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ABSTRACT
The objective of this experiment was to determine the diffusion parameters for neutrons in light water
at room temperature. Am-Be sample was used as a neutron source placed at the center of a water filled
tank of volume one cubic-meter. The diffusion parameters comprise Fermi age, Thermal Diffusion
Length, Migration Area, Migration length, Extrapolated Length. The values measured in this
experiment were found to be 7.10 cm
2 , 8.21 cm, 74.50 cm
2 , 3.97 cm respectively.
Contents
6.1.1 For area under the Curve calculation of r
6.2.1 For area under the curve calculation of r
- ABSTRACT
- INTRODUCTION...............................................................................................................................
- EQUIPMENT
- EXPERIMENTAL SETUP
- BLOCK DIAGRAM
- PROCEDURE
- 5.1 Determination of Fermi age ..........................................................................................................
- 5.2 Determination of thermal diffusion length ...................................................................................
- 5.3 Determination of migration area ..................................................................................................
- 5.4 Determination of extrapolation length .........................................................................................
- OBSERVATIONS AND CALCULATIONS
- 6.1 Calculation of Fermi Age ( ) - P(r)
- 6.1.2 For area under the curve calculation of r4P(r)
- 6.2 Calculations of Diffusion Length (L) - P(r)
- 6.2.2 For area under the curve calculation of r4P(r)
- 6.3 Calculations of Migration Length (L)..........................................................................................
- 6.4 Calculations of Extrapolation Length (d)....................................................................................
- DISCUSSION
- REFERENCES
2. EQUIPMENT
BF 3 detector with electronic setup
Cadmium covers
1Ci neutron source
One cubic meter water tank with arrangements to move BF 3 detector horizontally and vertically
3. EXPERIMENTAL SETUP
4. BLOCK DIAGRAM
5. PROCEDURE
5.1 Determination of Fermi age
The equipment was arranged as shown above and the BF 3 detector covered with Cd was placed
in the water tight stainless steel tube dipped in the water at the height shown in the above figure.
The neutrons (resonant with Cd i.e. 0.4eV) count rate P′(r) was measured as a function of
horizontal distance r from the source; r was increased with regular steps of 1cm.
ln (r
4
P′(r)) and ln (r
2
P′(r)) were plotted as the function of r and the areas under the curves were
calculated using Simpson’s rule and analytical method of integration.
The mean squared Crow Flight distance <r
2
> was revealed from the ratio of the areas under the
curves which equals 6τ hence giving the Fermi age.
4
2
(^0 )
/
( )
6 ( , )
( )
6
r P r dr
E Eref r
r P r dr
A
A
5.2 Determination of thermal diffusion length
The above same procedure was repeated with uncovered detector in order to measure the count
rate P(r) by varying r in regular steps of 1cm.
P″(r) = P(r) – P′(r), the thermal neutron count rate was calculated at each distance r and the
above same method was used to calculate <r
2
for thermal neutrons which equals 6L
2 hence
giving the thermal diffusion length.
4
2 2
2
'
2
"( )
6
"( )
6
r P r dr
L r
r P r dr
A L
A
5.3 Determination of migration area
Migration area was determined by using the relation: M
2
= L
2
5.4 Determination of extrapolation length
The total count rate was measured starting from the source top in the vertical direction.
Count rate was plotted as a function of distance from the water-air interface; was joined up to
the interface and was extrapolated beyond the interface to make count rate zero.
The distance between the water-air interface and the point of zero flux was the extrapolation
length “d”.
r^2 p'(r) r^4 p'(r) r^2 p''(r) r^4 p''(r)
r(cm)
Log (r^2 (Avg+E))
Log (r^2 (Avg-E))
Log (r^2 (Avg+E))
Log (r^2 (Avg-E))
Log (r^2 (Avg+E))
Log (r^2 (Avg-E))
Log (r^2 (Avg+E))
Log (r^2 (Avg-E))
6.1 Calculation of Fermi Age ( )
6.1.1 For area under the Curve calculation of r
2
P (r)
Figure 1
The point A from figure is taken at 24cm from Figure 1.
Performing integration from 24cm to ∞
/ ( 0.039)
2
24
/ ( 0.039)(24)
2
/ 2 1
2
25750990.4 min
r A e dr
A e e
A cm
^
So,
Using Eq
42
(0.039)
1
30
4 1
1
220379525.9 min
r
A e dr
A cm
The value of A 1 is Calculated by Simpson Method i.e
A 1 = x /3{Yo+4(Y 1 +Y 3 +Y 5 +………+Yn-l)+ 2(Y 2 +Y 4 +Y 6 +………+Yn)}---------
x =1cm
Values of Yo, Y1, Y2, Y3 ………..Yn are taken from Table 2 (Y=
4 r P'(r) )
A 2 = 1017252985cm
4
min
1 2
4 1
1237632511 min
A A A
A cm
From values of A and A
/
we are able to calculate the Fermi age value because we know
4
2
(^0 )
/
( )
6 ( , )
( )
6
r P r dr
E E r
r P r dr
A
A
Putting the Values of A
/
and A we get value of Fermi age as
7.10 cm
6.2 Calculations of Diffusion Length (L)
6.2.1 For area under the curve calculation of r
2
P (r)
Figure 3
The value of point A is observed from figure 3; A=21cm
2
2 1
2 2
1
1 1
2 1
4 1
1 1
4 1
2 2
From table 1
For point 1, 22 and 12531486cm min
For point 2, 25 and 9642812.5cm min
Now solving equation (1) and (2) and solving them fo
c r
c r
c r
y c e
y c e
y c e
r cm y
r cm y
1
2
4 1
1
r selected poins we find the values
1093615.79cm min
c cm
c
/ / 2
2
/ / ( 0.109)
2
21
/ / 4 1
2
1
2022504.521 min
c r
rA
r
A c e dr
A e dr
A cm
The value of A
//
1 is Calculated by Simpson Method i.e
A
//
1 =^ x /3{Yo+4(Y 1 +Y 3 +Y 5 +………+Yn-l)+ 2(Y 2 +Y 4 +Y 6 +………+Yn)}
x =1cm
2 1 1
( 0.07)
1
31
2 1
1
328241454.4 min
A
c r
r
r
A c e dr
A e dr
A cm
The value of A 2 is calculated by Simpson Method i.e.
A 2 = x /3{Yo+4(Y 1 +Y 3 +Y 5 +………+Yn-l)+ 2(Y 2 +Y 4 +Y 6 +………+Yn)}
x =1cm
Values of Yo, Y1, Y2, Y 3 ………..Yn are taken from Table 2 (Y=
4 r P''(r))
A2 = 1.06524E+11cm
2
// 1 2
2 1
/ /
1.06852E 11 min
A A A
A cm
From values of A
//
and A//we are able to calculate the diffusion length value because we know
4
2 2
2
2 / /
/ /
r P r dr
L r
r P r dr
A
L
A
L cm
So the value of diffusion length is 8.21cm
6.3 Calculations of Migration Length (L)
The value of migration length is calculated with help of results obtained in above calculations i.e. from
Fermi age and Diffusion length. The expression is
Putting the values of L
2
and τ we get
2
2
7.10 67.
M
cm
6.4 Calculations of Extrapolation Length (d)
Figure 5
Figure 5 is obtained by plotting count rate as a function of distance (Vertical) from the water air
interface. The curve was extrapolated the curve tangentially to zero. So according to Figure 5, we
have extrapolated length is d = 3.97 cm
