Method for determining the absolute number of electron spins in a sample of extended size

1. A method for determination of the absolute number of electron spins in an extended sample with the assistance of an apparatus for measuring magnetic resonance, the extended sample being disposed within a measurement volume of a radio frequency (RF) resonator of the apparatus during an electron spin resonance measurement, the method comprising the steps of:

a) determining a spatial sensitivity profile of the RF resonator over the measurement volume;

b) determining, at a defined position within the measurement volume, a resonator sensitivity constant using a calibration sample which is small compared to the measurement volume, the calibration sample having a known number of electron spins;

c) measuring a magnetic resonance signal of the extended sample in the apparatus, wherein the extended sample has a known spatial distribution in the measurement volume;

d) weighting the magnetic resonance signal with an integral of the spatial sensitivity profile of the RF resonator over a partial volume of the measurement volume occupied by the extended sample; and

e) determining a number of electron spins in the extended sample as a quotient between a weighted resonance signal of step d) and the resonator sensitivity constant of step b).

2. The method of claim 1 , wherein the ESR measurement is carried out as a cw ESR measurement.

3. The method of claim 2 , wherein the weighting in step d) is carried out in accordance with the following formula:

DI=c·√{square root over (P)}·B m ·Q·V·C·S ( S+ 1)· n B ·f ( B 1 ,B m )

with

c=the resonator sensitivity constant

p=microwave power/mW

B m =the modulation amplitude/G

Q=the quality factor of the resonator

V=a sample volume/L

C=the sample concentration/M

S=the electron spin

n B =Boltzman factor for the temperature dependence

f(B 1 , B m )=the spatial sensitivity distribution of the RF resonator

B 1 =the RF field amplitude

DI=the double integral of the differential measured ESR absorption line.

4. The method of claim 1 , wherein step a) is effected using imaging ESR.

5. The method of claim 1 , wherein, in step b), the defined position in the measuring volume is chosen within a region of higher sensitivity of the RF resonator.

6. The method of claim 1 , wherein the spatial sensitivity profile of the RF resonator is approximated as being constant in two spatial directions (X, Z), wherein a third spatial direction (Y) lies along a longest extension of the extended sample within the measuring volume, wherein the three spatial directions (X, Y, Z) are mutually orthogonal.

7. The method of claim 6 , wherein the partial volume is cylindrical in shape and a cylindrical axis of the partial volume lies in the third spatial direction (Y).

8. The method of claim 7 , wherein the sample is disposed in a vial and a spatial distribution of the extended sample is determined by means of a fill height within the vial and a position of the vial within the measuring volume or a position of a lower vial end thereof.