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