Calculation the Cross Sections for 64 Cu ( n , p ) 64 Ni Reaction By Reciprocity Theory

In this study intermediate elements Ni , Cu for Ni (p,n)Cu reaction with proton energy from (1.0) MeV to (132) MeV with threshold energy (2.496) MeV are used according to the available data of reaction cross sections. We calculated the cross sections for Cu(n,p)Ni reaction by application in nuclear technology (reciprocity theory). In reciprocity theory we derive the mathematical formula for Cu(n,p)Ni and we deduced high probability to produced Ni because it is very important such as it used in technology field .The evaluated cross sections as a functions of neutron energy between (En =0.504MeV) to (En=129.506MeV) of (0.0106barn) (0.254barn) respectively and statistical factor (gp,n=1 and gn,p=1/3) . Introduction When two charged nuclei, overcoming their Coulomb repulsion, a rearrangement of the constituents of the nucleus may occur. Similar to the rearrangement of atoms in reacting molecules during a chemical reaction this may result as a nuclear reaction. Nuclear reactions are usually produced by bombarding a target nucleus with a nuclear projectile , in most cases a nucleon (neutron or proton) or a light nucleus such as a deuteron or an αparticle [1]. At low excitation energies (< 10 MeV), the majority of nuclear reactions involve the formation of two nuclei, one nearly equal in charge and mass number to the target nucleus. Such reactions are represented by an equation of the type : a + X → b + Y -----(1) Or X ( a,b ) Y Where (a) is the light projectile nucleus (proton , neutron, deuteron, 3H, 3He, or 4He) and (X) is the target nucleus at rest in the laboratory system. (Y) is the produced nucleus and (b) is a light nuclear particle which carries away the major share of the kinetic energy. If the product nucleus (Y) is left in an excited state after the emission of the light particle (b), it usually subsequently decays by radiating one or more gamma rays. Alternatively if (Y) is beta unstable, it decays at some later date by electron or positron emission followed by gamma emission [2]. Nuclear reactions of low excitation energies include the following types : (n,γ) , (n,p) , (n,α) , (α,n) , (p,γ) , (p,n) , (d,n) , (d,p) , .....etc. X + a, X*+ a, X + a Y + b, -----(2) Y* + b, In the first two reactions of the set (2) the outgoing particle is of the same kind as the incident particle, and the process is called scattering. The first reaction represents elastic scattering and the second reaction represents inelastic scattering in which the target nucleus ( X ) is raised into an excited state (X*). The other reactions of the set represent different possible nuclear transmutations in which the product nuclei may be found in their ground states or, more often, in excited states. The excited product nucleus usually decays very quickly to the ground state with the emission


Introduction
When two charged nuclei, overcoming their Coulomb repulsion, a rearrangement of the constituents of the nucleus may occur.Similar to the rearrangement of atoms in reacting molecules during a chemical reaction this may result as a nuclear reaction.Nuclear reactions are usually produced by bombarding a target nucleus with a nuclear projectile , in most cases a nucleon (neutron or proton) or a light nucleus such as a deuteron or an αparticle [1].
At low excitation energies (< 10 MeV), the majority of nuclear reactions involve the formation of two nuclei, one nearly equal in charge and mass number to the target nucleus.Such reactions are represented by an equation of the type : a + X → b + Y ------(1) Or X ( a,b ) Y Where (a) is the light projectile nucleus (proton , neutron, deuteron, 3H, 3He, or 4He) and (X) is the target nucleus at rest in the laboratory system.(Y) is the produced nucleus and (b) is a light nuclear particle which carries away the major share of the kinetic energy.If the product nucleus (Y) is left in an excited state after the emission of the light particle (b), it usually subsequently decays by radiating one or more gamma rays.Alternatively if (Y) is beta unstable, it decays at some later date by electron or positron emission followed by gamma emission [2].
Nuclear reactions of low excitation energies include the following types : (n,γ) , In the first two reactions of the set (2) the outgoing particle is of the same kind as the incident particle, and the process is called scattering.The first reaction represents elastic scattering and the second reaction represents inelastic scattering in which the target nucleus ( X ) is raised into an excited state (X*).The other reactions of the set represent different possible nuclear transmutations in which the product nuclei may be found in their ground states or, more often, in excited states.The excited product nucleus usually decays very quickly to the ground state with the emission of -rays.

Sections Of Nuclear Reactions:
To characterize the probability that a certain nuclear reaction will take place, it is customary to define an effective area of the nucleus for that reaction, called a cross section [1].The reaction cross section data provides information of fundamental importance in the study of nuclear systems.The cross section is defined by [3]: The cross section has the units of area and is of the order of the square of nuclear radius and a commonly used unit is the barn: 1 barn = 10 -24 cm 2 In general, a given bombarding particle and target can react in a variety of ways producing a variety of light reaction products per unit time.The total cross section is then defined as [4]: Where σ i is the partial cross section for the process [1].

Reverse Reaction:
If the cross-sections of the reaction A(p,n)B are measured as a functions of T p (T p = Kinetic energy of incident proton), the crosssections of the inverse reaction B(n,p)A can be calculated as a function of T n (T n = Kinetic energy of neutron) using the reciprocity theorem [5] which states that : Where σ (p,n) and σ (n,p) represent crosssections of A(p,n)B and B(n,p)A reactions respectively, g (p,n) and g (n,p) represent a statistical factors of A(p,n)B and B(n,p)A reactions respectively  is the de-Broglie wave length divided by 2π and is given by Where ħ is Dirac constant (h /2π ), h is Plank constant, M and V are mass and velocity of p or n .From eq.( 6) ,we have The statistical g-factors are givens by [5] The conservation low of the momentum and parity implique that : c and π c are total angular momentum and parity of the compound nucleus .10) ,we have : The reactions A(p,n)B and B(n,p)A can be represented with the compound nucleus C as in the following schematic diagram.It is clear that there are some important and useful relations between the kinetic energies of the neutron and proton.
One can calculate the separation energies of proton (S p ) and neutron (S n ) using the following relations: 17a) , (17b) , ( 18) , ( 19) And the equation of Q-value of the reaction A(p,n)B which is given by : Then the threshold energy E th is : Thus eq .( 5) can be written as follows: It is clear from this equation that the cross sections of reverse reaction are related by a variable parameters which can be calculated if the nuclear characteristics of the reactions are known.
[7]Chiba,Chadwick,ate.; ENDF/B-VII Library ; (1999) IA and π A are total angular momentum and parity of nucleus A.I B and πB are total angular momentum and parity of nucleus B.Ip and π p are total angular momentum and parity of proton.In and π n are total angular momentum and parity of neutron .