Beta Spectroscopy

Beta Spectroscopy

Wolfgang Pauli

Nobel Prize 1945

Enrico Fermi

Nobel Prize 1938

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Beta Spectroscopy

The double focusing magnetic ß-spectrometer is a classical instrument for

the measurement of continuous or discrete ß-spectra with magnetic fields. It

is a scanning spectrometer which measures the momenta of the beta’s by

varying the electric current through the coils of the magnet. Double focusing

is achieved by choosing a toroid-sector-field spectrometer. The obtained ß-

spectra are displayed in a so-called Fermi-Kurie-plot from which after a

correction for the forbiddeness (form factor) the endpoint energy of the

spectrum can be obtained. In this experiment the double-forbidden ß-decay

of 99 Tc is investigated.

ß-instable nuclei emit electrons or positrons with a continuous momentum

and energy distribution because this decay involves three partners in the

outgoing channel: an e ± , a neutrino and the final nucleus. The ß-spectrum

can be explained by the Fermi-theory of ß-decay.

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Nuclear ß-decay

We define the Q value to be the difference between the initial and final nuclear mass energies.

For the following case

the Q value would be:

n

Q

→

p

+

e

−

+ ν

2

( m − m − m − m ) c

=

n p

−

e

0

Let us consider the three cases of ß-decay in a nucleus:

β − - decay :

A

z

X

→

A

z+

1

X'

+ e

−

+

υ

Q

−

β

=

[m

N

(

A

z

X) − m

N

(

A

z+

1

X') − m

e

]c

2

In the above case m N

indicates nuclear masses. In order to use the tabulated atomic masses

we have to convert these using the following

m(

A

X)c

2

= m

N

(

A

X)c

2

+ Z

m c

e

2

−

Z

∑

i=

1

B

i

B i

is the binding energy of the i th electron. Replacing in the formula above we obtain:

Q

−

β

= [m(

A

X) − m(

A

X') ]c

2

The Q value represents the energy shared by the electron and the neutrino

Q = T + E

−

β

e

υ

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β + -decay

In the case of positron decay and using similar arguments we obtain:

A

A +

Z

X →

Z−1X'

+ e + υ

Q

+

β

=

[m(

A

X) − m(

A

X') − 2m

e

]c

2

EC-decay

For the electron-capture process such as:

A − A

Z

X + e →

Z−1X'

+ υ

We obtain:

Q

−

β

=

[m(

A

X) − m(

A

X') ] c

−

B

n

where B n

is the binding energy of the captured electron

All the above expressions assume ß-decay between a specific state and the ground state. If

the final state is an excited state this must be taken into account.

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Detector Bias Supply

Canberra 3102/2

Preamp

Tennelec TC 170

Spectroscopy Amp

Ortec 471

Pre-Vacuum Gauge

Vacuubrand

Vap 5

ß-Spectrometer

Vent Valve

Digital

Multimeter

Keithley

195A

Magnet

Power

Supply

BEHA

NG315

Biased Amp

Ortec 408

Diaphragm

Pump

Neuberger

N 735.5 ANE

High Vacuum Gauge

Varian

Cryopump

(Absorption pump with

Zeolithe)

8K ADC

Aptec Card

# 5008

Computer

DSM Industrial PC

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100 mm

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Beta Spectroscopy : Required Knowledge

‣ Discovery of b-decay and of the

continuous spectrum (history)

‣ Why is the β-spectrum continuous ?

‣ Pauli principle and Fermi theory of β-

decay

‣ Is the knowledge of the nuclear

matrix element necessary ?

‣ Some ideas about forbiddenness in

β-decay, rules, log ft-value

‣ Weak force and weak interaction

‣ Symmetries and parity

‣ Helicity, left-handedness and righthandedness,

Parity violation, Wu

experiment, Goldhaber experiment

‣ What is Internal Conversion and how

can one make use of it ?

‣ Particles in electromagnetic fields, how

is momentum, energy and velocity selection

achieved ?

‣ Principles of β-spectrometers

‣ Focusing techniques

‣ How is an electromagnet working ?

‣ Some vacuum techniques, how is a

clean vacuum achieved ?

‣ Techniques of thin source preparation

‣ Electron backscattering and energy

loss : Bethe-Landau equation

‣ Electronic set-up, noise, pre-amp, main

amp, MCA

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Beta Spectroscopy : Tasks and Goals

‣ Produce and check vacuum; about

3 x 10 -5 mbar should be achieved in

the chamber; after check: switch off

ionization vacuum gauge (interference

with the spectroscopy)

‣ Detector bias is +60 Volts (slowly)

‣ Signals are noisy, therefore threshold

for ADC at about 8-9%

‣ The current through the spectrometer

coils is in the range 8-30mA

and should be kept constant

(current mode)

‣ The line of the β’s should be clearly

visible in the whole range

‣ Set the MCA to 512 channels

‣ Measure the momentum spectrum of 99 Tc

by taking spectra for every mA between 8

and 30 mA

‣ 99 Tc has no conversion lines, so the spectrometer

has to be calibrated by the endpoint

energy of the spectrum

‣ Calculate the Fermi-Kurie-Plot for the

measured 99 Tc spectrum, a double forbidden

β-decay

WARNINGS

‣ Shut down bias when measuring has

been finished

‣ Close the gate valve after finishing

‣ Don’t forget the filling of the dewar every

10 hours