Angular Correlation Experiments John M. LoSecco April 2, 2007 Angular Correlation Experiments J. LoSecco Notre Dame du Lac
Nuclear Spin In atoms one can use the Zeeman Effect to determine the spin state. Under the influence of a strong external magnetic field the multiple degenerate levels of a spin system with spin s are split into 2s + 1 levels. This method can not be used for nuclei. The magnetic moments are 2000 times smaller and the natural energy level spacing between states is 6 orders of magnitude greater than in atoms (MeV vs ev). The Mossbauer effect is a special case. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 1
Radiation The energy of a gamma ray depends on the energy difference between nuclear levels. Gamma ray transitions depend on the spin and parities of the parent and daughter states Angular Correlation Experiments J. LoSecco Notre Dame du Lac 2
Multipole Moments The potential of a charge distribution can be expanded in a series of multipole moments. Monopole, dipole, quadrupole etc. These have different angular and radial distributions. 4π Q m l (r, θ,φ) = q 2l + 1 rl Yl m (θ, φ) Angular Correlation Experiments J. LoSecco Notre Dame du Lac 3
In classical physics oscillations of particular multipole moments give rise to different radiated angular distributions. For example dipole radiation vanishes along the pole and is maximum in the plane normal to the dipole. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 4
Selection Rules Based on the addition rules for angular momentum Electric dipole Magnetic dipole Electric quadrupole Magnetic quadrupole Electric octupole (E1) (M1) (E2) (M2) (E3) Rigorous rules J = 0, ±1 J = 0, ±1, ±2 J no J = 0 0 no J = 0 0, 1 or J = 1 2 1 2 no J = 0 0, 1, 2 M J = 0, ±1 M J = 0, ±1, ±2 M J Parity π f = π i π f = π i π f = π i Higher transitions suppressed over lower ones. So the transition is dominated by the first allowed one. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 5
Correlated Photons Simple Example 0 + 1 0 + For states a, b, c Both transitions (a b and b c) are electric dipole (E1) In transition a b M J = 0,+1, 1 are equally probable. For M J = 0 angular distribution is proportional to 1 cos 2 θ For M J = ±1 angular distribution is proportional to 1 2 (1 + cos2 θ) So since each M J is equally likely the photons are isotropic. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 6
But M J = 0 from a b must be followed by M J = 0 from b c. M J = ±1 must be followed by a transition M J = 1 The z direction is arbitrary. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 7
Can pick z along the first photon direction. Can not get to state b with M J = 0 since the M J = 0 angular distribution is proportional to 1 cos 2 θ which vanishes in the z direction. So the b c transition must be via M J = ±1 to get to the J = 0 ground state. The M J = ±1 transitions have the angular distribution 1 2 (1+cos2 θ) which is what is measured. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 8
Correlated Photons in 60 Ni 60 Ni is formed by beta decay of 60 Co to an excited state Photons of energy 1.172 MeV and 1.332 MeV are emitted In 60 Ni the levels have spins 4, 2 and 0. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 9
Both transitions are quadrupole. Angular correlation is: 1 + 1 8 cos θ2 + 1 24 cos θ4 Angular Correlation Experiments J. LoSecco Notre Dame du Lac 10
γγ Correlation Experiment Angular Correlation Experiments J. LoSecco Notre Dame du Lac 11
Particle Physics In particle physics the spin of unstable particles can be determined from the angular distribution of decay products. One frequently uses the production process to define the coordinate system. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 12
Coincidence Methods W. Bothe 1930... Nobel 1954 Consider two counters, 1 and 2. Let ω 1,2 be the solid angle subtended and ǫ 1,2 be the counter efficiency and t 1,2 be the pulse width. The singles counting rate is: R i = Nω i ǫ i where N is the decay rate of the source. The correlated coincidence rate is: R c = Nω 1 ǫ 1 ω 2 ǫ 2 The accidental count rate is R a = R 1 R 2 t So the ratio of accidental to true coincidences is: Angular Correlation Experiments J. LoSecco Notre Dame du Lac 13
R a R c = N t So one wants a small t One can not lower N arbitrarily because other sources of background like cosmic rays, will enter. Want a high efficiency ǫ to get a high rate. One should not increase ω since the angular resolution will become poorer. t is the sum of the pulse widths from channel 1 and 2: t = t 1 + t 2 Angular Correlation Experiments J. LoSecco Notre Dame du Lac 14
Since a coincidence is recorded for any overlap of the pulses. The coincident circuit will be open for a fraction of time given by f = R 1 t. So accidental coincidences with counter 2 are R 2 f Angular Correlation Experiments J. LoSecco Notre Dame du Lac 15
Vacuum Methods A significant step forward for modern science. Permitted the study of cathode rays, electron beams which led to the discovery of x-rays, which led to the discovery of radioactivity. Similar to the use of spaced based observations in modern times to eliminate absorption and resolution effects of the Earth s atmosphere. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 16
How to measure vacuum. Vacuum Gauges SI unit of pressure is the Pascal = 1 Newton per square meter. 1 atmosphere is 101325 Pascals or about 101 kpa. Units: Torr or mmhg. 1 Torr = 133.322 Pascals Angular Correlation Experiments J. LoSecco Notre Dame du Lac 17
Thermocouple gauges measure the thermal conductivity of the gas. Useful range 10 3 to 10 torr. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or Resistance Temperature Detector (RTD) can be used to measure the temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 18
Ion gauges measure the current due to ionization of residual gas. Useful range 10 10 to 10 3 torr. Thermionic emission emissions generate electrons, which collide with gas atoms and generate positive ions. The ions are attracted to a suitably biased electrode known as the collector. The current in the collector is proportional to the rate of ionization, which is a function of the pressure in the system. Hence, measuring the collector current gives the gas pressure. There are several sub-types of ionization Angular Correlation Experiments J. LoSecco Notre Dame du Lac 19
gauge. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 20
Mechanical gauges are based on a metallic pressure sensing element which flexes elastically under the effect of a pressure difference across the element. Bourdon gauge uses a coiled tube which as it expands due to pressure increase. commonly used on pressure regulators. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 21
Diaphragm gauge uses the deflection of a flexible membrane that separates regions of different pressure. Used in barometers. Bellows gauge altimeters. Useful range above 10 2 torr. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 22
Hydrostatic gauge measurements are independent of the type of gas being measured, and can be designed to have a very linear calibration. They have poor dynamic response. Height of mercury or other liquid in a column. McLeod gauge is a type of hydrostatic gauge in which the gas is compressed to increase sensitivity Useful range: above 10 4 torr Angular Correlation Experiments J. LoSecco Notre Dame du Lac 23
Vacuum Pumps Mechanical pumps Atmosphere down to 10 3 Torr Cryopumps Sorption pumps 10 3 Torr Oil diffusion pumps 10 6 to 100 Torr Turbomolecular pump 10 6 to 1 Torr Sputtering pumps or sputter-ion pump 10 4 to 10 10 Torr Ion pumps 10 3 to 10 12 Torr Angular Correlation Experiments J. LoSecco Notre Dame du Lac 24
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Regeneration Some pumps, such as Sorption pumps and Sputtering pumps needed to be regenerated after use. Regeneration of a cryopump is the process of evaporating the trapped gases. This can be done at room temperature and pressure, or the process can be made more complete by exposure to vacuum and faster by elevated temperatures. Best practice is to heat the whole chamber under vacuum to the Angular Correlation Experiments J. LoSecco Notre Dame du Lac 26
highest temperature allowed by the materials, allow time for outgassing products to be exhausted by the mechanical pumps, and then cool and use the cryopump without breaking the vacuum. Angular Correlation Experiments J. LoSecco Notre Dame du Lac 27