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# 物理代写|PHYS5011 Nuclear Physics

## PHYS5011课程简介

This unit is normally undertaken as part of the Master of Medical Physics or the Graduate Diploma in Medical Physics. Nuclear properties and models, and the main types of radioactive decay (alpha, beta, and gamma decay) are covered. There is also a brief introduction to nuclear reactions. This UoS also includes fundamentals of nuclear magnetic resonance spectroscopy, and magnetic resonance imaging.

## Prerequisites

At the completion of this unit, you should be able to:

• LO1. demonstrate an understanding of basic nuclear structure, mass, and binding energy
• LO2. demonstrate an understanding of nuclear shells and nuclear collective states
• LO3. demonstrate an understanding of the main processes of radioactive decay
• LO4. demonstrate a basic understanding of nuclear reactions
• LO5. demonstrate an understanding of the physics of NMR and MRI
• LO6. demonstrate an understanding of image acquisition in MR
• LO7. demonstrate an understanding of quality assurance principles in MRI
• LO8. demonstrate an understanding of room shielding and safety aspects of MRI
• LO9. demonstrate an understanding of clinical applications of MRI

## PHYS5011 Nuclear Physics HELP（EXAM HELP， ONLINE TUTOR）

Compare the mass of $1 \mathrm{~mm}^3$ of nuclear matter and the mass of the Earth $\left(\sim 6 \times 10^{24} \mathrm{~kg}\right)$.

A commonly used quantity is the mass excess defined as
$$\Delta \equiv m(A, Z)-A \times 1 \mathrm{u} .$$
Derive an expression for $\Delta$ in terms of the nuclear binding energy $B(A, Z)$.

Consider the reaction $\gamma+{ }^{12} \mathrm{C} \rightarrow 3{ }^4 \mathrm{He}$. What is the threshold energy of the reaction? If two $\alpha$-particles have the same momentum in the c.m. system, what fraction of the energy is carried by the third particle?

The $A=40$ isotopes of calcium $(Z=20)$, potassium $(Z=19)$ and argon $(Z=18)$ have respective binding energies $-332.65 \mathrm{MeV},-332.11 \mathrm{MeV}$ and $-335.44 \mathrm{MeV}$. What $\beta$ decays are allowed between these nuclei? Specify the available energy $Q$ in the final state. What peculiarity appears?

Consider a quantum system of $A$ pairwise interacting fermions with twobody attractive interactions of the form $V(r)=-g^2 / r$. Using the uncertainty relation ${ }^8\left\langle p^2\right\rangle \geq A^{2 / 3} \hbar^2\langle 1 / r\rangle^2$ show that $\langle E\rangle / A \simeq-A^{4 / 3} \cdot g^4 \mathrm{~m} / 8 \hbar^2$, and $r \simeq 2 \hbar^2 A^{-1 / 3} / \mathrm{mg}^2$. This is a usual cumulative effect for attractive forces: energies per particle increase and radii decrease as the number of particles increases. The powers $4 / 3$ and $-1 / 3$ are specific to the Coulomb-type interactions but one can verify that, for a harmonic potential, one obtains $|E / A| \sim A^{5 / 6}$ and for a spherical well, $|E / A| \sim A^{2 / 3}$. This shows that the Pauli principle alone cannot lead to saturation of nuclear forces.

Consider a quantum system of $A$ pairwise interacting fermions with twobody attractive interactions of the form $V(r)=-g^2 / r$. Using the uncertainty relation ${ }^8\left\langle p^2\right\rangle \geq A^{2 / 3} \hbar^2\langle 1 / r\rangle^2$ show that $\langle E\rangle / A \simeq-A^{4 / 3} \cdot g^4 \mathrm{~m} / 8 \hbar^2$, and $r \simeq 2 \hbar^2 A^{-1 / 3} / \mathrm{mg}^2$. This is a usual cumulative effect for attractive forces: energies per particle increase and radii decrease as the number of particles increases. The powers $4 / 3$ and $-1 / 3$ are specific to the Coulomb-type interactions but one can verify that, for a harmonic potential, one obtains $|E / A| \sim A^{5 / 6}$ and for a spherical well, $|E / A| \sim A^{2 / 3}$. This shows that the Pauli principle alone cannot lead to saturation of nuclear forces.

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