25. The differential cross section
Roughly
speaking, the cross section is a measure of the relative probability
for the reaction to occur. If we have a detector placed to record
particle b emitted in a direction with respect to the beam
direction, the detector defines a small solid angle
at
the target nucleus (Figure 1). Let the current of incident particles
be
particles per unit time, and let the target show to the beamN
target nuclei per unit area. If the outgoing particles appear at a
rate Rb.
then the reaction cross section is
.
Where
.
The quantity
is
called the differential
cross section.
and its measurement gives us important information on the angular
distribution of the reaction products. Because solid angle is
measured in steradians , units of differential cross section are
bams/steradian.
34.Coulomb barrier
The
Coulomb barrier, named after Coulomb's law, which is named after
physicist Charles-Augustin de Coulomb (1736–1806), is the energy
barrier due to electrostatic interaction that two nuclei need to
overcome so they can get close enough to undergo a nuclear reaction.
This energy barrier is given by the electrostatic potential energy:
.
A positive value of U is due to a repulsive force, so interacting
particles are at higher energy levels as they get closer. A negative
potential energy indicates a bound state (due to an attractive
force). Coulomb's barrier increases with the atomic numbers (i.e. the
number of protons) of the colliding nuclei:
.
To overcome this barrier, nuclei have to collide at high velocities,
so their kinetic energies drive them close enough for thestrong
interaction to
take place and bind them together.
It was the absence of a Coulomb barrier for the neutron.
37.The laws of conservation angular momentum, parity, charge, baryon charge, isospin.
The law
of conservation of angular momentum states
that when no external torque acts
on an object or a closed system of objects, no change of angular
momentum can occur. Hence, the angular momentum before an event
involving only internal torques or no torques is equal to the angular
momentum after the event. The conservation of angular momentum is
used extensively in analyzing what is called central
force motion. The
time derivative of angular momentum is called torque:
The baryon number is conserved in nearly all the interactions of the Standard Model. 'Conserved' means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.
Isospin is a term introduced to describe groups of particles which have nearly the same mass, such as the proton and neutron.
One of the conservation laws which applies to particle interactions is associated with parity.
Quarks
have an intrinsic parity which is defined to be +1 and for an
antiquark parity = -1. Nucleons are defined to have intrinsic parity
+1. For a meson with
quark and antiquark with antiparallel spins (s=0), then the parity is
given by
