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PHYS-406: Nuclear Physics-II
Chapter 3: Nuclear Reactions
Dr. Quazi Muhammad Rashed-Nizam
Associate Professor
Department of Physics
University of Chittagong
Chittagong-4331, Bangladesh
Chapter 4: Nuclear Reactions
Outline of syllabus
- Partial wave analysis from cross
sections
- Breit-Wigner formula
- Compound nucleus hypothesis
- Discrete levels and level width, life
time
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Evolution History of NP
Ref: Fundamentals in Nuclear Physics, Basdevant, Rich and Spiro, Springer publications, 2005
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Evolution History of NP
Ref: Fundamentals in Nuclear Physics, Basdevant, Rich and Spiro, Springer publications, 2005
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Evolution History of NP
Ref: Fundamentals in Nuclear Physics, Basdevant, Rich and Spiro, Springer publications, 2005
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Nuclear Physics: Why
One of the aims of nuclear physics is to calculate the
energies and quantum numbers of nuclear bound states.
Forces between nucleons are neither simple nor fully
understood. One of the reasons for this is that the
interactions between nucleons are “residuals” of the
fundamental interactions between quarks inside the
nucleons.
Studies on cross sections and angular distribution of
disintegration products, coupled with the various
theoretical developments, have led to a better
understanding of the nature of the nucleus and nuclear
forces. 6
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Nuclear Reaction
Consider a beam of neutron incident on a Pb208 target.
Then the following could happen:
Ref: Nuclear Physics, H.S. Gupta
Ref: Nuclear Physics, Roy and Nigam 7
Cross sections
The nuclear cross section of a nucleus is used to
characterize the probability that a nuclear reaction
will occur.
The concept of a nuclear cross section is
somewhat difficult to conceptualize but can be
quantified physically in terms of "characteristic
area" where a larger area means a larger
probability of interaction.
The standard unit for measuring a nuclear cross
section (denoted as σ) is the barn, which is equal
to 10−28 m² or 10−24 cm².
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Cross sections
• A small particle incident on a slice
of matter containing 𝑁 = 6 target
spheres of radius R.
• If the point of impact on the slice is
random, the probability 𝑑𝑃 of it
hitting a target particle is
𝑑𝑃 = 𝑁𝜋𝑅 /𝐿 = 𝜎𝑛𝑑𝑧
• where the number density of
scatterers is 𝑛 = 𝑁/(𝐿 𝑑𝑧) and the
cross section per sphere is
𝜎 = 𝜋𝑅 [𝜎 = ].
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Reaction cross section
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Reaction cross section
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Reaction cross section
𝑑𝜎
𝜎 = 4𝜋
𝑑Ω
Prove it with proper explanation.
Ref: Krane, page 392-393 12
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Cross sections
Shape elastic or potential scattering: is caused
by the interaction of the neutron wave with the
potential at the nuclear surface. Effectively the
incident neutron does not enter the target nucleus
and the compound nucleus is not formed. It results
from the diffraction of those neutrons which pass
close by, but not into the nucleus.
Compound elastic or Resonance scattering: In
the case of elastic resonance scattering the neutron
is captured by the target nucleus when its energy is
close to one of the quantum states and it is re-
emitted. Ref: Nuclear Physics, Roy and Nigam 13
Cross sections
Ref: Introductory Nuclear Physics, Krane 14
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
Ref: Anwar Kamal, 5.2.3, p-293.
Krane, 11.8,p-408 16
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Partial wave anlysis
Partial wave analysis is a method used to describe nuclear
reaction cross sections by decomposing the scattering
wavefunction into a sum of angular momentum components
(partial waves). This technique is particularly useful in
quantum mechanical scattering problems, where the
interaction potential is spherically symmetric.
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Partial wave analysis
Ref: Krane, Section 11.8, 408
*HW-Problem 5.8-5.10, Anwar kamal, P-345 18
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Cross sections: Quantum mechanical approach
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Compound Nucleus Theory
- Was proposed by Bohr in 1936.
- The compound nucleus theory
work best for low incident
energies (10-20 MeV) where
the incident particle has low
chance to escape with its
density and most of its energy
intact.
- The angular distribution is
isotropic (same in all
directions).
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Compound nucleus model
For high energy neutrons the scattering and absorption
cross section is lower.
For low energy neutron the cross section is higher.
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Compound nucleus model
In 1936 Bohr proposed the compound nucleus theory for
nuclear reaction. According to this, reaction takes place in
two steps (for low energy of particle specially):
1. The incident particle together with target nucleus formed
the compound nucleus in which energy is shared among
all nucleons.
2. The compound nucleus then decays to the final products.
Since the life time of compound nucleus is much greater
than the time taken by the incident particles to traverse
the nucleus 10 , it is assume that the mode of decay
of the compound nucleus is independent of its mode of
formation except for the requirements for the various
conservation law.
Ref: Nuclear Physics, Roy and Nigam 30
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Compound nucleus model: Ghoshal Experiment
*Anwar Kamal-447
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Compound nucleus model: John Experiment
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Compound nucleus model: John Experiment
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Compound nucleus model: Decay width
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Compound nucleus model: Decay Rate
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Compound nucleus model: Decay Rate
*Reciprocity
theorem, 7.7
(Inverse
Reaction),
Anwar Kamal,
P-439
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Compound nucleus model: Cross section
Ghoshal-P-390 37
Compound nucleus model: Cross section
Ghoshal-P-391 38
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Compound nucleus model: Cross section
Ghoshal-P-391 39
Compound nucleus model: Cross section
For the particle having angular momentum, l (in case of
high energy)
Ghoshal-P-393 40
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References
1. Nuclear Physics-Hironmoy Shen Gupta**
2. Nuclear Physics- Azaharul Islam & Nurul Islam.
3. Fundamentals in Nuclear Physics, Basdevant, Rich and
Spiro, Springer publications, 2005**
4. Nuclear Physics: Theory and Experiment; R.R Roy and
B.P. Nigam
5. Nuclear reactions: An introduction, Hans Paetz gen.
Schieck
6. Nuclear Physics, Anwar Kamal
7. Theoretical Nuclear Physics, Blatt and Weisskopf
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Compound Nucleus Theory
- Was proposed by Bohr in 1936.
- The compound nucleus theory
work best for low incident
energies (10-20 MeV) where
the incident particle has low
chance to escape with its
density and most of its energy
intact.
- The angular distribution is
isotropic (same in all
directions).
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Nuclear Terminology
The parity is the sign by which the total constituent
wavefunction changes when the spatial coordinates of all
nucleons change sign.
The ground states of even-even nuclei are found to be 0+.
By convention both neutron and proton have the even
parity (+).
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Spin Half
The spin number describes how many symmetrical facets
a particle has in one full rotation; a spin of 1/2 means that
the particle must be rotated by two full turns (through
720°) before it has the same configuration as when it
started.
a spin of 1/2 means that the particle must be rotated by
two full turns (through 720°) before it has the same
configuration as when it started.
The dynamics of spin-1/2 objects cannot be accurately
described using classical physics; they are among the
simplest systems which require quantum mechanics to
describe them. As such, the study of the behavior of spin-
1/2 systems forms a central part of quantum mechanics.
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