Design of a High-Precision β Telescope Russell TerBeek, Hillsdale College Mentor: Dr. Dan Melconian, Texas A&M Cyclotron Institute August 6th, 2009

Topics to be Covered Parity Violation Detecting β+ decay of 37K Nature and non-conservation of P operator Is P violation maximal? Detecting β+ decay of 37K Designing the β-Telescope GEANT simulations Putting it all together August 6th, 2009

The P operator P ( r ) → - r This operation conserves the length of a vector r while inverting its direction about the origin. Axial vectors and scalars do not change sign under P. August 6th, 2009

Violation of P symmetry In 1957, C.S. Wu demonstrated the breakdown of P symmetry. In the experiment, electrons show a strong tendency to emit antiparallel to the atomic spin. August 6th, 2009

Motivation: Is P violation maximal? The Standard Model assumes that P violation is a maximal effect. This tacit assumption has no theoretical grounding, however, and a measurement of Bν will provide an upper limit on the degree to which parity is conserved. August 6th, 2009

Detecting β+ decays of 37K We can determine whether or not parity is maximally violated by studying the β+ decay of 37K, which is a weak interaction. In order to obtain good results, we need to be able to trap the 37K atoms into a very small volume, and polarize them so that we know along which axis the atomic spins point. August 6th, 2009

Basic MOT physics In order to do this, we use magneto-optical trapping (MOT) to confine the 37K atoms and cool them down to hundreds of μK. This provides us with a source radius of 3 mm FWHM. August 6th, 2009

Basic MOT Physics (cont’d) The MOT lasers are slightly detuned just below 37K’s resonant frequency. If an atom were to travel in the direction of one of the beams, the energy would be Doppler-shifted up and the atom would begin absorbing photons at resonance. August 6th, 2009

Basic MOT Physics (cont’d) The MOT lasers are slightly detuned just below 37K’s resonant frequency. If an atom were to travel in the direction of one of the beams, the energy would be Doppler-shifted up and the atom would begin absorbing photons at resonance. August 6th, 2009

Basic MOT Physics (cont’d) The MOT lasers are slightly detuned just below 37K’s resonant frequency. If an atom were to travel in the direction of one of the beams, the energy would be Doppler-shifted up and the atom would begin absorbing photons at resonance. August 6th, 2009

Basic MOT Physics (cont’d) The MOT lasers are slightly detuned just below 37K’s resonant frequency. If an atom were to travel in the direction of one of the beams, the energy would be Doppler-shifted up and the atom would begin absorbing photons at resonance. August 6th, 2009

Experimental Setup Positrons are emitted with initial kinetic energy 6 MeV in all directions, and are “caught” by the β-telescope at right. Recoiling 37Ar nuclei are detected by the microchannel plate. August 6th, 2009

Computational Techniques In order to simulate the interactions of positrons with the telescope, GEANT 3 (GEometry ANd Tracking) software generated 106 monoenergetic (6 MeV) positrons, and emitted them into a 2π coverage containing the telescope. Different geometries of the scintillator-silicon detector combination could be tested by entering parameters like radius and thickness into GEANT, and comparing results. August 6th, 2009

Statistics Vs. Annihilation Ideally, we would like a huge detector to take in all possible events, to improve our statistics. However, e+/e- annihilation adds “extra” energy to the detector (up to 1.022 MeV) that throws off our data. August 6th, 2009

Mediating the Extremes In order to get the optimum detector, a quantitative way is required to see which combinations can absorb all of a positron’s kinetic energy while not absorbing the 511 keV photons. Response functions are histograms of how much energy gets left in the scintillator, and we can use them to test how good a particular combination is. Ideally, we would like a delta-function at the incident positron energy. August 6th, 2009

Combining Methods The response function can be aided by tandem use with an “escape plot,” which lists the last point at which a positron left energy. The more positrons leave out the sides, the thicker the black band. August 6th, 2009

A few examples 12.0 cm radius, 100 cm thickness This scintillator is far too big; although it retains almost all of the incident positrons (no thick bands), it has a significant high-energy tail due to Compton effects, and gives misleading data. August 6th, 2009

A few examples 4.5 cm radius, 1.0 cm thickness This scintillator overcompensates by being far too small; annihilation events are kept to a minimum, but practically no positrons deposit their full energy. August 6th, 2009

A few examples 6.0 cm radius, 3.2 cm thickness The above dimensions are an example of a middling value that were shown to minimize the adverse effects in GEANT simulations. August 6th, 2009

Final Results This is the design I came up with after researching scintillators, silicon detectors, and photomultiplier tubes. The end product is a series of electrical signals which may be reconstructed to determine the positron’s energy. August 6th, 2009

Final Results (cont’d) After fitting the simulation data, I came up with an optimal radius of 5.56 cm and an optimal thickness of 2.95 cm. August 6th, 2009

Recap Again, the whole purpose of the experiment is to make a measurement of Bν, as well as other parameters. It is important to remember that each detail be planned out to precision, because we are looking for a very small effect that has never been seen before in experimental nuclear physics. The values obtained for the dimensions of the β telescope are those which will deliver the most confident results for a measurement of Bν, perhaps indicating a “re-conservation” of parity at higher energies. August 6th, 2009

Acknowledgments Thanks to Dr. Melconian and Spencer Behling for their help in teaching me the physics of the experiment, and helping me with this summer’s research. Also, thanks to the NSF and the DOE for funding the Cyclotron’s REU program. August 6th, 2009