Angular Correlation ExperimentsBourdon gauge uses a coiled tube which as it expands due to pressure increase. commonly used on pressure regulators. Angular Correlation Experiments

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


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)


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.


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.


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.


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.


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.


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.


Both transitions are quadrupole.

Angular correlation is:

1 +1

8cos θ2 +

1

24cos θ4


γγ Correlation Experiment


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.


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:


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


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


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.


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


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.


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


gauge.


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.


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.


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


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



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


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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Angular Correlation ExperimentsBourdon gauge uses a coiled tube which as it expands due to pressure increase. commonly used on pressure regulators. Angular Correlation Experiments