if the Coordinates system is

R

r

b (impact parameter

Type of Nuclear traction Depends on the impact parameter

1- for b > r+R

Scattering reaction

The scattering reaction could be

1- elastic sacattering or

2- inilastic scattering

2- if b<r+R

Transfer reaction

a- Stripping reaction

2H + zAX 1H+ z

A+1X

b-Pick Up reaction

1H + zAX 2H+ z

A-1X

If b<<R+r

Fusion reaction or compund nucleus reaction

1327Al+ 1H [14

28Si]*

12Mg+ He

14Si +n

14Si + gamma

11Na + 3 H + n

+

+

S

NIR ob

Suppose a beam of particles is incident on a thin target of area S, which contain a total number of N nuclei. The effective area of each nucleus is and total effective area will be N. the fraction of the target area which this represents is N/S

Example

in the following reaction 56Fe (1H , 1n)56Co has a cross section of 0.6 b. if a target in the form of a 1 cm square, 1, micrometer thick had been bombarded with a beam of protons equivalent to 3 microAmper . At what rate are the neutrons produced

In a reactor the intensity of neutrons is expressed neutron flux n/cm2/s, which is defined as the rate at which the neutrons cross a unite area to the beam.

Example

30 mg of 197Au are exposed to neutron flux 3 1012 n/cm2//s for one minute . The neutron capture cross section of gold is 99b. Find the resultant 198Au (T1/2=2.7 d).

M

mσ10 6.02R 23

Radioisotope production in nuclear reactions

In a time interval dt the number of Y nuclei produced = R dt .

Since Y is radioactive, the number of Y that decay in time dt =Ndt

The net change

dN = Rdt- Ndt

dN/dt= R - N

The solution of this differentia equation is

N(t)= (R/ ) (1-e -t)

The activity is

A(t)= N= R(1-e -t)

At t= 0 A=0

t >> t1/2 A(t) = R[1(1- t+….)]

= R t

Examples30 mg of 197Au are exposed to neutron flux 3 1012 n/cm2//s for one

minute . The neutron capture cross section of gold is 99b. Find the resultant 198Au (T1/2=2.7 d).

The radioactive 61Cu (t1/2=3.41 h) is produced by a 12 A beam of particles on 1.5 cm x 1.5 cm x 2.5 m target of 59Co. If =0.64 b.

a) What is the production rate of Cub) what is the activity of Cu after 2 h of irradiation.

copmute the Q value for the reaction 63Cu(2H, n)64Zn If the energy of 2H is 12 MeV, “” n is16.85 MeV find the kinetic energy of 64Zn

Calculate the threshold KE for the reaction 3H(1H,2 2H) If the proton incident on 3H at restIf the 3H incident on proton at rest