Showing posts with label crosssection. Show all posts
Showing posts with label crosssection. Show all posts

PHYSICS DICTIONARY

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Critical Temperature

The highest temperature, below which a gas can be liquefied only by increasing the pressure and above which a gas cannot be liquefied how so ever high pressure may be applied.


Critical Volume

Volume of unit mass of gas at the critical temperature and critical pressure is called critical volume of gas.


Crookes Tube

A Crookes tube is an electric discharge invented by British chemist and physicist William Crookes in the early 1870’s. It consists of a sealed glass tube which is evacuated to an air pressure between 0.005Pa and 0.1Pa and incorporates two electrodes (cathode and anode) connected to external DC power supply. When high voltage is applied to the tube, electric discharge in the rarefied air inside the tube ionizes some air molecules. Positive ions move in the electric field toward the cathode and create more ions through collisions with air molecules. As positive ions strike the cathode, electrons are released from the cathode, move toward the anode in the electric field that is present between the cathode and anode.     


Cross Product

Cross product of two vectors is a vector whose magnitude is equal to the product of magnitudes of those two vectors and the sine of angle between them. Direction of this vector is perpendicular to plane containing those two vectors. 


Crossection

It is defined as the probability that an event may occur when a single nucleus is exposed to a beam of particles of total flux containing one particle per unit area.


Cryocan

Container used to store super cooled liquids like liquid nitrogen. They are designed in such a fashion to minimize heat transfer due to radiation, conduction or convection.


Cryogenics

Study of low temperatures less than -150 oc including production of low temperatures and behavior of materials at low temperatures is called as Cryogenics.


Cryoscope

Instrument used to determine freezing point of a substance.


Cryotron

It is magnetically controlled electronic switching device that operates at extremely low temperatures. It uses principle of varying magnetic field that can cause resistance of a superconducting element to change rapidly between its high normal and low superconductive values. It is used as a switch and as a computer memory element.


Crystal Momentum

It is momentum associated with dynamical behavior of electron in periodic potential. It is defined as product of effective mass of electron and group velocity associated with electron in periodic potential.


Crystal Oscillator

Oscillations made from crystals exhibiting Piezo-electric effect. These oscillators oscillate at constant frequency which changes by less than 0.1% due to temperature and other changes.


Crystal Structure

For crystalline materials, the manner in which atoms or ions are arrayed in space is conveyed by crystal structure. It is defined in terms of unit cell geometry and the atom positions within the unit cell.


Crystal System

It is a scheme by which crystal structures are classified according to unit cell geometry. This geometry is specified in terms of relationships between edge lengths and inter-axial angles. There are seven different possible combinations of 3 edge lengths and 3 inter-axial angles referred to as crystal systems.


Crystal

Material in which atoms are situated in a repeating or periodic array over large atomic distances; that is long range order exists such that upon solidification, the atoms will position themselves in a repetitive three dimensional pattern, in which each atom is bonded to its nearest neighbor atom.


Crystalline Defect

A lattice irregularity having one or more of its dimensions on order of atomic diameter is called as crystalline defect.


Crystalline

The state of a solid material characterized by a periodic and repeating atomic arrangement is achieved by molecular chain alignment.


Crystallite

A region within a crystalline polymer in which all the molecular chains are ordered and aligned is called as crystallite.


Crystallographic Direction

It is defined as vector between two points in a crystal lattice.


Curie Law

The intensity of magnetization is I=AH/T  ; ‘H’ is magnetic field strength, ‘T’ is absolute temp, ‘A’ is curies constant. It is applicable for paramagnetic substance.


Curie Temperature

The temperature above which a Ferromagnetic Material becomes paramagnetic is called as Curie temperature.


Curie

It is the unit used to describe the strength of a radioactive source in terms of number of disintegrations it undergoes in a unit time. It is designated by Ci. One curie equals 3.7 x 1010 disintegrations per second. It has originated based on rate of decay of a gram of Radium. Experiments have yielded the result that there are about 3.7 x 1010 disintegrates per second per gram of Radium. This number is taken as standard and called as Curie.


Curie–Weiss Law

The Curie law was modified by Weiss to state that susceptibility of a paramagnetic substance above the Curie point varies inversely as excess of temp above that point. This law is not valid at or below Curie point.


Current (Electric)

The net charge flowing through a crossection of a conductor in unit time is called current.


Cyclic Process

It is a process in which a system undergoes a series of changes and ultimately comes back to initial state.


Cyclotron

Type of accelerator invented by Ernest Lawrence of university of California, Berkely, in 1932. The 1939 noble prize in physics was awarded to Lawrence for the invitation and development of the cyclotron.  Cyclotron is a particle accelerator used to accelerate charged particles using high frequency alternating voltage applied between two “D” shaped electrodes. A static magnetic field is applied perpendicularly to the plane of electrons for accelerating particles at same phase. Particles escape electrodes by traversing spiral path.


ALL ABOUT NUCLEAR CROSSSECTION

The probability of a Nuclear Reaction can be defined in terms of number of particles emitted or number of nuclei undergoing transmutation for a specified number of incident particles.

It is usually expressed in terms of an effective area presented by a Nucleus towards the beam of bombarding particles, such that the number of incident particles that would strike such an area, calculated upon a purely geometrical basis, is the number observed to lead to Nuclear Reaction given in question.

This effective area is called crosssection for that reaction.

Thus the probability of occurrence of a particular Nuclear Reaction is described by effective crosssection for that process.

The crosssection may also be defined as 

1) The probability that an event may occur when a single nucleus is exposed to a beam of  particles of total flux one particle per unit area.

2) The probability that an event may occur when a single particle is shot perpendicularly at a target consisting of one particle per unit area.

The idea of crosssection gives imaginary area associated with each nucleus, the area is so chosen that if bombarded  particle passes through it the reaction takes place, otherwise it is not.

The total nuclear crosssection is effective area possessed by a nucleus for removing incident particles from a collimated beam by all possible process.

This can be written as sum of several partial crosssections which represent contributions to various distinct, independent processes which can remove particles  from incident beam.

Thus,

𝛔t  = 𝛔s  + 𝛔r                                                    ---------------(1)

𝛔t  is "Total crosssection"

𝛔s is "Scattering crosssection"

𝛔r is "Reaction Crossection"


Scattering Crossection

Scattering crosssection can be classified as 

i) Inelastic scattering

ii) Elastic Scattering

Thus, we get

𝛔s  = 𝛔el  + 𝛔inel                                                          --------(2)

These partial crossections can still be subdivided.

In case of elastic scattering separate partial crosssections cannot be written because of possibility of interference between them.

On other hand all inelastic scattering processses are incoherent and their crosssections are additive.  

𝛔inel  = 𝛔1  + 𝛔2 + 𝛔3 + .........                                      ------(3)

Differential crosssection

The distribution in angle of emitted particles in a nuclear reaction can be described in terms of a crosssection which is a function of angular coordinates in problem.

The crosssection which defines a distribution of emitted particles with respect to solid angle is called differential crosssection. It is defined by  d𝛔/d.

Partial crosssection for a given process is

𝛔  = ∫(d𝛔/dΩ)*dΩ                                                                ------(4)

Expression of crosssection for a Nuclear Reaction


Consider a mono energetic beam of particles incident on a target shown in Fig.

Let the beam be uniform and contain ‘n’ particles per unit volume moving with a velocity ‘V’ with respective to stationary target.

Clearly the product ‘nV’ gives number of particles crossing a unit area perpendicular to beam per unit time. It defines flux ‘F’ of particles in incident beam.

                                            F = nV -------------------------------(1)

It is customary to normalize number of particles to one particle per volume ‘V’.

                                            n = 1/V ------------------------------(2)

The detector detects all particles scattered through an angle ‘𝛳' into solid angle d.

The number of particles dN detected per unit time depends on following factors:

i)                    Flux of incident beam, F

ii)                   The solid angle, d

iii)                 Number of independent scattering centers in target that are intercepted by the beam. Let these be N.

                                   dN = 𝛔(𝛳)*F*dΩ*N ---------------------(3)

𝛔(𝛳) is constant of proportionality defines differential scattering crosssection.

We can put

                                   𝛔(𝛳)*dΩ =d𝛔(𝛳) 

                       𝛔(𝛳) =d𝛔(𝛳) / d -----------------------(4)

  The total number of particles scattered per unit time is obtained by integrating over  entire solid angle.

                                       N = F*N*𝛔total  --------------------------(5)

where,

    Total Crosssection  𝛔total  = ∫𝛔(𝛳) d ---------------------(6)

 𝛔total has dimensions of area.

Unit used to express crosssections is barn.

1 barn = 10⁻²⁸ cm².


The area 'a' intercepted by beam contains 'N' scattering centers. Total number of incident particles per unit time is given by

Nincident = F*a, where 'a' is area intercepted by beam; 'F' is incident flux.

Total number of scattered particles per unit time is

NscatteredF*N*𝛔total

(Nscattered/Nincident) = (N*𝛔total)/a   ------------------------(7)

𝛔total is equal to area effective in scattering for one scattering center.