Video summary
This lecture explores the cosmic origins of heavy elements, beginning with the life cycle of stars and the specific challenge of creating carbon. Stars evolve from molecular clouds into massive objects that eventually end as supernovae, neutron stars, or black holes depending on their mass. A critical hurdle in stellar nucleosynthesis is the "A equals 8 bottleneck," where no stable nuclei exist for mass numbers 5 through 7, and beryllium-8 decays almost instantly. To overcome this, a specific resonance in carbon-12, known as the Hoyle state, allows three alpha particles to fuse efficiently. This mechanism was theoretically proposed by Fred Hoyle and later confirmed experimentally at Caltech, enabling the production of carbon and subsequently heavier elements like oxygen and iron through fusion processes up to nickel-58.
Once stars reach the peak of binding energy per nucleon around iron and nickel, further fusion becomes endothermic and cannot sustain the star against gravity. To create elements heavier than iron, stars must rely on neutron capture rather than charged-particle fusion, as neutrons do not face the Coulomb barrier. This occurs via two primary mechanisms: the slow neutron capture process (s-process), which happens in red giants and produces elements near the stability line, and the rapid neutron capture process (r-process), which occurs in extreme environments like supernovae or neutron star mergers. The r-process allows nuclei to rapidly absorb neutrons before they can decay, pushing them toward the neutron drip line where they subsequently undergo beta decay to form stable heavy isotopes found in nature.
The lecture highlights the significance of the neutron star merger observed in 2017, which provided direct evidence that these catastrophic events are likely the primary source of the universe's heaviest elements. While gravitational waves confirmed the masses and nature of the merging objects, the detection of electromagnetic radiation across various spectra further validated the r-process models. Although neutrinos from such distant events were not detected due to flux limitations, future facilities like the proposed Inner Core detector aim to improve sensitivity for observing these rare phenomena. Current experimental facilities worldwide are already capable of measuring properties of unstable nuclei, but reaching the extreme conditions near the neutron drip line remains a challenging frontier for nuclear astrophysics.
In conclusion, the synthesis of cosmic elements is a multi-stage process involving stellar fusion up to iron and subsequent neutron capture for heavier materials. The abundance patterns observed in the solar system reflect contributions from both low-mass stars via the s-process and massive stars or mergers via the r-process. Understanding these mechanisms requires advanced nuclear physics facilities to measure cross-sections, masses, and half-lives of exotic nuclei. As technology advances, scientists hope to better model the complex physical processes involved in element formation, particularly within the dynamic environments of neutron star collisions, thereby refining our understanding of the chemical evolution of the cosmos.
Read the full video transcript
In this lecture we will talk about how
heavy elements are synthesized in the
cosmos. So cooking heavy elements in the
cosmos. So just a slide on the life
cycle of stars. Then how do we cross the
A equal to8 bottleneck? Because we have
to make carbon. Carbon is the very basis
of life. But apart from that it is also
very common in the universe and so how
was it made? Then we how are elements up
to iron and nickel made. Uh then neutron
capture for the heavier elements and
finally why you you need a nuclear
astrophysics facility in an underground
lab including one in India perhaps. So
uh these are the main references. This
is called the B squ
reference. Uh this is an early seinal
paper by these authors in the reviews of
modern physics uh in 1957 and it's a
very simple title synthesis of the
elements in stars. Uh so there is also
another review uh this is archive. It
must have been published in some good
journal. Uh this is on the new concepts
in neutron capture measurements of
astrophysical interest. Okay. So the
life cycle of stars and this is taken
from a reference in the Wikipedia
uh is that you start out with a gas uh
that is shown here started with a
molecular cloud of gas then you form uh
you know clusters and then you have
so-called protoars
and then you can go into a massive star.
If this is big, very big, you go into a
massive star, a red super giant and so
on. And then you could have a type two
supernova ultimately and the for inance
the crab nebula picture is shown here.
Uh and then if it is again if it is uh
heavier than about 20 solar masses, it
could go into a black hole. If it is
between let's say 10 and 20, then it
could go into a neutron star. And which
is uh then if it is spinning then it is
called a pulsar. And in this if a black
hole is uh uh is rotating and invariably
most of them do then there is a
possibility that you can have x-ray
emission from there and uh you might be
able to measure that if it is not too
far away. Uh then there are these luma
stars. So you which can for instance go
into a brown dwarf or you can have a red
giant and then a you know binary white
dwarf or you can have a planetary nebula
and you can have a type 1A supernova.
This is important in the calibration of
distances of uh the stars and finding
out how they
what are the stellar velocities as a
function of distance. uh then there are
these nova smaller explosions uh as
compared to the supernova and then you
might end up uh in this case of a
planetary inbul into a white dwarf or
into a black dwarf and so in the case of
the white dwarf you cannot go further
down because there is the uh degeneracy
degeneracy pressure of the electron gas
in a neutron star that is mainly because
of the you cannot go down below because
you have a degeneracy C pressure of the
neutrons. U okay so of course these are
uh there's a birth of a uh let's say a
star and then you have a main sequence
and then you have old age and then a
death and then there is a remnant. So
these are the broad categories of with
respect to time as uh the molecular
cloud evolves.
Okay. Now if you want to make carbon 12
there's a problem because uh there are
no stable nuclei uh of mass number
eight. It so happens that and they have
other than berilmade they have even
shorter lifetimes. Berlemate uh ground
state has a lifetime of about 10us 16
seconds which gives a width of about a
few electron volts and uh so this is the
candidate for forming carbon 12 through
the bilament alpha reaction. So right in
the beginning Beth proposed the three
alpha reaction. So three alphas come
together in the core of the star and uh
if it is dense enough maybe you can get
this reaction to produce uh the carbon
12. But when this was worked out it
turned out that this is too rare a
process for you to account for the
carbon that exists in stars. So then
somebody thought opaque oil opaque and
salt peter looked at the possibility of
it being a two pro two two-step process
that means you have resonant production
of berilmate first and then within 10us
16 seconds it can capture a alpha
particle and then produce carbon 12
again this turned out to be too low rate
a process for us to account for the
carbon 12 and indeed the higher heavier
element events like oxygen 16, neon 28
so on. So there is this brilliant
insight of Fred Hy in 1953 who said that
there must be a resonance in carbon 12
close to the bilmate plus alpha uh
energy.
uh so then of course if there is a
resonance there then the there is a
resonant enhancement of the
cross-section for this process alpha
plus brilliate going to carbon 12 okay
and uh it must be at about 7.6 6 MV and
uh this was indeed found by Dunbar in a
Caltech experiment in 1953.
Okay. So this is the experiment that was
carried out by Dunbar uh Pinley
and his colleagues at the Caltech. Uh
this accelerator was used extensively by
uh Fowler uh for many many such
reactions of astrophysical interest.
Indeed he got the Nobel prize which he
shared with uh I think it was Chandra
Shaker probably that he shared it with.
Okay. So the way this 7.68 MV state was
found was by doing the nitrogen 14 D
alpha reaction and they found uh a group
which corresponds to a transition of
4.43me 43me
and
so the the alpha particle that comes out
when this is at an excited state is of
course uh
is some energy but if you want to go to
the 7.68 6 8 MAV state then of course
that alpha energy is lower just because
of energetics but indeed the most
important thing was that they found
evidence for this state okay so this was
taken with a spectrometer with a thick
uh ammonia target
and uh no other groups are observed at
1% level of the exitation of uh the or
the population of this 4.4 4 MV state in
this range of alpha energies. Okay. So
this was the group that this this alpha
group was the one which pointed out to a
state being very close to what H oil had
predicted should be there. Okay. So this
is this private communication of H oil
which uh made them look for this state.
Okay. So this is the a equal to 8
you know lowlying scheme of levels
excited states of bilament and the
ground state decays by two alphas uh
it's it is about 92 kV above the
threshold so it can decay to two alphas
of 46 kV each in the center of mass of
the berilium 8 and the lifetime as I
said is 10us 16 seconds as you can see
these uh nuclei lithium 8 and boron 8
live for less than a second. So it is
very hard to uh get these nuclei to
combine with something to form heavier
nuclei. So this is the so-called A equal
to 8 bottleneck that I mentioned.
Okay. So the carbon 12 lowlying states
are these ground state then the first
excited state at 4.44 MV then the 7.65
65 m which is now of course known as the
hil state. It has a very narrow width
because it's a it mainly decays by alpha
plus berilium 8 but it is just above
threshold and the gammaray decay width
to this 4.43 m state is uh the partial
width is small. So that's how it has a
width of about 8 and a half electron
volts in total. So this decays to the
alpha plus bil limit which is at uh 7.37
mv or so. So this is just about uh 300
KV or so above this threshold for alpha
B limit.
So
the f once you of course form carbon 12
then you can through the alpha gamma
reaction you can form oxygen 16 and we
have seen the CNO cycle uh in an earlier
lecture. So then you can form oxygen 16,
neon 20, magnesium 24, silicon 28 and so
on uh using proton and alpha induced
reactions and of course there are some
nuclei in between as well that you can
produce uh through proton and alpha
induced reactions in heavier stars where
the temperatures are higher and why do
have the temperatures to be higher in
order to go to higher heavier nuclei
that's because the coolum barrier for
proton and alpha induced reaction
increases. So unless you have a big
enough star such that you have very high
temperatures in the core uh then only
you can get heavier nuclear but in some
of the heavier stars you can go all the
way up to 56 iron 58 nickel and so on or
56 nickel and so on. Having reached the
top of the binding energy per nucleon
curve uh as a function of a actually 62
nickel is the most uh bound but that is
not very easily made then the further
fusion reactions actually require some
energy to be so they are not exothermic
okay and uh so they cannot contribute
significantly to production of heavier
nuclei also it becomes harder and harder
because the larger coolum barrier and uh
if nothing else happens happens then of
course gravity takes over and the whole
star starts uh coming down in radius.
So then how do you synthesize elements
beyond iron and nickel?
So that is done through neutrons because
neutrons don't face the culum
interaction uh being neutral neutron
themselves and capture has a usually a
positive Q value of the order of 8 MAV
for nuclei near the stability line of
stability and of course as you go up to
more and more neutron-rich nuclei then
this Q value decreases and ultimately
you come to the so-called neutron drip
line where the binding energy of the
last neutron is close to zero or even uh
negative. So which means that it'll
throw out a neutron if it is produced by
a nuclear reaction. So now first of all
you have to find a source of these
neutrons. Uh and then the two main
processes as discussed in that B squ
paper is that you can have slow neutron
capture and you can have rapid neutron
capture. Now slow neutron capture the
process uh I mean these sites are not
very clearly identified but perhaps uh
they reactions like carbon 13 alpha n
can contribute to these uh neutrons
which then this sort of having a low
neutron flux and that will produce
nuclei basically close to the uh
stability line. Okay. uh and this might
be they taking place in low mass stars
one to three times the solar mass. The R
process on the other hand is the one
which we believe contributes to the
heavier elements. Uh and these can
happen in supernova explosions or in
neutrons as we now know neutron star
neutron star merges. uh for instance uh
this is one of those cases where uh of a
neutron star neutron star merger through
the gravitational waves that we have
detected.
Okay. So the slow neutron capture
nucleiosynthesis which so-called S
process uh you can have you know nuclei
like 58 iron they go to 59 iron which
can then bet you can read 59 cobalt and
so on. So but these are all basically on
the stability line or a little away from
the stability line one or two nucleons
away. So if 59 iron captures another
neutron before decay 60 iron is formed
and more likely because of the
relatively rare encapture events uh you
can even get 60 cobalt which is halfife
of about 5.3 years and so on. Uh this I
already said that most nuclei that are
formed are close to the line of
stability.
Now neutrons for the S process can be
produced in red giants during the helium
burning. And one example is through the
alpha reaction on carbon 13. But there
are others. Oxygen 16 or oxygen 16 can
give you 31 sulfur plus neutron. Then
alpha on nitrogen 14 can give you 18
florine plus a gamma. And then this can
decay producing 18 oxygen. 18 oxygen
plus alpha can give you this gammaray
reaction. And then neon 22 plus uh uh
you know this is a product which when it
interacts with four helium can give you
25 magnesium plus a neutron. Uh of
course this sounds a little more likely
although these other reactions can also
contribute such as this again this is
oxygen 16 or oxygen 16. So these are
relatively I mean heavy nuclei heavy
light nuclei I should say. And so the
coolum barrier is somewhat higher than
in this case. And so this is very likely
the source of these neutrons and perhaps
also in smaller measure these these
reactions. This is 22 neon plus alpha
going to magnesium 25 plus neutron.
Okay. So this is that was the S process.
There is a process which actually
contributes mainly to the heavy limit
production that is the explosive
nucleiosynthesis. So this occurs in
supernova or in neutron star merges
where there are huge neutron densities.
So as we saw in supernova you can have a
electron combining with a proton and
producing a neutron plus a neutrino and
uh when this happens this happens so
rapidly in less than a second. So the
neutron densities are huge and these can
get captured on whatever nuclei there in
the environment of in the inner part of
the star or even the outer portions and
then they can lead to uh
nucleiosynthesis. So uh what will happen
is that a neutron star uh sorry a
neutron is absorbed. Now there are two
ways in which it can go. It can either
capture another neutron or it can if the
weak decay is uh reasonably fast then it
can weak decay. Of course, initially it
is neutron capture that dominates. But
as you come close to the drip line,
neutron drip line, then of course the
betadk also decrease and you can have
betadk competing with the uh with the
absorption of neutrons. And of course
when you go to the neutron dipline then
it doesn't survive the nucleus just
doesn't survive because it can emit
neutrons on a time scale which is much
faster 10 to the minus 23 24 seconds.
Okay. So this is a this is an example of
nucleiosynthesis. Let's see what is
shown is that you can produce heavier
and heavier nuclei uh in this is a
simulation of course from this ja
2012 and uh this animation shows how
heavier nuclei are produced and how you
can actually produce nuclei close to the
neutron drip line. Okay. So here you can
see that this goes all the way up to
okay I don't have an axis here but you
can see that these are the heaviest
elements and then of course they can
beta decay and then they come down to
the stable nuclei okay so this this line
uh shifting up uh is a tells you that
there is beta minus decay is going on
and uh you finally come to the stable
line. Okay. So,
okay. So, the heaviest elements are
thought to occur in a neutron star
neutron star merges and in on August 17,
2017 the gravitational wave event was
observed in which they could identify
what are the masses of these uh objects
that are causing the gravitational
waves. From that they could infer that
these are actually neutron stars and not
black holes. And in fact this merger was
also seen in other channels not just
gravitational waves but in the optical
region in the X-ray region in the RF
part of the electromagnetic spectrum. Of
course no neutrinos were seen because
this was too far away for nutrino
detectors at that time.
This is about 130 million uh light
years. If uh if you remember the
supernova SN1 1987A was about uh 50 kilo
par 6 and uh this was in a nearby
galaxy. This one is taking place much
further away and therefore the nutrinos
uh flux would go down like 1x r squar.
So even for the biggest uh detectors
that we have as of now this was not at
that time sorry 2017 it was not possible
to see them. Of course the kilometer
cube detector has improved our
capability but not just the uh ice cube
but also there is going to be a inner
core which is going to be populated with
a denser uh number of uh photo
multiplier tubes. Of course, it'll be
smaller uh in size. So, it won't be like
a kilometer cube, but it'll be maybe a
tenth of that or something or 20th or
50th of that. So, it would be able to we
would be able to expand our uh
capability of seeing these events. But
uh uh actually this is probably a good
uh problem to work out for students that
for uh seeing even one neutrino from or
let's say let's say not say one let's
say five neutrinos from an neutron star
neutron star merger
and would it be possible to see them if
that is about uh this 130 million uh
light years away.
Okay. So the simulated R process
abundances in a neutron star merger is
this is from this reference reviews of
modern physics in 2021. Uh is uh this uh
this is the solar abundance in dark uh
data points and these are the various
models that you have and they very
closely uh you know follow the solar
abundance. Of course there are
discrepancies but these kind of
discrepancies are sort of normal in uh
astrophysical measurement because of
course there are these neutron star
neutron star merges we can model but we
really don't know uh the all the
physical processes that are involved
because uh these have only recently been
observed. Okay, perhaps in future we
will be able to model them better and we
will also have more events from
gravitational waves and from other
windows that we have. So in any case
this is just to point out that uh in we
we have some models maybe the first kind
of models uh which say that most of the
heavy elements are actually coming from
neutron star merges. This is shown in
this uh you know figure where uh the
merging neutron stars are shown in
purple. You can see that many of these
elements uh are probably coming about in
neutron star neutron star merges. Uh
what is there from the
other exploding massive stars? This is
here that is these heavy elements of
rubidium. And of course there are uh
contributions
uh also from uh this process exploding
massive stars and dying low mass stars
which contribute to these. But
if we think we have a reasonable model
of neutron star neutron star merger then
we believe that most of the heavy
elements are actually created in neutron
star neutron star merges.
Okay. So the experimental facilities
worldwide for these rare iron beams or
radioactive iron beams as you as you
like to call them. Uh these are
facilities plenty of facilities are
there in Triumph in Canada. Uvascula in
uh Scandinavia, the GSI
storage ring in Germany, CERN sold you
know facility is sold facility and then
they you know they have various they can
measure cross-sections as well as masses
and things like that. Then there is the
Argon National Lab trap for measuring
masses of these these uh very unstable
nuclei which are produced through
neutron absorption and uh so this in uh
this is the reach of these future Riv
facilities and uh if you really want to
go to this drip line it's going to be
difficult but perhaps there'll be uh
technology will improve and we might be
able to get there. Okay. Uh this is the
reach with present day facilities,
present day arrival facilities. Uh and
then you can also measure half lives and
branching ratios and stuff like that.
The elemental abundances in the solar
system.
So in blue we have a plot of the uh data
and uh what are the sources of these uh
elements that is shown here. Stellar
burning is this region up to iron. Then
the S process uh there is a small peak
in the stronium region. The R process
peak is there which gives rise to zenon.
But of course you also have heavier
elements. So for platinum and so on. Uh
then there are small peaks in the lead
region which comes about from the S
process. Uh then the a peak in the
berium region also. uh where you have
this could be both from neutron
absorption as well as uh fish from
heavier elements in case those are
there. So in summary you have seen how
how elements above the a=8 bottleneck
are created uh up to about a equal to 58
through fusion reactions and the heavy
elements through neutron capture. Okay.
So I think I'll stop here. Thank you.
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