Nuclear Physics Flashcards
beta -
n -> p + e- + v_bar
beta +
p -> n + e+ + v
electron capture
p + e- -> n + v
activity - production + decay
R(1 + e^(-lambda t)), R = N0 sigma I
barns to m^2
1b = 10^-28 m^2
amu to kg
1 u = 1.66054 x 10^-27
average binding energy of a nucleon
8 MeV
uncertainty principle
as distribution of momentum increases (lower momentum) distribution of position decrease (is everywhere)
what is the range of the nuclear force?
6fm
in an incident energy vs xs graph, what do the oscillations mean?
comes from energy being quantized. each spike represents a state. as energy increases there are more states, until there get to be such a dense number that it is represented as a smooth line.
What is the peak of the binding energy curve? Where is there a spike?
Iron 56 is the Peak, spike at He4
equation for radius of a nuclide
R = R0A^1/3
what is the force behind gamma decay?
electromagnetic
what’s the force behind beta decay?
the weak force
exposure rate
activity/distance^2
greys to joules/kg to rad
1 gy = 1 j/kg=100rad
what quantities can be related to each other via the uncertainty principle?
momentum and position, energy and time, angular momentum and angle
how are energy and cross section related?
as neutron slows down (lower energy) it has a higher cross section
When does the wave function look like an exponential decay
when E < U0
When does the wave function look oscillatory?
when E > U0
can we usually ignore binding energy of the electron?
yes
what are some ways you can show a nuclide is unstable using mass data?
Check to see if either type of beta decay is energetically favorable.
growth of daughter activities
dN2 = L1N1dt - L2N2dt, N2(t) = N0 L1/(L2 -L1)(e^-L1t - e^-L2t)
what assumption about growth of daughter can we make when L1 «_space;L2?
e^-L1t = 1 which gives N2(t) = N0 L1/L2(1 - e^-L2t)
what is secular equilibrium?
in a decay chain, as time gets large, nuclei are decaying at the same rate they are being produced.
why is alpha decay rare at nuclei of A = 56?
That’s the peak of the binding energy curve. Alpha particles are less likely to break off when binding energy is high. You can also calculate Q value there and see that it is not positive.
Q for electron capture
Q = [m(x) - m(x’)]c^2 - Bn
Q for beta -
Q = [m(x) - m(x’)]c^2
Q for beta +
Q = [m(x) - m(x’) - 2m_e]c^2
de Broglie wavelength
lambda = h/p, relates wavelength and momentum
fermi beta decay
no change in parity or spin.
gamow teller
0 or 1 spin change, no parity change
first forbidden decay
delta J = 0, 1, 2, delta pi = 1
second forbidden decay
delta J = 2, 3, delta pi = 0
third forbidden
delta J = 3, 4 delta pi = 1
fourth forbidden
delta J = 4, 5 delta pi = 0
find allowed multipolarity
every integer in between abs(J_i - J_f) and J_i + J_f, if parity changes must be odd L for electric, even for magnetic. Opposite for no parity change.
how does an increase in multipole order correspond to strength?
Increase in multipole order corresponds to a reduction in strength by approximately 10^-5
what’s the relationship between energy and velocity?
E = (1/2)mv^2
conversion between ev and J
1 ev = 1.602189 x 10^-19
what force governs alpha decay?
nuclear force and electromagnetic
how does alpha decay happen?
Tunneling process. As the width of the barrier increases, alpha decay is less likely
Why are alpha particles more likely to be emitted than single protons/neutrons?
Conservation of wave function symmetry prevents single nucleon emission. Also high binding energy of the alpha particle.
How big is the nucleus?
1.75 to 15 fm. Depending on the nuclide.
Define mass defect?
The number of protons + the number of neutrons - the mass of the nuclide.
What is the ground state spin parity of even-even nuclei?
0+
What is usually the first excited state spin parity of even-even nuclei?
2+
After how many half-lives do we usually reach secular equilibrium?
5ish
how many nucleons can be stored in each level?
2J + 1
How do you find the moment of inertia in a rotational band?
E = (hbar^2/2I)(2J + 1) where I is the moment of inertia.
What is the promiscuity factor?
How far away a nuclide is from a shell closure. P = NpNn/(Np + Nn) where Np and Nn are the numbers of valence protons and electrons.
What are the first seven magic numbers?
2, 8, 20, 28, 50, 82, 126
When is a nuclei deformed?
If it has promiscuity factor greater than 4.
What state will a 0+ nucleus feed?
0+ since they tend to feed similar states.
What are the units of exposure?
Coulombs/kg or roentgens. Conversion is 3876 roentgens = 1 C/kg
Exposure
Exposure = Gamma A/r^2
Whats the difference between dose equivalent and absorbed dose?
The equivalent dose calculates how much damage is expected based on the absorbed dose and type of tissue.
What are we likely to see in a fission graph?
A staircase pattern spaced by about 6MeV, the binding energy of a nucleon. Beware of log log plots as you can see this better on a linear scale.
mean lifetime
t = 1/lambda
What are the different cases for pairing energy?
0 if A odd, if nucleus is even-even then positive, if odd-odd then negative
what leads to the formation of quantized energy orbitals?
nuclear potential
what does nlj mean?
describes where nucleons can be. n is the principle harmonic oscillator phonon number like a frequency. l is orbital angular momentum (because we are in 3D). j is spin.
why is g9/2 aligned?
because g is 4, so it is 4 +1/2
energy of vibrational nuclei?
E = n_phononE_phonon
energy of phonon in vibrational nuclei?
energy of first 2+ state
is rotation collective behavior?
yes
what does the collective behavior say about the speed of transitions between the states?
collective is faster because all the nucleons are doing the same thing. gamma lifetimes get shorter for collective states.
energy spacing and moment of inertia
inversely proportional
typical alpha energy
5 MeV which means non-relativistic kinematics OK
kinetic energy of the alpha particle
T_alpha = Q/(1+4/A)
ell barrier for alpha decay
favors decay to same state, not as strong as for beta decay though.
energy spectrum of alpha and beta decay
alpha has these peaks and there are only two particles so the linear momentum is conserved and fixed. Beta has three particles emitted and so its more of a continuum.
what does the wavefunction affect in beta decay?
lifetime.
what does a change in parity say about the permitted multipoles?
E odd and M even
what does no change in parity say about permitted multipoles?
E even and M odd
which multipole in gamma decay is the most intense?
the one with the lowest l.
