions between particles made of quarks, such as fast-moving protons and neutrons in cosmic rays. Mesons are also produced in cyclotrons or other particle accelerators.
Prerequisites
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction.Particles have corresponding antiparticles with the same mass but with opposite electric charges. For example, the antiparticle of the electron is the positron. The electron has a negative electric charge, the positron has a positive charge. These antiparticles can theoretically form a corresponding form of matter called antimatter. Some particles, such as the photon, are their own antiparticle.
PHY357H1S Particle Physics HELP（EXAM HELP， ONLINE TUTOR）
In this course we will often use “natural” units in which $\hbar=c=1$, where $\hbar=h / 2 \pi$ is Planck’s constant and $c$ is the speed of light in vacuum. If we also define the unit of mass/energy to be the mass of the proton, what are the units of length and time in this system, expressed in SI units.
More commonly, we will take the unit of energy to be $1 \mathrm{GeV}$ (or $1 \mathrm{MeV}$ ) in our “natural” units. Since the mass of the proton is $0.94 \mathrm{GeV}$ (in these units), the units of length and time in the GeV- $\hbar-c$ system differ only by $6 \%$ from the values you computed above. That is, a GeV is a rather “natural” unit of energy in a system that emphasizes protons.
The cross section $\sigma$ for the reaction $\pi^{-}+p \rightarrow \Lambda^0+K^0$ is about $1 \mathrm{mb}=10^{-27} \mathrm{~cm}^2$. Noting that $m_\pi \approx m_p / 6$, estimate the dimensionless coupling constant $\alpha_S$ for the (strong) interaction of this process. Hint: $\sigma \approx \alpha_S^2 \sigma_{\text {geometric }}$ in the lowest approximation, which suffices for this problem.
The lifetimes $\tau$ of the $\Lambda^0$ and $K_0$ particles are both around $10^{-10} \mathrm{~s}$. Noting the $m_{\Lambda} \approx$ $2 m_K \approx m_p$, estimate the dimensionless coupling constant $\alpha_W$ that is relevant to the (weak) decay processes for these particles.
What is your estimate for the ratio $\alpha_W / \alpha_S$ of the relative strengths of the weak and strong interactions?
Use classical electrodynamics to deduce the Thomson scattering cross section $\sigma_{\gamma e \rightarrow \gamma e}$ for the scattering of unpolarized light by an electron nominally at rest. Hint: Rather than slogging through a derivation based on the differential cross section, as in the text of Jackson, note that $\sigma=P_{\text {scattered }} / S_{\text {incident }}$, where $\mathbf{S}$ is the Poynting vector and $P_{\text {scattered }}=P_{\text {radiated }}$ where the latter can be gotten quickly from the so-called Larmor formula. And, it’s simpler to use Gaussian units if you are familiar with these.
The so-called quantum electrodynamic critical field strength $E_{\text {crit }}$ is that such if an electron were accelerated in this (static, uniform) field for a distance equal to the (reduced) Compton wavelength $\lambda_C$ of an electron, it would gain energy equal to its rest mass. Deduce an expression for $E_{\text {crit }}$ (in Gaussian units), but give a numerical value for it in the hybrid units of volts $/ \mathrm{cm}$.
One also speaks of the critical magnetic field strength, $B_{\text {crit }}=E_{\text {crit }}$. Deduce the value of $B_{\text {crit }}$ in gauss, which is the field strength at the magnetic poles of some neutron stars (called magnetars).
If the QED critical field strength could be achieve, the “vacuum” would “spark,” in that “virtual” electron-positron pairs of nominally zero mass would be given enough energy by such a field, while still separated by the size $\lambda_C$ of the quantum fluctuation for the particles to become “real” with mass/energy $m c^2$.
What is the electric field strength at the surface of a lead nucleus, in units of $E_{\text {crit }}$ ?
Note that if a “virtual” electron-positron pair is created (with zero rest energy) out of the vacuum near a nucleus, the electron could be captured into an atomic level with binding energy $U$, and this energy given to rest energies of the electron and positron. If $U>2 m_e c^2$, then the electron and positron become “real,” and we say that the vacuum has “sparked;” otherwise the electron-positron pair must go back into the “vacuum.” Use a nonrelativistic Bohr model of an atom with a nucleus of charge $Z e$ to predict the minimum value of $Z$ such that this kind of “sparking the vacuum” could occur. Relativistic corrections reduce this $Z_{\text {crit }}$ significantly. Hint: express the parameter of an atom in terms of $\lambda_C$, the electromagnetic coupling constant $\alpha_{E M}=\alpha=e^2 / \hbar c$, and the electron rest energy $m_e c^2$.
Searches for “sparking the vacuum” in collisions of uranium nuclei, where briefly the total $Z$ is 184 , have led to ambiguous results. In an experiment by the author, electronpairs were produced when a high-energy photon probed a very intense laser beam, whose electric field strength was close $E_{\text {crit }}$ in the rest frame electron-positron pair; the results can be interpreted in the complementary ways of “sparking the vacuum” or the nonlinear reaction $\gamma+n \gamma_{\text {laser }} \rightarrow e^{+} e^{-}$. See sec. IVb of C. Bamber et al., Phys. Rev. $D$ 60, 092004 (1999), http://kirkmcd. princeton. edu/examples/QED/bamber_prd_60_092004_99. pdf
Note that a strong laser beam (plane electromagnetic wave) cannot by itself “spark the vacuum” in that an electron-positron pair has a rest frame, while there is no rest frame for a collection of identical photons.
MY-ASSIGNMENTEXPERT™可以为您提供UTORONTO PHY357H1S PARTICLE PHYSICS电动力学课程的代写代考和辅导服务！
