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Optical Pumping Simulation of Copper for Beta-NMR Experiment

Optical Pumping Simulation of Copper for Beta-NMR Experiment. Julie Hammond Boston University ISOLDE, CERN 24.3.14. ISOLDE. NMR (continued). Beta-NMR Requires less atoms. 10 orders of magnitude better precision than traditional NMR. Uses radioactive isotopes. .

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Optical Pumping Simulation of Copper for Beta-NMR Experiment

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  1. Optical Pumping Simulation of Copper for Beta-NMR Experiment Julie Hammond Boston University ISOLDE, CERN 24.3.14

  2. ISOLDE

  3. NMR (continued) • Beta-NMR • Requires less atoms. • 10 orders of magnitude better precision than traditional NMR. • Uses radioactive isotopes.

  4. NMR (nuclear magnetic resonance) • A sample is wrapped in two solenoids between two strong magnets. One solenoid is pulsed with a signal corresponding to the Larmor frequency, and the other solenoid is attached to an oscilloscope which measures the response frequency of the sample. • Larmor frequency is the resonant frequency. ( = , where e is the charge of an electron, g is the gyromagnetic ratio, B is the magnitude of the applied magnetic field, and m is the mass of the particle.) • This response frequency is then Fourier transformed to show the various resonances which correspond to the electrons’ spin.

  5. Purpose of Magnets • Presence of magnetic field gives rise to energy splitting between the states. A weak magnetic field (0.1 T) gives rise to the Zeeman effect, which splits according to the nuclear spin. A stronger magnetic field (0.2 T) gives rise to the Paschen-Back effect, which splits according to the electronic angular momentum.

  6. Polarizing the Valence Electrons • A laser whose frequency matches the energy difference between the electron orbitals is used to bump the electrons into the more energetic orbitals. • At ISOLDE, dye lasers are used, whose frequency is variable. • Polarization comes from the spin of the photon which, as bosons, have spin-1, as opposed to fermions who have spin-1/2. • Can be done using positively polarized light (+σ), negatively circularly polarized light (-σ), or linear polarized light (0) (a superposition of the two circular polarizations). • Selection rules: ∆ l = +/- 1.

  7. Optical Pumping

  8. Simulating Optical Pumping in C • The rate of the change in each population corresponds to a differential equation which is dependent on the current population as well as the populations of the other states. • These differential equations are coupled and are approximated by the Runge-Kutta method. • Using a computer simulation will give us better accuracy, as the number of repetitions may be very large as the increment is very small.

  9. What I’m Doing • Getting my computer to recognize the IT++ library. • Learning energy splitting diagrams to find the possible energy transitions in copper. • Calculating nuclear spin. • Finding the constants to putinto the differential equations: • Einstein emission and absorption coefficients • Using the Heisenberg Uncertainty Principle to calculate the lifetimes of the different states. (∆E ∆t >= h/4π) • Larmor frequency. • Coding this in C to run the approximation.

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