Lecture 9: Nucleosynthesis of Light Elements

Question 1

When we talk about nucleosynthesis we mean

Answer 1

the formation of the light elements

Question 2

the light elements

Answer 2

hydrogen
deuterium
helium-3
helium-4
lithium-7

Question 3

Heavier elements can be formed through

Answer 3

nuclear fusion in the centres of stars

Question 4

the abundances of the light elements reflect the

Answer 4

primordial state of the universe
and the conditions that existed at that time.

Question 5

The theory of primordial nucleosynthesis is able to successfully predict

Answer 5

the abundances over about 9 orders of magnitude

this makes it one of the strongest pieces of evidence for the Hot Big Bang Theory

Question 6

ratio of neutrons to protons - 4 important facts

Answer 6

1. protons lighter than neutrons
2. free neutrons decay into protons
3. neutrons bound into stable isotopes of the light elements do not decay
4. neutrinos decouple from the rest of the cosmic plasma at T=10^10K

Question 7

which are lighter, protons or neutrons?

Answer 7

protons (938.3MeV to 939.6MeV)

Question 8

free neutrons decay into protons with a half life of

Answer 8

610s

Question 9

Consider the period before nuclei form but late enough that protons and neutrons are non-relativistic.
This is equivalent to

Answer 9

kBT «mpc^2
or
T«10^13K

Question 10

Consider the period before nuclei form but late enough that protons and neutrons
are non-relativistic.
the number density N will be

Answer 10

in a maxwell boltzmann distribution

Question 11

Nn/Np is approx 1 when

Answer 11

kBT&raquo_space; (mn-mp)c^2

ie the typical thermal energy of photons significantly exceeds the rest-mass
energy of the proton-neutron mass difference

Question 12

The relevant reactions involve neutrinos, mediated by the weak force:

Answer 12

n + ve <-> p + e-

n + e+ <-> p + anti ve

Question 13

when kBT is approx 0.8MeV, neutrinos

Answer 13

decouple and the cosmic neutrino background is formed

Question 14

what does neutrinos decoupling and the cosmic neutrino background forming mean?

Answer 14

the reactions can no longer occur and neutrons freeze out, though free neutrons can still decay

Question 15

R=

Answer 15

Nn/Np

approx exp(-1.3MeV/0.8MeV)
approx 1/5

(numerator - mass difference, denominator - neutrino decoupling temp)

Question 16

If it were not possible to ‘lock away’ neutrons in stable nuclei eventually

Answer 16

all of the free neutrons would have decayed into protons.

We’d have a universe consisting only of hydrogen: we would not exist.

Question 17

why do we not have a universe consisting only of hydrogen

Answer 17

deuterium can be formed via

p+n –> d + gamma

Question 18

deuterium

Answer 18

one proton + one neutron

Question 19

deuterium formation: High-energy photons in the tail of the distribution cause

Answer 19

photo-disintegration
of the deuterium d until the temperature of the universe drops to about T=8x10^8K at t=300s

Question 20

deuterium formation: By the point of photo-disintegration, the ‘frozen-in’ value of R = Rf will have reduced because

Answer 20

of the decay of the free neutrons

model as a radioactive process

Question 21

R at freeze out

Answer 21

R=Rf=0.2 at freeze out

valid at t=300s

Question 22

light element abundances in the early universe - assume

Answer 22

that all the free neutrons end up as helium-4 nuclei.

Question 23

if all free neutrons end up as helium-4 nuceli, NHe=

Answer 23

1/2Nn

Question 24

Y4 is the

Answer 24

mass abundance ratio
=mass of He4/total mass

Question 25

for R300=0.135, Y4=

Answer 25

0.24 ie helium-4 makes up around 1/4 of the universe

Question 26

As well as helium-4 we can predict the abundances of

Answer 26

deuterium (10−4) helium-3 (10−5), and lithium-7 (10−10) as a function of the density of baryons.

Question 27

There is an agreement between theory and observed abundances over about

Answer 27

nine orders of magnitude

Question 28

caveat of success of 9 order of magnitude

Answer 28

the baryon density be no more than 4% or 5% of the critical density (for h = 0.7). ie lots of other stuff (dark matter etc)

Question 29

the predicted abundances depend on

Answer 29

a number of different parameters

Question 30

if we tweak the neutron lifetime, we can see how

Answer 30

Y4 changes

Question 31

baryon to photon ratio, n also influences

Answer 31

the predicted abundances

Question 32

what other parameters affect the predicted abundances

Answer 32

1. neutron half-life 2. number of neutrino species 3. baryon to photon ratio 4. non-degeneracy of neutrinos

Question 33

neutron half-life: increasing the nurton half life...

Answer 33

increases Y4 because fewer neutrons will have decayed by t=300s which means more neutrons are available to be captured in deuterium nuclei to then form helium neutrons freeze out earlier so there are even more neutrons available to form helium

Question 34

number of neutrino species - the standard model predicts 3 neutrino species Nv, increease Nv...

Answer 34

increases Y4 because it increases the relativistic energy density at nucleosynthesis. This means a higher value of H at that time so the neutron freeze out occurs at higher temperature and a higher R

Question 35

baryon to photon ratio, increasing n causes

Answer 35

an increase in Y4 because it means there are less high-energy photons in the tail of the distribution, resulting in a less severe deuterium bottleneck, thus the build-up of He-4 begins earlier and more of it will form we expect a decrease in deuterium with an increase in n

Question 36

non degeneracy of neutrinos: neutrinos are fermions and obey the Pauli Exclusion Principle. At low temps, neutrinos...

Answer 36

fill up states to Fermi level, anti-neutrinos do the same but to different Fermi level. If there are many more neutrinos than anti-neutrinos a chemical potential results from the difference in Fermi levels so n to p reactions occur more often than p to n so Y4 decreases

Question 37

comparison with CMBR constraints - there is a discrepancy between planck and observations called

Answer 37

the cosmological lithium problem due to difficulty in making accurate observations of primordial Li-7