Nuclear Physics equations and more Flashcards
What is the atomic length and energy scale?
What about nuclear?
Atomic length: ~10pm (10^-10), energy: ~1-100eV
Nuclear length: ~1fm (10^-15), energy: ~1MeV (10^6eV)
What is the approximate value of hbar c in MeVfm?
~200MeVfm
What is the de broglie wave equation?
lambda = h/p
What are the heisenberg relations for position-momentum and energy-time?
energy width * lifetime ~ hbar
momentum width * position width ~ hbar/2
Derive the equation for half life in terms of the decay constant lambda.
N is total # nuclei.
time derivative of N is -lambda N
Integrate to give N(t)
N(t1/2) = N0 / 2
What are the spectroscopic notation terms for angular momentum values?
0: s
1: p
2: d
3: f
g, h, i…
How can we extract nuclear mass from atomic mass?
What have we neglected?
Nuclear mass = Atomic mass - Z * electron mass
**we have neglected the electron binding energy (small)
What is the definition of the mass excess?
Mass excess = Atomic mass - A * atomic mass unit
How can we extract the nuclear mass from the mass excess?
Nuclear mass = Mass excess + Au - Zm_e
How can we extract the binding energy using atomic masses?
Binding energy = [Z*(atomic mass of hydrogen) + (#neutrons * neutron mass) - Atomic mass] * c^2
(the sum of constituent parts - the mass)
positive for stable nuclei
How should we interpret binding energy?
Usually binding energy per nucleon is considered.
Positive binding energy implies that a bound state is energetically favourable!
What is a direct method of measuring nuclear masses?
Use a uniform magnetic field and measure circular motion radius. Then use the lorentz force law to calculate the mass.
How is the Q-value defined for a reaction?
Initial rest mass energy - final rest mass energy.
IN TERMS OF NUCLEAR MASSES
**i.e: final KE - initial KE
How should the Q value be interpreted?
Positive: exothermic, energetically favourable
Negative: endothermic, unfavourable
What is Gamow’s saturation hypothesis?
What is the value of the constant as found by matching the model to empirical data?
The nuclear force is “saturated” within a nucleus, i.e: as A increases, the volume per nucleon remains the same:
R = R_0 * A^(1/3)
R_0 = ~1.2fm
What is the definition of “skin thickness”?
What is its usual value?
Skin thickness is the radial distance over which the density of the nucleus falls from 90% to 10% of the central value.
~2.3fm for all nuclei
What distribution do we often use to approximate the charge density distribution in a nucleus?
The fermi-dirac distribution:
rho_0 / [1+ e^((r-R)/a)]
How can we investigate the matter density of a nucleus given information about its charge density?
The matter density is linearly related to the charge density.
rho_mass ~ A/Z * rho_charge
What are the two key observations from measurement of nuclear size?
Density at the nuclear core is ~constant, regardless of A. This suggests saturation of the nuclear force and that the nuclear force is repulsive at very short range.
Skin thickness t is ~constant, regardless of A. This suggests that the nuclear force is attractive at short range.
What is the meaning of charge symmetry and independence?
What is some evidence for this?
The nuclear force acting between two protons ~ that between two neutrons ~ between a proton and a neutron.
Approximately equal mass of the three pions (the exchange particles for nucleon interactions.
-> scattering
The similar properties of mirror nuclei (charge symmetry) and isobaric multiplets (charge independence).
What are the 5 terms in the SEMF (semi-empirical mass formula)?
Volume term, Surface term, Coulomb term, Asymmetry term, nucleon pairing term.
What are the three classical SEMF terms, and their physical interpretation?
Volume term: assumes binding energy per nucleon constant so energy proportional to A.
Surface term: accounts for nucleons at the surface being bound less tightly.
Coulomb term: accounts for the electromagnetic repulsion between protons. (assuming homogenous nucleus)
For what range of mass number is the SEMF sucessful?
A > 20
What is the role of the asymmetry term in the SEMF?
Nuclei prefer N = Z. This effect decreases for heavier nuclei.