angular correlation experimentsbourdon gauge uses a coiled tube which as it expands due to pressure...
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Angular Correlation
Experiments
John M. LoSecco
April 2, 2007
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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.
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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
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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.
Qml (r, θ, φ) = q
√
4π
2l + 1rlY m
l (θ, φ)
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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.
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Selection Rules
Based on the addition rules for angular momentumElectric 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 =12→
12
no J = 0 → 0, 1, 2
∆MJ = 0,±1 ∆MJ = 0,±1,±2 ∆MJ
Parity πf = −πi πf = πi πf = −πi
Higher transitions suppressed over lower ones.
So the transition is dominated by the first allowed
one.
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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 ∆MJ = 0,+1,−1 are equally
probable.
For ∆MJ = 0 angular distribution is proportional
to 1− cos2 θ For ∆MJ = ±1 angular distribution is
proportional to 12(1 + cos2 θ)
So since each ∆MJ is equally likely the photons are
isotropic.
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But ∆MJ = 0 from a → b must be followed by
∆MJ = 0 from b → c.
∆MJ = ±1 must be followed by a transition
∆MJ = ∓1
The z direction is arbitrary.
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Can pick z along the first photon direction.
Can not get to state b with MJ = 0 since the
∆MJ = 0 angular distribution is proportional to
1 − cos2 θ which vanishes in the z direction.
So the b → c transition must be via ∆MJ = ±1 to
get to the J = 0 ground state.
The ∆MJ = ±1 transitions have the angular
distribution 12(1+cos2 θ) which is what is measured.
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Correlated Photons in 60Ni
60Ni is formed by beta decay of 60Co to an excited
state
Photons of energy 1.172 MeV and 1.332 MeV are
emitted
In 60Ni the levels have spins 4, 2 and 0.
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Both transitions are quadrupole.
Angular correlation is:
1 +1
8cos θ2 +
1
24cos θ4
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γγ Correlation Experiment
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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.
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Coincidence Methods
W. Bothe 1930 ... Nobel 1954
Consider two counters, 1 and 2.
Let ω1,2 be the solid angle subtended and ǫ1,2 be
the counter efficiency
and ∆t1,2 be the pulse width.
The singles counting rate is: Ri = Nωiǫi where N
is the decay rate of the source.
The correlated coincidence rate is: Rc = Nω1ǫ1ω2ǫ2
The accidental count rate is Ra = R1R2∆t
So the ratio of accidental to true coincidences is:
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RaRc
= 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 = ∆t1 + ∆t2
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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 = R1∆t. So accidental
coincidences with counter 2 are R2 × f
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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.
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Vacuum Gauges
How to measure vacuum.
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
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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.
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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
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gauge.
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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.
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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.
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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
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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
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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
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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.
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