Beta SpectroscopyBeta Spectroscopy

Wolfgang PauliNobel Prize 1945

Enrico FermiNobel Prize 1938

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 99Tc 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.

Beta Spectroscopy

Nuclear ß-decayWe define the Q value to be the difference between the initial and final nuclear mass energies.

ν++→ −epn( ) 2

0epn cmmmmQ −−−= −

For the following case

the Q value would be:

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

β− - decay :2

eA1zN

AzNβ

A1z

Az

c]m)X'(mX)(m[Q

υeX'X

−−=

++→

+

−+

−

In the above case mN indicates nuclear masses. In order to use the tabulated atomic masses we have to convert these using the following

∑=

−+=Z

1ii

2e

2AN

2A BcmZcX)(mcX)m(

Bi is the binding energy of the ith electron. Replacing in the formula above we obtain:

2c])X'(mX)m([Q AAβ

−=−

The Q value represents the energy shared by the electron and the neutrino υeβETQ +=−

β+-decay

EC-decay

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

For the electron-capture process such as:

υeX'X A1Z

AZ ++→ +

−

2e

AAβ

c]m2)X'm(X)[m(Q −−=+

nAA

βc])X'm(X)m([Q B−−=−

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.

We obtain:

υX'eX A1Z

AZ +→+ −

−

where Bn is the binding energy of the captured electron

ß-Spectro-meter

Diaphragm Pump

NeubergerN 735.5 ANE

Magnet Power SupplyBEHA NG315

PreampTennelec TC 170

Detector Bias SupplyCanberra 3102/2

Spectroscopy AmpOrtec 471

Biased AmpOrtec 408

8K ADCAptec Card

# 5008

ComputerDSM Industrial PC

Digital Multimeter

Keithley195A

Cryopump

(Absorption pump with Zeolithe)

Vent Valve

High Vacuum GaugeVarian

Pre-Vacuum GaugeVacuubrand

Vap 5

100 mm

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-decayIs the knowledge of the nuclear matrix element necessary ?Some ideas about forbiddenness in β-decay, rules, log ft-valueWeak force and weak interactionSymmetries and parityHelicity, left-handedness and right-handedness, Parity violation, Wu experiment, Goldhaber experiment

What is Internal Conversion and howcan one make use of it ?Particles in electromagnetic fields, howis momentum, energy and velocity se-lection achieved ?Principles of β-spectrometersFocusing techniquesHow is an electromagnet working ?Some vacuum techniques, how is a clean vacuum achieved ?Techniques of thin source preparationElectron backscattering and energyloss : Bethe-Landau equationElectronic set-up, noise, pre-amp, mainamp, MCA

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 (interfer-ence with the spectroscopy)

Detector bias is +60 Volts (slowly)

Signals are noisy, therefore thres-hold for ADC at about 8-9%

The current through the spectro-meter 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 99Tc

by taking spectra for every mA between 8

and 30 mA99Tc has no conversion lines, so the spec-

trometer has to be calibrated by the end-

point energy of the spectrum

Calculate the Fermi-Kurie-Plot for the

measured 99Tc spectrum, a double forbid-

den β-decayWARNINGS

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