Search
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/05%3A_Nuclear_Structure
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/07%3A_Radioactive_Decay_Part_IIThis decay, or loss of energy, results in an atom of one type, called the parent nuclide, transforming to an atom of a different type, named the daughter nuclide. We already introduced the general pri...This decay, or loss of energy, results in an atom of one type, called the parent nuclide, transforming to an atom of a different type, named the daughter nuclide. We already introduced the general principles of radioactive decay in Section 1.3 and we studied more in depth alpha decay in Section 3.3. In this chapter we consider the other two type of radioactive decay, beta and gamma decay, making use of our knowledge of quantum mechanics and nuclear structure.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/03%3A_Radioactive_Decay_Part_IThumbnail: Alpha particle decay of a nucleus. (Public Domain; Inductiveload via Wikipedia)
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/06%3A_Time_Evolution_in_Quantum_Mechanics/6.02%3A_Evolution_of_Wave-packetsAs usual, the variance of the initial wavefunction and of its Fourier transform are relates: \(\Delta k=1 /(2 \Delta x)\), where \(\Delta x\) is the initial width of the wave-packet and \(\Delta k\) t...As usual, the variance of the initial wavefunction and of its Fourier transform are relates: \(\Delta k=1 /(2 \Delta x)\), where \(\Delta x\) is the initial width of the wave-packet and \(\Delta k\) the spread in the momentum.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/04%3A_Energy_Levels/4.03%3A_Solutions_to_the_Schrodinger_Equation_in_3DThen, we can solve for each electron separately, as we did for the Hydrogen atom equation, and find for each electron the same level structure as for the Hydrogen, except that the since the potential ...Then, we can solve for each electron separately, as we did for the Hydrogen atom equation, and find for each electron the same level structure as for the Hydrogen, except that the since the potential energy is now \( \frac{1}{4 \pi \epsilon_{0}} \frac{Z e^{2}}{r_{j}}\) the electron energy (Bohr’s formula) is now multiplied by Z.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/02%3A_Introduction_to_Quantum_Mechanics/2.05%3A_Operators_Commutators_and_Uncertainty_PrincipleDefine C = [A, B] and ΔA and ΔB the uncertainty in the measurement outcomes of A and B: \( \Delta A^{2}= \left\langle A^{2}\right\rangle-\langle A\rangle^{2}\), where \( \langle\hat{O}\rangle\) is the...Define C = [A, B] and ΔA and ΔB the uncertainty in the measurement outcomes of A and B: \( \Delta A^{2}= \left\langle A^{2}\right\rangle-\langle A\rangle^{2}\), where \( \langle\hat{O}\rangle\) is the expectation value of the operator \(\hat{O} \) (that is, the average over the possible outcomes, for a given state: \( \langle\hat{O}\rangle=\langle\psi|\hat{O}| \psi\rangle=\sum_{k} O_{k}\left|c_{k}\right|^{2}\)).
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/01%3A_Introduction_to_Nuclear_Physics/1.02%3A_Binding_energy_and_Semi-empirical_mass_formulaThe total binding energy is instead the difference between the interaction of a nucleon to its neighbor and the kinetic energy of the nucleon itself. This correction (and the following one) can only b...The total binding energy is instead the difference between the interaction of a nucleon to its neighbor and the kinetic energy of the nucleon itself. This correction (and the following one) can only be explained by a more complex model of the nucleus, the shell model, together with the quantum-mechanical exclusion principle, that we will study later in the class.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/06%3A_Time_Evolution_in_Quantum_Mechanics/6.04%3A_Fermis_Golden_Rule\[\sum_{k}\left[i \hbar \dot{c}_{k}(t) e^{-i \omega_{k} t} u_{k}(x)\right. \left.+\hbar \omega c_{k}(t) e^{-i \omega_{k} t} u_{k}(x)\right]= \sum_{k}\left[c_{k}(t) e^{-i \omega_{k} t} \hbar \omega_{k}...\[\sum_{k}\left[i \hbar \dot{c}_{k}(t) e^{-i \omega_{k} t} u_{k}(x)\right. \left.+\hbar \omega c_{k}(t) e^{-i \omega_{k} t} u_{k}(x)\right]= \sum_{k}\left[c_{k}(t) e^{-i \omega_{k} t} \hbar \omega_{k} u_{k}(x)+\right. \left.c_{k}(t) e^{-i \omega_{k} t} \hat{V}\left[u_{k}(x)\right]\right] \nonumber\]
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/00%3A_Front_Matter
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/06%3A_Time_Evolution_in_Quantum_MechanicsUntil now we used quantum mechanics to predict properties of atoms and nuclei. Since we were interested mostly in the equilibrium states of nuclei and in their energies, we only needed to look at a ti...Until now we used quantum mechanics to predict properties of atoms and nuclei. Since we were interested mostly in the equilibrium states of nuclei and in their energies, we only needed to look at a time-independent description of quantum-mechanical systems. To describe dynamical processes, such as radiation decays, scattering and nuclear reactions, we need to study how quantum mechanical systems evolve in time.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/02%3A_Introduction_to_Quantum_Mechanics
