Determination of activity of 51Cr source on gamma radiation measurements

V.V.Gorbachev, V.N.Gavrin, T.V.Ibragimova, A.V.Kalikhov, Yu.M.Malyshkin,A.A.Shikhin

Institute for Nuclear Research, RAS

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The Intrnational workshop on Prospects of Particle Physics:Neutrino Physycs and AstrophysicsValday, Russia, Feb 1-8 2015

BNO INR RASBNO INR RAS

Neutrino experiments of new generationon search of thin effects, accuracy <5%

Experiments with artificial sources of a neutrinoTransitions to sterile statesMagnetic moment, …

Experiment BEST (The Baksan experiment on sterile transitions)Radiation of the Ga target (50 t) of the solar neutrino detector of SAGENeutrino source 51Cr, 3 МCiTotal systematic uncertainty ~2.6%The expected error of measurement of activity of the source <1 %

How to measure the activity of 51Cr:1) On thermal emission – calorimetric method (36.7 keV/decay)2) On gamma radiation

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BEST: 2-zone gallium experiment on search for short baseline oscillations

(Δm2 ~ 1 eV2)

Target – 50 t of metallic GaMasses of target in zones: 8 t and 42 tPath length in each zone <L>=55 cm51Cr source: T1/2=27.7 d, 3 MCi

Eν = 750 keV (90%), >95 % captures

430 keV (10%)

• measurements on two bases

•experiment on nuclear capture

71Ga+νe → 71Ge + e–

Evidence for oscillations:

1) different capture rates in zones of target

2) suppression of capture rates in both zones

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Gamma radiation 51Сr

1. 320 keV, 10% decays

2. IB, <430 keV, 1.2·10-4 x 0.0983

3. IB, <750 keV, 3.8·10-4 x 0.902

xxAxy 2)1()(

Internal Bremsstrahlung:

Q

Ex

Radiation spectrum in the source

Activity is distributed unevenly on volume

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The method of measurement

We divide (mentally) the source on N parts(for example, with uniform activity):

Source: Cr, 7.2 g/cm3, cylinder ø8.6 x 9.5 cm

Shield: W alloy, 16.6 g/сm3, thickness 2.5 сm

In the detector we register a signal –

the sum of signals from all parts :

N

ii ESES

1

)()(

Details are in the paper of V. Gorbachev, Yu.M.Malyshkin, to be published in Instruments and Experimental Techniques,(2015)

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Signal in detector: ),(),()(1

i

N

ii xExEAES

)(),()(' EfxEE ii и)(

1),(

EfxEAB ii

Here Вi – absolute activity of i-th part and it does not depend on Е;

f(E) – release of photon with energy Е per 1 decay

And total activity:

)(')(1

EBES i

N

ii

N

iiTot BA

1

Then signal is:

or entering replacement

А(Е,xi) – activity of i-th part of the source on photons with energy Е

xi – i-th part of the source coordinate

ε(E,xi) – efficiency of detection of photons with energy Е from part xi

or in matrix form:

One forms a system of linear equations for Nj energy intervals {Еj} :

BS '

N

iiijj BS

1

'

SB 1)'(0)'det( ij

In case Nj=N, the solution will be :

Condition for solution:

It is convenient to solve the system of equations using method χ2:

1) more information is used (Nj can be more than N)

2) the errors are estimated directly

jN

j j

N

iiijj BS

1

2

12

'

For uncorrelated errors:

2min

22 The errors σ(Bi) are determined on the

boundaries of areas:7

Calculation of the Compton scattering

Spectrum of photons, which leave the shielding of the source, is distorted: monochromatic photons with energy Е have continuous spectrum with energies Е’ ≤ Е

Δj – signal from photons, registered in the energy range Ej, but emitted with energy E > Ej:

Result: где

jN

jjijjij

'' '"

εijj’ – exit from the i-th part of the source of photons with energy Ej, generated with energy Ej’ > Ej

I.e. the notation of the signal does not change and all described operations (solutions) remain the same after the change εij’ to εij’’

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N parts of the source requires Nj ≥ N energy ranges

In case the source is separated in 3 parts in each coordinate, N=33=27

I.e, it is necessary to separate the spectrum of 51Cr from 300 to 750 keV in N~27 ranges

The width of one range Δ ~ (750-300)/27 = 15 keV

Detector resolution~ 15 keV/ 750 keV= 2%

I.e. one can use the Ge SCD

On detector resolution

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Why we need the collimator:

1) To limit the regions with equal efficiency in the detector

2) To remove the reflected (from the walls) radiation

3) To separate the registration efficiency on directions, to fit the condition

10Uniformity of efficiency: simulations for ø=1cm and ø 2 cm

Collimator

0)'det( ij

Expected counting rate

From Monte Carlo (Geant4)

Exit beyond the limits of the primary shielding:

320 keV – 2.8·10-6

IB 430 keV – 1.5·10-6

IB 750 keV – 5.1·10-4

The total number of photons outside the shielding will be 5.1·1010 s-1 per decay

Of them 320 keV – 61%, IB 750 keV – 39%, IB 430 keV– 4·10-3 %

At a distance of 10 m with collimator 1 сm one can expect 3000 photons/sec

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12

1

1010 __,0

_,{)(

xx

xxyxy

ij

jjii yyy 012

),()( 11012 xxyyxy

For arbitrary signal:

On detector response

y0(x) – spectrum before the detector

y1(x1,x) – detector response function

y2(x) – spectrum, registered in detector

x=E – current energy in spectrum

x1 – the energy of photon line

Forming of signal:For photon line:

Spectrum in detector will be:

In the assumption that xj > xi by j > i

Reconstruction of the spectrum y0(x) using monochromatic lines on y2(x)

Function of the response y1(x1,x)

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For continuous spectrum the function y2(x) is determined using only one point x = xk :

kk

N

kjjjkk

k y

yyy

y1

1012

0

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How to take into account the radiation of impurities

K

k

N

iijk

kij cП

1 1

)(

We can write our system of equations:

Signal from impurities:

− the efficiency εij for k-th impurity

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The activity of impurities for 51Cr 3 MCi, obtained on results of the 1994 yr source experiment:

59Fe 6∙109 Bk, 182Ta 9∙109 Bk, 60Co 2∙1010 Bk, 46Sc 3∙1011 Bk

kicijk

− the activity of k-th impurity from the i-th part of the source

kiki pBc Assuming the dependence of the activity of

impurities on the source activity :

N

i

K

kijkkijij pBS

1 1

)"(

The number of unknowns: N+K: {Bi} + {pk}

The signal in detector in presence of impurities:

Uncertainties of the method

1) Geometry of source and of detector

(size, density of medium for absorption, relative location of the source and detector, direction of collimator,…)

2) Knowledge of spectrum of the source irradiation

(accuracy of the available calibration of γ-sources > 3%, the IB spectrum is known only in the first approximation, …)

3) Accuracy of calculation of efficiencies and response functions

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4) Statistics of events:

The number of events on the «average» part of the spectrum:

in case the efficiencies of the signal recorded from the «near» and «far» parts of the source differ on the order, then

NN 1.0)1.01( I.e. the minimal statistics N > 1100 for one Е interval

And the summarized statistics > 27∙1100 = 3∙104.

Absolute measurements of statistics and spectrum of IB of 51Cr

We shell use 2 point sources of 51Cr with activities:

1) ~ 20 mCi (109 Bq) and 2) ~ 1 kBk

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Source №1

1) Measurement of the IB spectrum above 320 keV through collimator

2) The same measurements with collimator covered with Pb 2.6 cm: to control of the quality of measurements spectrum because of the pulses imposition

Source №2

1) Measurement of the total counting rate in 4π-geometry with a couple of NaI detectors

2) Measurement of the rate of 320 keV line in Ge detector through collimator

Summary

1) Measurements of activity of intense source on measurement of continuous spectrum of γ-radiation

2) Reconstruction of spectra on measurements in SCD

3) Absolute calibration of the activity and of the measurement of the IB spectrum of the 51Cr source

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The following methods have been developed:

Thank you

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