Acta Polytechnica CTU Proceedings 2(1): 311–320, 2015
doi: 10.14311/APP.2015.02.0311
311
311
Who Discovered the Hoyle Level?
G. Shaviv1
1
Department of Physics, Israel Institute of Technology, Haifa, Israel 32,000
Corresponding author: [email protected]
Abstract
12
The prediction of Hoyle that the nucleus of C must have a resonance at 7.62MeV was the trigger to the Anthropic
Principle. We review the history of the discovery of this level and investigate to what extent this was a genuine prediction.
Keywords: anthropic principle - nuclear physics - stellar evolution.
1
Who Is Who
the 12 C is converted into 16 O. But stars do evolve and
we know that somehow carbon is synthesized. In view
of the impass, Hoyle predicted therefore, that 12 C has
an energy level just at the right place and the reaction
of carbon synthesis proceeds via this resonance level.
The level was then discovered in the laboratory. This
chain of events: prediction the existence of a nuclear
level from astrophysical constraints, wa s considered as
a big victory for astrophysics and the level was named
the Hoyle level.
Three dominant personalities were involved in the
present story: Sir Fred Hoyle FRS (1915-2001), who
was one of the greatest astrophysicists in the second
half of the twentieth century with major contributions
to Stellar structure (nuclear astrophysics - synthesis of
the elements) and to Cosmology - (Steady state theory dubbed the name Big Bang) as well as planetary
formation. William A. Fowler (1911-1995), who can
be considered as the father of nuclear astrophysics and
Edwin Salpeter (1924-2008) top theoretical astrophysi3 What Is the Anthropic Principle
cist, who has numerous seminal contributions in many
astrophysical fields as well as in physics.
The Anthropic Principle is a philosophical hypothesis
that measures of the physical Universe must be compatible with the existence of conscious life that observes
Willy
Fowler
Ed
Salpeter
Fred
Hoyle
Edwin E, Salpeter
William A. Fowler
Fred Hoyle
it. The phrase ”Anthropic Principle” appeared first in
Brandon Carter’s contribution to the 1973 Krakow symposium honoring Copernicus’s 500th birthday. Carter
argued as well, that humans do not occupy a privileged
position in the Universe. The trigger to the idea that life
as we know it, and the cosmos around us, ”are tuned”,
emerged from Hoyle’s prediction of the existence of a
special energy level in the nucleus of 12 C. If such a
Figure 1: The dominant personalities involved in this
level did not exist, argued Hoyle, life could not have
story: The discovery of the triple α process.
develop in the cosmos, more accurately, 12 C based life
could not emerge. Was it really so amazing? Was it a
full prediction?
2 What Is the Hoyle Level
The basic astrophysical problem emerged when
The synthesis of helium into carbon in stars proceeds Hoyle and Schwarzschild calculated, in the early
via resonant reaction, namely the three α particles fuse nineteen-fifties, the evolution of stars off the main seinto an excited energy level in the 12 C nucleus. The quence into the red-giant using reaction rates known
rate of the reaction was calculated before the existence at the beginning of the nineteen fifties and got that as
of this level was known and was found to be very low soon as 12 C is synthesized from helium, it absorbs ancompared to the rate of destruction of 12 C by collisions other α particle and becomes 16 O leaving no carbon.
with α particles. As a consequence, it was impossible to The reaction forming 12 C was much slower than the repredict the evolution off the main sequence towards the action that destroys it. If so, argued Hoyle, life should
Red-Giant branch and the calculation implied that all not exist! Alternatively, as 12 C does exist in our uni311
G. Shaviv
verse, there must be a resonance in this nucleus that that any fusion reaction leading to this nucleus will not
accelerates the formation of carbon by many orders of create it. The so formed nucleus may live a short time
8.1. This
UNSUCCESSFUL
ATTEMPTSatTO
THE A=8itBARRIER
237
magnitude.
was ’reverse engineering’
its OVERCOME
best. but eventually
decays.
You know what should happen and find out how can it
Energy
be.
Could 12 C be synthesized
elsewhere?
The
only
Energy The N+Z=12 system
known alternative was the Big-Bang. But Hoyle ar26.32
28.09
gued that all elements were synthesized in stars. On the
8C
8He
other hand, Gamow argued that all elements were
syn17.42MeV
thesized in the Big Bang. However, the various
models
12N
16.92
17.02
7
16.36
13.37MeV
of Big-Bang nucleosynthesis
failed to produce elements
8Li
8B
12
B
12
like C and higher5 (in atomic weight),
11.35
β+ and left stars
12
as the only cosmic site for
synthesis
of
C
and
heavier
β
τ1/2=11.00ms
nuclei.
τ1/2=20.20ms
3.03
4
0
12C
The Nuclear Barrier
6
-0.0918
4He+4He 8Be
Reference level
2
3
4
5
6
Z
Two nuclear barriers
the synthesis
Z=5 exist in Z=6
Z=7of the elements from hydrogen up (see fig. 2). The barriers are
3: 8.3:
TheThe
relative
ground
states
the non existence
of a The
stable
A=5
andsystem.
A=8 nuclei
as Figure
Figure 8.2:
A=12
nuclei
The diagram
Figure
energyenergies
levels of of
thethe
nuclear
system
N+Z=8
nuclei.
Theatomic
numbers
are the
energies
shown in the
figure.why
This
means
synthesis
explains
of all
nucleithat
with the
12 protons
and of
neu-of the
with
A=8 for
di↵erent
numbers
Z. The
nu- in
8
8
8
relative
to decay
the ground
state ofstate
Be,
has the
trons,
the 12 Cfrom
is thehydrogen,
most stablemust
one. jump
The other
B can
into an excited
of which
Be, which
the elements,
if started
overnu-MeVcleus
+
8
CHAPTER
8.
HOW
NATURE
OVERCOMES
ITS
OWN
BARRIERS
ground
energy
of allBeA=8
nuclei.
orlowest
may
decay state
eventually
to the
ground
state.However,
But
these nuclei.clei with A=12 are all unstable and decay via
8
of twostate
freeofα’s
still the
lower
energy.
Hence,
into 12 C. The energies above the ground state ofthe state
the ground
Behas
is above
state
of two free
N carbon are given in MeV. Also given the half-lifetimethere↵isparticles
no
stable
nucleus
with
A=8.
(colored
green)
and
hence,
the
fast
break18
ht elements in the N, Z plane. Staed brown. Unstable elements with
inted yellow. Unstable nuclei with
are painted red. The A=Z+N=5
lear barriers are shown as straight
orces do not yield a stable nucleus
ns of protons and neutrons. There
with A=4 stable or unstable. Alble and has a large binding energy,
te, only the ground state.
10
9
9ms
0.75s
O
of the unstable nuclei. After Ajzenberg-Selove and
17O
14ms 2.45s
Lauritsen 2008.
8.7ms
8
7
174ms
14C
5730yr
15N
16O
5
20ms
down of 8 Be is unavoidable. Consequently, 8 Be does
not exist in nature.
Why Nuclear Physicists Were
Interested in the Problem?
energy in the contraction towards extremely
4 and hence, have enough gravitational
limiting
mass
high
119ms
177ms
9.97m
6
densities, -21even as high as nuclear densities5 . However,
no
detailed
calculations
were
carried
out,
The fundamental problem in nuclear physics atjust
the be20.3m 11ms
5
3.10 s 0.84s
speculation. Weizsacker attempts and ideas to explain
the giants
were
typical
to thewas
hopeless
situation
ginning
of
the
nineteen
thirties
the
nuclear
struc10-17s 8.10-19s 19.29s
in4 front 807ms
of the insurmountable
A=5, 8 barriers.
ture. It was already known that the α particle is the
3
8.10-22s
7Be 4.10-22s
most bound nucleus as it has the highest binding en6 in which he brought up an idea
16
3.10-22s 5.10-21s
In
paper on Relativisticergy
Cosmology
Wigner
12.3 yr1949 Gamow published
per nucleon.
Similarly, nuclei like 12 C,
O,20 Ne
A=8aBarrier
238
CHAPTER 8. HOW NATURE OVERCOM
1
communicated to him in private. Another ingeniousetc
method
the massenergy
5 crevasse
proposed
haveofa crossing
higher binding
thanwas
their
neighborby0 E.1H Wigner. It is known as the method of the ’nuclear
chainThe
bridge’.
Wigner’s
is thatare
all these
that so
ing nuclei.
question
was plan
therefore,
8.2
Thewas
pursuit
after
the
structure
of the carbon n
is required
for
building
a
chain
bridge
is
an
assumption
that
there
originally
one
single
nucleus
on
called
α
nuclei
composed
of
α
particles
1
2
3
4
5
6
7
8
Z
H
He
Li side
Be of B
C
N
OSuch an assumption can easily be granted argued Gamow, since some
the right-hand
the crevasse.
building up is still maintained across the crevasse by the reaction 4 He +3 T !7 Li + in spite of the low
Figure namely,
2: The
nuclear
barriers
atGamow
A=5 and
A=8, his rejection of Wigner’s idea in a book7 just when the
of its
occurrence.
published
examined the triple body reaction,probability
the three
↵ particles
interact simultaneously
namely
thecollisions
non and
existence
of with
stable
nuclei
these ↵ process which ended few years later with the detailed
o produce the carbon nucleus.
Since
of an
↵-particle
one
particle,
Salpeter
Hoyle
started
theother
work
onwith
the triple
do not lead to stable nuclei
the alternative
was to
assume
a triple
collision
of which to where Wigner published his suggestion.
number
of protons
and
neutrons.
nuclear
physics.
Gamow
gave
no
reference
4
6
4
9
4
12
2
plausible: (a) He + 2p ! Be, (b) 2 He + p ! B,
and (c) 3 He ! C.
tions were rejected because they do not lead to a stable nucleus. The third reaction
Many
attempts
and
suggestions
to inovercome
the
2 C. However, Bethe knew from Eddington’s models that the temperatures
main
4
7
barriers
were
suggested.
We
mention
here
only
Bethe’s
Chandrasekhar,
MNRAS,
95, 207,
226, 676, (1935)
around 2 ⇥ 10 K, while the triple collision
of ↵-particlesS.,
requires
according
to Bethe’s
9 K, which are5way beyond the range of temperatures according
atures of the order of 10attempt,
Nuclear adensities
densities
at whichBethe
the nuclei
touch each other. The radius of the nucleus is about 10 5 the radius
namely
three are
body
reactions.
knew
8.4: has
Twoan
possible
of electronic
the carbon shells
Figure 8.5: The struc
main sequence stars. Hence, Betheofdropped
the idea
of a three
body reaction.
the
atom,
namely,
the
radius
of
the
outer
occupied
electronic
shells.Figure
The atom
infinitestructures
number of
from Eddington’s stellar models what are the central Figure
4:
The two
possible
options
for
the structure
nucleus.
the they
left,
the
nucleons
randomly
withclaimed
radiusthat
increasing
to infinity.
But
asbe
the
number of electrons in each
atom isOn
finite,
occupy
only move
the lowest
in energyrevised ↵-particle nucle
eizsacker1 discussed the problem and
the energy
source can
still
gravitemperaturesand
and
in stars
and soon
the
carbon
the Normal
left are
wematter
see clus12
nucleons
inside
thenucleus.
nucleus.
OnOn
thelevel.
right,
there
three
for densities
this areason
has a realized
finite radius,ofthe
radius
of the
last occupied
densities
condensation is extremely large2 , levels
which is essentially
Milne the
typeactual
model.atoms
Weizsacker
3 too rare under such con3
15
ters
of
↵
particles
and
the
↵
particles
move
randomly
that
a
3-body
reaction
is
much
moving
independently
of
each
other
and
on
the
on the
earth
⇠ 1g/cm
. If Namely,
the matter
compressed to densities as high as 10 gm/cm the nuclei touch each otherright
and we
were giants among the old population
of stars
as are
defined
by Baade.
theseis stars
insideofthe
nucleus.
form
one
gigantic
nucleus.
ThisIfisgiants
nuclear
long life time. Consequently,
these
stars
must
be low
mass stars.
arematter.
main derived see groups
ditions.
We
note
that
Eddington’s
results
were
4
nucleons
moving
as
a
bound
unit.
6
ich have exhausted their
hydrogenreference
fuel
in the core
and
energy
is Phys.,
not
produced
in (1949)
the of stars
Gamow.
G.,what
Rev.
Mod.
21, 367,
without
to
is the
energy
source
The1952.
story starts as early as 1917, when Harkins8 observed that the bindin
7
hen there need not be any temperature
gradientG.,
in the
Weizsacker
thatViking press, New York,
Gamow.
Thecore.
Creation
of thethought
Universe,
or
of
just
an
and neutrons,
(which
he
did
not
know
but
hypothesized,
already
in
↵
nuclei,
(12equal
C,16 O,20number
Ne,24 Mg, of
. . . protons
) are particularly
large. Consequently he
to He is the only process that could operate in stars because he believed that there
for nuclei
basis for this
periodic
table state
was Harkin’s idea tha
come the A=5, 8 barriers.
Consequently,
nuclearbe
energy
not anof
option
for these into he- as shown
1919,
that it must
thewas
fusion
hydrogen
in (cf.
fig. fig.??).
4. In The
particular,
is the
excited
is the
↵-particle.
original idea
was put to
forward before th
he assumption that theylium).
exhausted
and no
other
fusion can of
take
C nuclei
a three
body
state? Harkin’s
Consequently,
attempts
In their
fig. hydrogen
3 we show
the
structure
allplace.
nuclei with of 12of
view, Weizsacker put the giants and the white dwarfs in the same category of stars.
After the discovery of the neutral particle the model12was modified to: the nuc
Theknown
instability
of there
the isA=8
nucleus
the energy
level structure of the excited C were
dded a reservation thatN+Z=8.
in view of results
at his time,
a possibility
for implied find particles
and up to 3 nucleons moving around it (cf. fig.??)
outside the isothermal core3 . However, the idea Weizsacker put forward was that the
Consequently, the following fundamental question was raised: to what ext
white dwarfs and giants should be that giants have masses above the Chandrasekhar
C.F., ApJ, 114, 165, (1951)
erkunft der Sterne, 1947, p 38.
312
would yield a nucleus of type 4n, where n = 1, 2, 3, . . . and an ↵ particle, if bom
atomic weight 2, namely a deuterium. In symbols the reaction is: 4n+2 X2n+1
X is any nucleus and Y is the element the precedes the element X in the perio
e ↵ particles (in seconds). The second row gives the crossing time.
Energy excess in keV
R = 2.5 ⇥ 10 13 cm
crossing time (sec)
R = 2.5 ⇥ 10
13 cm
crossing time (sec)
50
100
4 ⇥ 10
13
4 ⇥ 10
7 ⇥ 10
8 ⇥ 10
22
14
22
3 ⇥ 10
200
14
2.8 ⇥ 10 22
4 ⇥ 10 17
5.6 ⇥ 10 22
2 ⇥ 10
15
2.0 ⇥ 10 22
3 ⇥ 10 19
4 ⇥ 10 22
300
2 ⇥ 10
19
400
5 ⇥ 10
20
1.6 ⇥ 10 22 Who
1.4 ⇥
10 22 the Hoyle Level?
Discovered
3 ⇥ 10 20
1 ⇥ 10 20
22
3.2 ⇥ 10
2.8 ⇥ 10 22
carried out long before any astrophysical interest in the
Crane and Lauritsen observed γ’s from the reaction:
problem arose. Actually, even before Bethe discovered 11 B+2 D → 12 C+p. These experiments which were carthe CN cycle powers the Sun (today we know that ried out in the
12 early 1930th made it clear that 12 C has
Back tohow
new
developments
in
the
structure
of
C
the CNO cycle contributes about 4% of the total energy excited states but their energy was not known to better
produced by the Sun and the pp chain contributes the than ±1M eV .
correct explanation
was put forward five years later, in 1940, and
rest.)
tner and Pardue25 , then in the Kellogg radiation laboratory in
6 same
Thenuclear
History
of the14Discovery
of theGaerttner
. Using the
reaction,
N+2 D ! 12 C+↵,
7.8
12
C Nuclear
due discovered that
on top ofLevels
the emerging ↵, also rays at 1.9,
7.68
5.3 and 7.0MeV
produced
their
origin
Alreadywere
in 1933
Lewis et and
et al.explained
experimented
with
the as due 8 Be
+Αα
+
Be
12
4
12 C at14energies
N+2 D → of
C+
He.
The7.2
nucleus
of 12 C above
so
7.366
d levels inreaction:
4.32
and
± 0.4MeV
the
7.275
formed
has
significantly
more
energy
than
the
ground
tate. The authors even stated that the level at 7.2MeV is weakly Αα
3
state as it forms in an excited state. The decay of the
7.1
with the ground
state, namely, the probability for a transition
excited state to the ground is performed by one or more
7.2MeV emissions
state to ofthe
groundInstate
is very
and
γ photons.
principle,
if yousmall
measure
thewas not
4.43
8
0
the the
γ s you
can easily
figure
energies above
. Here weenergy
note of
that
energy
of Be
+ ↵outisthe
7.367MeV
the
levels
in the
newlyabove
formedthis
nucleus.
nd state ofof12
C.energy
Hence
only
a level
rest Lewis
mass energy
et et al. did not measure any γ 0 s as they 8did not have
kinetic energy can be directly reached by the Be + ↵. At stellar
the equipment, they
however,
discovered the emitted α
8
9 K the
tures of the
order of
10not
have emitted
kinetic energy
particles.
As 10
they did
detectnuclei
all particles
0.01 0.1MeV,
so that
thefound
kinetic
is not
the dominant
in the reaction
they
that energy
the emitted
α particles
8
have
about
half
the
energy
difference
and
it
was
We conclude that for the colliding Be and ↵-particle tonot
enter into
12 C
known
where the other half was lost.
12
y level of C, the energy must be above 7.366MeV but not by
Lawrence et al (1935) repeated the
experiment,
12 C
ch. The knowledge
ofany
thedevice
structure
of the
nucleus
again without
to measure
γ 0 s. However,
they at that
8.6: The
ofas known
Figure
The structure
of energy
the 12 C levels
nucleus
0
hown in fig.??.
green zone
spans
uncertainty
the 6:Figure
measuredThe
the energies
of the α
s and the
found
two groups in
12 at 7.68MeV can decay into a 8 Be + α
in
1940.
The
level
the
C
nucleus
relative
to
the
8 Be
of α level
particles
having
different
energies,
so+were
of the energy
just
above
the energy
ofand
↵ orable
3↵. Since
8 range where the var3α. The
green
color
spansofthe
12
rest
mass
energy
Be + ↵ and
to
infer
that
C
has
two
energy
levels:
at
3.8MeV
and or
ion rate is very sensitive to the exact value of the energy
level,
ious
experiments
gave
an
indication
of an energy level.
4.7MeV. Actually, the interpretation of the experiment
3↵. The level at 7.68MeV can depositions was
are not
mandatory.
All
energies
are
in
MeV.
complete. As shown in fig. 5, there are two
8
cay into a Be + ↵ or 3↵. The
possibilitiesat
to interpret
this experiment.
nuclear reactions
low energy
have two quite independent green color span the range where
In 1940 Gaerttner & Pardue of the Kellogg labo14
rmation and decay.
various
experiments
gave an
ratory at the
Caltech
investigated
the reaction
N+2 D →
8.5
12
C+α and discovered that on top of the emitted α
e formation: So far we discussed the probability of formation. indication of an energy level. All
particles also γs with energies 1.9,3.1,4.0,5.3 & 7.0 MeV
energies are in MeV.
he strong interaction between the particles and the relatively
were emitted. It became clear already at this epoch that
e the particles stay together, the 0 nucleus forgets how the
particular
level
was
reached
The
there
exists a level
at ∼
7.2MeV
but0 .it is
weakly cou12
8
4.7
pled
to
the
ground
state,
namely
the
transition
rmed excited C lives for a while, exactly like the Be nucleus lives for a while, before it decays. to the
physicists call the new nucleus
nucleus0 . ground state was too weak to be observed! Hence, only
3.8 the 0 compound3.8
an upper limit to the rate of transition could be found.
The implication
was that indeed,
if the
reaction
e decay: The new nucleus may have several modes of decay.
It can disintegrate
back
into
the product
goes to excite this level in 12 C, then extremely few 12 C
constituents or lose energy in one way or another and descend into a bound state, provided there
nuclei would decay from this state to the ground state.
r even the ground state. No 0bound nucleus can
loss ofthat
energy.
The nucleosynthesis
most
00 be formedItwithout
appearedany
therefore,
from stellar
12
Ground
state
way of losing energy is by emitting a , however, other ways,
probabilities,
this is though
not likelywith
to belower
the way
C forms. But this
question of transition probability was not yet raised.
Figure 5: The interpretation of Lawrence et al. result.
One alternative can be two levels at 3.8 and 8.5MeV
In the same year Holloway and Moore (1940) retner, E.R., &with
Pardue,
L.A.
, Phys. Rev.,
57, 386,
allows
transitions
between
these(1940)
two levels and peated the experiment 14 N+2 D → 12 C+4 He and conelevant particles
are those
with energies
Gamow
peak
not with
the average
energy.
forbidden
transition
directlyequal
from to
thethe
8.5Mev
level
to and
firmed
the existence
of the
levels at 4.37 & 7.62MeV and
the ground state. The other alternative is two levels suggested that in most cases the (excited) 12 C∗ disinwith allowed direct transition to the ground state and tegrates by emitting an α particle. They wrote that:
forbidden transition between the levels. Lawrence et al The corresponding excited state of 12 C would be unstaassumed the latter case but as we will see that in reality ble against α emission, but it is still easily conceivable
it was the first alternative.
that such a state could not actually emit an α because
313
G. Shaviv
of selection rules. Clearly, in the first case this is not This factor enters into the rate. Moreover, despite the
the way to form carbon while if carbon is formed in this fact that the energy level in the 8 Be continuum was alway we can claim that astrophysical situation implies ready known, Öpik overlooked it. Öpik assumed that
that the channel in which 12 C∗ disintegrates by emit- He burning lasts 1014 sec. The question then was at
ting an α may exist but along with the decay to the what temperature would helium burning last this time
ground state.
and with his wrong reaction rate Öpik derived that heAs for our particular reaction, what Holloway and lium burning takes place at 6 × 108 K. This is known
Moore argued was that in the reaction 8 Be+α ↔12 C+γ today as far off and it implies a discrepancy between
the compound nucleus disintegrates mostly into the in- the formation of 8 Be via two α0 s and the formation of
12
C, as we will shortly see. Öpik’s paper did not attract
coming channel.
Terrell (1950) examined the 9 Be+α → 12 C+n and the astrophysical community and from its publication
found no evidence for excited states in 12 C. In the same in 1951 till 2009 Öpik’s paper was cited just once, and
year Johnson (1952) investigated the 11 B+2 D → 12 C+n it was by Salpeter...
reaction and found the 4.4 & 9.6MeV levels but not the
In 1972 Marshal Wrubel wrote a review on Ernst
one around 7MeV. It should be realized that these ex- Öpik’s contributions to Red Giants and did not menperiments are very difficult and tricky and hence no tion his contribution to the 3α process.
wonder that it took such a long time to find the accuThe uncertainty in the energy levels prevailed in
rate structure of the nucleus of 12 C.
1950. Guier and Roberts looked at: 9 Be+α → 12 C
In 1950 Hornyak et al. summarized the known data +n and claimed the level is at 7.8MeV. The experiment
of the 12 C nuclear structure as depicted in fig. 6. The was repeated with Bertini joining the team, and no level
246
CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS
7.86MeV level is shown but very weak, namely only rare was observed.
transitions into it, and hence
a problem
to experimenin a figure
which provided
the structure ofIn
energy
in 12 C. &
AsLauritsen
can be seenprepared
from fig.??,
a level
1952levels
Azjenberg
a compilatalists. Lauritsen and Fowler
were
co-authors
this appeared as well as the quantum numbers J = 2+ and J = 0,
at 4.43MeV and a level at on
7.5MeV
tion of all the experiments and provided the following
respectively49 . No parity is assigned to the upper level. The only reference given for this information is
paper.
summary
in fig.
7. However,
Our particular
level is well
marked.
0 cloud-chamber investigation0 without the
details of the
paper.
the only researchers
to apply
a
In 1951 Miller & Cameron followed the motion of
50 back in 1935.
cloud
chambers
on
a
close
problem
were
Crane,
Delsasso,
Fowler
and
Lauritsen
8
Be nuclei in nuclear emulsion and observed their dequantum
cay. They found a lifetime The
of 5data
± 1on×the
10−14
sec. numbers
This of
the energy levels is important. It was
6
lifetime is 10 times longer
than the two α’s mutual
well known that the ground state of 12 C
crossing time. This was the
to that
a a
is Jpaper
= 0+ . that
It is put
also an
wellend
known
transitionalternatively
from a J = 0+that
to J 8 Be
= 0+ is
long line of papers that claimed
The spin
of the photon
is unstable and unstable. strictly
Millerforbidden.
& Cameron
succeeded
is 1.
8 Hence a zero spin to a zero spin tranto watch the motion of the
Be nucleus in emulsion and
sition does not leave room for the photon,
see its decay. We mentioned
α-like can
nuclei
so thatabove
angularthat
momentum
be conare expected to be moreserved.
boundHence,
thanif their
neighbors.
a bound carbon nucleus
is to be the of
end
product,
is not suffiHere we have a nucleus composed
just
two αit nuclei
cient to have this energy level because no
and it is unstable!
direct transition from the 7.5MeV state to
the ground state is possible. Another en7 The Wrong Solution
ergy level above the ground state and below the level at 7.5M eV must exist and
Some people claim that must
Salpeter,
who
the so
have the
rightdiscovered
quantum numbers
the transition
to the the
ground
state can
basis for the triple alpha that
process,
must share
credit
go through
an intermediate
state.the
with Öpik. Öpik, according
to this
claim, solved
problem of the helium fusion to carbon already in 1951.
8.9claim,
Salpeter
- The
solution
The trouble was, so goes the
that Öpik
published
is
two
plus
one
his paper in the Proc. Royal Irish Acad. 1951. A seldom visited by astrophysicists
In journal.
the early nineteen fifties, Willy
Fowler, who
thenwith
the insaBut Öpik’s paper is wrong
and was
not already
identical
tiablehad
forcemany
behind important
the Kellogg laboratory,
that of Salpeter. Öpik, who
and
in CalTech, consulted extensively Hans
very original contributions,
apparently did not read the
Bethe, who was at Cornell. After a while,
nuclear literature or ignored
because
hetoignored
theof his
Betheit,agreed
to send
Fowler one
Figure7:
8.12:The
The structure
of 12of
C as
was 12
known
in 1952. For
Figure
structure
the
C nucleus
as the
sumfact the 8 Be is unstable, abest
fact
known
already
1951.(1924young
men and
Edwin in
Salpeter
ease of reading this heavy with data figure, we marked energy level
marized
in
1952.
The
energy
level
under
discussion
wascollision.
his choice. The
Salpeter
spent
So Öpik assumed a 32008)
body
α+
α the at 7.5MeV with red and the level of 8 Be + ↵ is marked with green. is
−20
in red and is at 7.5MeV. Note that the authors
summer
of
1951
in
the
Kellogg
Laboratory.
penetration takes about 0.8 × 10 sec and the third marked
Note that the spin of the level is given, indicating that the 8 Be + ↵
It is during this and subsequent stays that
assigned
thethelevel
J 12=C 0,
which
identical
with
that
excited
nucleus.
It isisthis
coincidence
which
led of
α must collide within this
time. Clearly, the lifetime how can create
Salpeter carried out his research on
later
to philosophical
hypothesis.
From
Ajzenbergare
and forbidden.
Lauritsen
8
6
the
ground
state.
But
0
→
0
transitions
of Be as assumed by Öpik,
offbeby
a factorinto
of carbon.
10 .
heliumiscan
synthesized
1952.
On October 1952 Salpeter submitted his first short paper to the Astrophysical Journal51 . In the
same month of October, the Physical Review published a paper by Ajzenberg and Lauritsen, who worked
314
in the same Kellogg Laboratory, in which the resonance level in 12 C was marked at 7.5MeV and with
quantum number assignment of J = 0. No parity was given. Salpeter submitted his paper after returning
Who Discovered the Hoyle Level?
8
Salpeter Enters the Game
Salpeter did not cite him and added: His method of
calculation is not quite clear from his brief note. It
Salpeter entered the game in 1951 just after the pub- seems that the reaction 2α → 8 Be∗ he has treated in a
lication of the Bethe-Salpeter equation. It was upon manner similar to ours, where as in 8 Be+4 He → 12 C
Fowler’s request for help in the theory, that Bethe de- +γ he has postulated a resonance process. The outcome
cidedNEW
to sendEXPERIMENT
his distinguished young physicist Salpeter is a formula yielding 1.4 × 1013 times higher an energy
8.12. THE
249
to the Kellogg laboratory at Caltech. Salpeter spent generation with practically similar temperature as our
two summers in Caltech. On October 1951 Salpeter formula. How many errors can be written in a single
submitted his first paper to the ApJ: 12 C had no level sentence?
around 7.6MeV. On October 1951 Ajzenberg & Lauritsen submitted
a paper to Physical
7.59
0+ Review in which
12
C had a level at 7.5MeV with J=0 (no known parity).
Two of the most important results for the triple alpha
Gγthe same time by people from
3.16
process were published
at
the same laboratory in two different journals and no ci+
tation was4.43
given to one another. 2They simply did not
know of each other.
When Gamow considered
Gγ in 1938 the possible en4.43
ergy source of MS stars he assumed, in an attempt to
overcome the A=5 barrier, that: 24+He ↔ 8 Be, namely
0
the reaction is in a dynamic
equilibrium and assumed
12
8
C was unaware of this publicaBe to be stable. Salpeter
tion of Gamow but knew already that 8 Be is unstable.
TheThe
veryclear
nice discovery
of the
levels
Salpeter,
as Gamow,
Figure So
8.13:
Thefacing
statustheofsame
the dilemma
level structure
of as- Figure
Figure 8:
8.14:
evidence for
theenergy
two groups
0
by
Beghian
et
al
(1953).
12 sumed that the two α s go into the 95KeV level (which
C after Beghian et al. 1953.
of rays as discovered by Beghian et al. 1953.
was known already to Salpeter) in the continuum and
In 1953 Beghian et al investigated the 9 Be+α →
the so formed nucleus lives long enough (just 10−14 sec
12
C+n
reaction. They detected two groups of γ rays:
which were inferred from the width of the level) for a
known and
documented
by
researchers
before.
many
of the that:
required
12
12 from Kellogg, as described
at
3.16MeV
and atHowever,
4.43MeV and
concluded
C
third α to collide and create a C nucleus. Salpeter
−14and above all Fowler did not trust
details were
still
missing
the
experimental
results.
has
two
levels:
at
4.43
&
7.59MeV
(The
first
alternative
realized that 10 sec is orderes of magnitude longer
than the two α0 s self-crossing time and hence his treat- is shown in fig. 5) . They did not find any γ rays with
8 the American Physical Society
The abstract
presented
Albuquerque,
September
to 7.5MeV. New
HenceMexico,
they concluded
that
ment was was
justified
becausein
Be lives a long time before energiesinclose
the
probability
of
the
7.59MeV
level
to
decay
to
the
it decays
and the assumption
equilibrium
fullyin
jus2-7, 1953.
The sensational
paper ofwas
the lastisone
the last session. The session itself was on nuclear
ground
state
is
<
1/2500.
Willy
Fowler
did
not
trust
tified.
If so, there is It
no was
need aforvictory
a cross section!
Next,
physics not
astrophysics.
to astrophysics
and Hoyle, in particular in front of skeptical
Salpeter assumed that the 12 C nucleus ”somehow de- any of the previous measurements of the carbon level
63
Fowler , that the location of a 12nuclear level that wandered
so much for
fromway
onetoexperiment
to the experiother,
carry out a trustful
cays” in flight (no level in C was known to certainly and searched
8.12. THEa NEW
EXPERIMENT
could be exists)
determined
observing
the
two papers were published, one by the experment.
into thefrom
ground
state of 12
C. stars. Shortly after,
imentalists in
the
Physical
Review
and
one
by
the
theoretician
in the Astrophysical Journal Supplement.
Salpeter stressed that he assumed no resonances in
12
16
20
24
This triumph
forged
collaboration
C, O,
Ne, the
MgFowler-Hoyle
. . .. Salpeter felt
uneasy aboutthat
it contributed immensely to nuclear astrophysics
and
wrote
that:
The
nuclear
γ-ray
width
for
the
formafor many years to come.
7.59
0+
tion of 12 C (but not the one for 8 Be) is required. This
width has
not yetisbeen
measured, by
andHoyle,
the position
of et al.64 with the title: A State in 12 C Predicted
The exact
reference
an abstract
Dunbar
Gγ
3.16
resonance levels was not known accurately enough and
from Astrophysical Evidence. The idea was that: the observed 0 cosmic0 ratio of He:C:O can be made to fit
an estimate of 0.1eV was used for this width. Hence
8 Be + ↵ ! 12 C +
the yield the
calculated
for theserate
reactions
the reaction
has a4.43
resonance near 0.31MeV,
2+
correct production
could beifsmaller
by a factor
12
corresponding
to a as
level
7.68MeV
The abstract
also claimed that: A level had previously been
of as much
10 at
or larger
by asinmuchC.as 1000.
Thus
reaction rate
known
the literature
estimated1952. In the same abstract they report
reported the
at 7.5MeV,
based
on inAjzenberg
andwas
Lauritsen
Gγ about the
4.43
ignoring
the
possible
existence
of
unknown
resonances.
experiment which led to the discovery of the level at 7.68 ± 0.03MeV. The mode of decay of the level is
Two comments: In 1954 Öpik wrote a paper about
0+
not discussed.
12
WD and the 3α. He wrote that: the lifetime of
C
the temporary nucleus 8 Be formed is assumed equal to
∼ 8 × 10−21 sec being an estimate of the duration of
8.13: The
status
the level
of
The structure
of 12 C
after of
Beghian
et alstructure
dis8.12 penetration.
The new
experiment
The lifetime
of true 8 Be is probably much Figure 9:Figure
12 direct transition from the 7.59MeV to the
−22
covery.
The
C
after
Beghian
et
al.
1953.
shorter, about 10 sec . . . No resonance capture is assumed in 65
this case. Moreover,
that ground state is forbidden.
14 Öpik2 complained
12
Does not
exist!
Figu
of
Dunbar et al. repeated the N + H ! C + ↵ experiment once more using a new special double
focusing magnetic spectrometer and discovered that the excited
leveland
is atdocumented
7.68 ± 0.03MeV
as can be
seen
known
by researchers
from
Kellogg, as descri
315
from fig.??. Unfortunately, they did not give the quantum numbers
thestill
levels,
and it
was
impossible
to did not trust th
detailsofwere
missing
and
above
all Fowler
determine whether the reaction a stable 12 C could be formed. This sophisticated and accurate experiment
G. Shaviv
The symmetry of the 12 C ground state leads to a
J = 0+ state. The state at question appears to have
also J = 0+ . Angular momentum conservation do not
allow the 0+ state to decay into the ground state which
is also 0+ . Hence, if eventually the decay of this state
leads to the ground state, there must be another intermediate level below the 7.59MeV one with the proper
spin, to which this level can decay. Hoyle never mentioned these requirements nor allowed and forbidden
transitions. He tacitly assumed that the 7.69MeV level
’somehow’ decays to the ground state.
9
1953 Kellogg Phase I
deed Whaling went to the lab and found the level exactly where Hoyle claimed it must be. The level was
rediscovered!
Hoyle spoke about the energy of the missing in calculation level and did not discuss any spin, selection
rules etc. The abstract was presented in the American
Physical Society meeting in Albuquerque, NM, Sep 2-7,
1953. The paper was presented in the session on nuclear
physics not astrophysics. It was a victory for Hoyle in
particular in front of skeptical Fowler.
10
How Did Hoyle Predict the Nuclear
Level in 12 C
When Martin Schwarzschild and Fred Hoyle tried to Hoyle assumed the that κ defined as:
evolve main sequence stars off the main sequence and
derive the Red Giant, the modeling failed and they
destruction
Rate(12 C + α →16 O + γ)
=
κ
=
A
could not get the Red Giant branch. Beside the failRate(3α → γ)
f ormation
ure to derive the branch, there was a problem with the
composition. The rate of 12 C + α (carbon conversion is given and calculated the resulting mass fraction of
into 16 O) was much greater than the rate of carbon for- 12 C after the burning of helium into carbon. Hoyle obTHE
LABORATORY GROUP PHASE II
251
CHAPTER 8. HOW NATURE OVERCOMES
ITSKELLOGG
OWN BARRIERS
mation and hence 8.14.
no carbon
was
left after
helium burn- tained in this way the results shown in fig. 11.
It is
ing. The model moved from helium to oxygen leaving easily
seen
that
κ
1
(the
destruction
is
much
faster
end of the helium burning.If the formation of 12 C is much slower than its destruction, the end product if
must have Carbon
in our Universe!
no carbon.
than formation) yields no carbon at the end of helium
almost pure 16 O.
Hence,
Hoyle
argued
that
there
should
be
a
level
at
burning.
66
n extensive research on the synthesis of the heavy elements and discussed
In
addition,
Hoyle
carried
out
theleads
inverse calabout
which
accelerates
the reaction
and
e starting point. This
is the7.6MeV
same paper
in which
Hoyle proposed
how the
in (relative
aassumed
style which
today as 0 reverse
formation
ofculation
carbon
to isdynamic
itsknown
destruction).
n the galaxy, see sec.to
??.the
Hoyle
followed Salpeter
and
the
0
engineering
, namely
must
and
Eres be so
and applied statistical
mechanics
findon
the
abundance
of the
thewhat
beryllium.
Hoyle
spoke to
only
the
energy
of
level
andThe
knew
as
get himself
the observed
abundance,
and he found
12 to
he equation and onlyat
quoted
the
result,
Hoyle
cited
for
the
equation
what energy in C it should8 be because he assumed
= 1.4 ⇥ 10 Kunder
and statistical
Eres = 0.33MeV (above
per Hoyle discussed the formation of the8Theavy
it takes place via8 the
Be + elements
α. This is8 exactly
the level we
amow’s 1938 paper and his equilibrium Be. rest mass of Be + ↵) which corresponds to
discuss here.
E = 7.705MeV in the 12 C nucleus.
d it can absorb an additional
n, which in turn can again
ome neon:
ed by
16
O + ↵ ! 20 Ne + .
pture another ↵ particle to
g Coulomb barrier reduces
ermissible to neglect the ↵
ucial point is therefore, that
esized at the same time and
, on one hand the carbon is
t is destroyed. By the end of
arbon depends on the ratio
and the rate of destruction.
meter:
In summary, Hoyle was able to apply astrophysical arguments to solve the problem of the carbon energy level, the exact location of which wandered from one experiment to the other. Shortly
after the idea that such a resonance must exist or Figure 8.16: The formation of carbon from helium as a
11: The argument by Hoyle that the resonance
else, the cosmos will have no carbon to supportFigure
life
. This is the figure which
mustfunction
exist. of Hoyle’s parameter
the way we are familiar with, was born. The fanconvinced Hoyle that 12 C should have a resonance.
tastic story about how astrophysical consideration
68 . al had the title:
The
paperofby
Dunbar
led to the prediction of a nuclear level triggered the
invention
theHoyle,
anthropic
principleet
A state in 12 C Predicted from Astrophysical Evidence.
abstract
also II
admitted that: A level had previously
8.14
The Kellogg LaboratoryThe
group
phase
been reported at 7.5MeV, based on Ajzenberg and Lauritsen
. on
the other
hand,
decay
mode of the
Hoyle’s victory was not complete. Cook et
al.69 1952.
found it
necessary
to carry
outthe
a new
experiment
12 Cnot
level
- a crucial
- was
discussed
at all.clear.
Beghian
again because the Experimental evidence on the
character
of thepoint
7.7MeV
state
is not entirely
It
seems
well
established
that
the
state
does
not
radiate
directly
to
the
ground
state
but
rather
cascades
via
discovery
of
the
7.59MeV
level
was
overlooked.
16
C + ↵ ! O)
the 4.43MeV state. Furthemore, Cook et al addedBut
that Hoyles
one mustvictory
(a) Makewas
surenot
thatcomplete
the 12 C level
can friends
be
12
his
↵ ! C)
formed by 8 Be+↵. The prerequisite for that aredid
the not
rightaccept
spin andthe
parity
and that
thereHoyle
is a non
vanishing
idea.
Could
invert
the proprobability that it decays by emitting these particles. (b) It must have a finite probability to decay to the
r, so that relevant values of
cess and learn nuclear physics from the 8stars? Cook,
excited
the ground
ity. Clearly,  depends on Figure 8.15: lower
Dunbar’s
et al.state
1953 or
result.
A beau- state. These questions should be best explored by bombarding Be with ↵
Fowler, T. Lauritsen and C.C. Lauritsen 1957 argued
8
particles,
since 7.68MeV
Be is unstable,
the properties of the energy tiful manifestation
of thebut
predicted
level. recourse must be made to study the two possible modes of decay of the
12
12
⇤
8
12 C⇤ ! 12 C + . Then
that:Experimental
evidence
theoncharacter
of the
excitedforstate
C, namely
one hason
to rely
the principle
Of all the data which enters into the expression
, itofis most
sensitive C
to ! Be + ↵ and
12nuclear reactions. Indeed, Hoyle
7.7MeV
state
is
not
entirely
clear.
It
seems
well
esof
reversibility
of
did
not
predict
the
quantum
numbers
of
the
level
and
ecause
Figure 10: The structure of C after Dunbar et al
without
these
the
prediction
is
not
terribly
powerful
tablished
that
the
state
does
not
radiate
directly
to
the
discovery.
(E E(8 Be+↵))
Eres
kB T
ground state but rather cascades via the 4.43MeV state.
 ⇠ e kB T = e
,
The experiment Cook et al. was innovative and di↵ered substantially from all previous ones. They
12
12 C that
When
Hoyle
came
to
Kellogg
in
the
first
time
he
The
authors
that:above
one the
must
(a) state
makeofsure
created the radioactive 12
isotope B, which has
an energy
of added
13.378MeV
ground
evel in the 12 C nucleus.
All energies
are above
the ground
state
ofthis
C. level
The and in- the level can be formed by 128 Be + α. The spins should
convinced
Ward
Whaling
to
look
for
and decays via a decay (in contrast to a decay) into all excited levels of C with lower energy and
ntial.
in particular into the two relevant levels for our discussion here, cf. fig.??. Special arrangement was
rate for the triple ↵ reaction and the problematic
later)
prepared to(see
detect
thesubsequent
emitted ↵’s using a strong focusing magnetic spectrometer.
316
e solved for the abundances of carbon and the results are shown in fig. ??.
The basic
problem
Cook
et al. faced with the 7.68MeV level was the following: It was established
that when  = 1/9 the amount of carbon produced
by the
time the
helium
w came the critical question, what is the probability to decay back into the incoming channel,
↵. Salpeter resorted to the Wigner theory81 and calculated an upper limit for the case 0+ which
% higher than the one adopted by Cook et al. The other possibility was proven by Salpeter to
dict the experimental results. To further provide support to his estimates of the probabilities,
Who Discovered
the Hoyle Level?
er derived the probabilities by assuming the ↵ model for the 8 Be nucleus. The
numbers agreed.
ally came the question what is the probability
agree.
(b) It4.43MeV
must have level.
a finite probability
decay to
ay into the
bound
After all,tothis
the ground state.
e dominant mode to form a stable carbon nucleus.
Γα
the direct
cannotfor
be the
investigated
the estimateNote:
depended
onreaction
the model
car- Qin1=0.278
8
the lab because the rate is very slow. Consequently, the
cleus. If one
that
the carbon
nucleus was Q2=0.094 Be+α
12
C assumed
level must be
populated
indirectly.
3α
of three ↵ particles,
probability
Cooks etone
al. got
hadaavery
seversmall
technical
problems: On
ay into theone
firsthand:
excited
state.
So after
some
lengthy
It was
established
that
there
is no direct
way toSalpeter
the ground
state. On
thethe
other
hand no one
tical discussion
adopted
that
probabil12
that the
compound
nucleus disintegrates
decay intoobserved
the8 ground
state
plus theCprobability
to
∗
into Be + α. There were conflicting estimates of the
into excited
state, namely
total probability
to
probability
to emit anthe
α. Uebergang
and independently
APTER 8. HOW NATURE OVERCOMES ITS 12
OWN BARRIERS
nto the ground
was
small.
Steffen, state,
got that
the0.00014,
excited quite
C nucleus
emits α at
J=0+
Γγ
7.654
Γe+eJ=2+
J=0+
4.43
0
about << 50% of the cases while Bent et al and inde-
71 and Ste↵en et al.72 estimated the probability to be ⌧ 50% and
ng
peter
made
an additional crucial assumption. Since Figure 8.18: The structure of 12 C assumed by 12
pendently Hornyak got that it emits an α in >> 97%
Figure 13: The part of the energy schemes of the C
Hornyak74 estimated it to be 97%.
obability to
decay
back into the incoming channel Salpeter
of the
cases.
in 1957.
of decay
nucleus
relevant to
thethe
3α probability
reactions as was
finally as↵ is
an
upper
limit
to
the
↵) is by far the largest, or in other words, the leak- emitting
sumed
by
Salpeter
in
his
final
paper
in
1957
an
↵
particle,
is
the
probability
of
ince this was by far
modes
decay
this level,ofthe
exact other than the mode of formation is decay emitting a
photon and e± is the probThe structure of 12 C as assumed
by Salpeter in 1957,
re
to rely
on permitted to assume an equilibrium
elyforced
small,
it is
ability
to decay
by13.emitting
anprobability
electron of
positron
⇤ Temis
given
in
fig.
Γ
is
the
decay emitydenburg
and
12
α
*
↵
) C . The unbound 2 ↵’s are reluctant to ab- pair. This is after Salpeter obtained the improved
hich was about 250
ting an α particle, Γγ is the probability of decay emitthird
↵ and
become bound. Once this is done and results
he
improved
(lower)
tingofaCook
γ photon
Γe± is the probability to decay
et al.and
1957.
heir
most
important
cal mechanics can be used to calculate the abunby emitting an electron-positron pair. This is a rare
for
decay to the
mode of
decay and ofThe
no importance
to our
story here.
thebut12not
C zero.
nuclei, the details of the nuclear reaction became
irrelevant!
probability
to form
yof
small
12
This
was
the
structure
of
C
after
Salpeter
obtained
yin
to the
decayground
through state is then the number of carbon nuclei in the excited state (as obtained form the
the
improved
results
of
Cook
et
al
1957.
5
pair is about 10
rium
condition) times the probability that they decay to theSalpeter
ground
state of carbon.
made some critical assumptions: The dis-
12 ∗
integration
channel
C decaying
intoIn8 Be
the end of January 1955 the American Physical Society had
its annual
meeting
in Newback
York.
a +α
is
the
dominant
channel
and
all
other
possibilities
ompleting
theof Transmutation and Nuclear Energy Level, Salpeter presented preliminary results are
on Reactions
very small leakages. Consequently, Salpeter assumed a
e↵ect of the 7.68MeV82 . By now, Salpeter became awaredynamic
of theequilibrium,
Ajzenbergnamely
and Lauritsen coming
0
0
12
mmary
appeared in his paper as to be published ) of the energy levels of C and derived for the
per77 was(it
submitted
12 ∗
and
the
two
me the fullpapers
reaction rate.
C ↔8 Be + α.
yakawa
et al.83 got the information from Salpeter, who also informed them about
the probability
7, the spin of the
If so, the concentration of 12 C is determined from the
e
7.68MeV
excited
state
decays
to
the
4.43MeV
level,
and
submitted
their
paper
to
the Progress in
ough very recent
ex- Figure
8.17:final
Cook
et al. 1957 by
created
theetra-al. 1957:
Figure
12: The
experiment
Cook
equilibrium (small sensitivity to the energy of the level)
12
12
12
ltical
proof Physics
of thecreates
quandioactive
nucleus
which
C. MostintoNovember
Japan,
on
JulyBB1956
to beinto
published
1956.
Salpeter’sispaper,
on the
otherto the
the nucleus
and decays
follow
its
decay
the and all
the uncertainty
in the small
leakage
nd Hofstadter78
were of the
decays
go into
the ground state and only
7.653MeV
level
(only
1.3%).
was
submitted
1957 to be published July 1957, that
to say, In
over
a year the
later.
before
otherischannels.
particular,
is noSo
need
for a cross
on beams
to investi- March
1.3% go into the investigated level.
12
section,to
evaluate
the
rate.
The
reaction
is
in
a statisnsidered
that the toCpublish his results in a journal, Hayakawa et al. published the calculation of the rate
er managed
To overcome
the problems
Cook et works
al 1957 cre- tical equilibrium.
barded 12 C with high
energy electrons.
This and subsequent
12
6
ng the excited
state
of Cnucleus
and wrote
that:
This rate
12
12 is about 10 times larger than that given by
79 Fregeau
ated
the
radioactive
which
decays
61 Nobel prize.
and Hofstadter
treatedBalready
in
1955(!)into C.
On January 1955 Salpeter presented the results in
r. They
They
continued
state
Such a great di↵erence is due mainly
Most
ofSalpeter
the decay
goes
thegive
ground
stateto
and
only that:
carbon
as someant
well established,
that1952.
they into
did
not
any reference
the New York meeting of the12Physical Society. By now
+
nfact
of thethat
7.68MeV
level,
they
state
that:
J
=
0
is
not
inconsistent
1.3%
decays
into
the
investigated
level.
he did not take the e↵ect of the recently discovered
resonance
in C into
account.
he became
aware oflevel
the Ajzenberg
& Lauritsen
old rey found. The levels emerged very nicely in their electron scattering
sult and
citedhave
it. been the most important
one of the most important conclusion obtained in our work.
It may
Fowler won the 1983 Nobel prize (with Chan-
+ or 2+ . If the 2+ was assumed
ed
that theresult:
only possibilities
were
t recent
M.0 and
5Finishes
authors, Proc.13th
Capture
Gamma-Rayto
Spect.,
AIP
Conf.
11 Chemykh,
1957 Salpeter
the JobInt. Symposium
drasekhar)
for contributions
nuclear
astrophysics,
± (symbolized in5 nuclear physics as e± ) could be theorettron
decay
009 is e = 6.2 ⇥ 10 eV .
but Fowler’s Nobel speech was one long discussion
be 1000 smaller than the one obtained if 0+ was assumed and this
tt, J., & Weisskopf,
V.,problems:
Theoretical
Nuclear
John
Wiley & about
Sons, Inc.
NY, 1952.
. . . Hoyles
contributions. As for Salpeter, Fowler
Remaining
What
is thePhysics,
spin of the
7.68MeV
peter,
E.E.,
Phys.
Rev.
98,
1183,
(1955)
, 279, (1954)
state? Fregeau & Hofstadter (1955) using electrons commented that he ignored the 7.68MeV state - which
H.,
Zeit. f. S.,
Phys.,
145, 156, (1956)Imoto, M., & Kikuchi, K. Prog. Theor. Physics, 16, 507, (1956)
akawa,
Hayashi,
scatteringC.,from
the nucleus (an experiment for which is a very wrong claim. He ignored it when it was un-
J. H., Ranken, W. A., Phys. Rev., 100, 771, (1955)
Ser, II, 1, 197, (1956)
Hofstadter got the Nobel prize 1961), claimed that
C. W., Phys. Rev. 104, 135, 143, (1956)
J=0+ is not inconsistent with experiment. So Salpeter
ys. Rev., 104, 123, (1956)
assumed J = 0+ or 2+ . The latter yields a result which
957)
Rev., 99, 1503, (1955).
Ibid.1000
104, 225,
(1956)than the first one.
is about
smaller
neering studies of electron scattering in atomic nuclei and for his thereby achieved
ucleons .
known to him. Fowler was a great experimental nuclear
physicists but without knowledge in statistical mechanics and he did not like that ’the nuclear physics’ was
eliminated from the problem.
317
er89 (3.5±1.2)⇥10 4 , Seeger and Kavanagh90 (2.8±0.3)⇥10
difficult to achieve high accuracy!
8
4,
Shaviv
CarbonG. structure
is half the story: The
and Mak et al.91 (4.30±0.2)⇥10
12
C + ↵ !16 O + reaction
We come to the destruction of carbon. The existence of excited1levels in 16 O
Hoyle and Salpeter shared
the 1997 Crafoord prize 19
92 , who
discovered by Burcham
andforFreeman
reaction F + p !
in particular
the physics
of theused
triplethe
α reaction.
+ ↵ and found The
the process
6.94MeV
and the
7.15MeV
levels.
They
is called
today
the Salpeter
process
andhowever, did
the energynumbers
level is called
thelevel.
Hoyle In
level.
etermine the quantum
of the
1950 Millar, Bartholomew
16 N ! 16et
Fightthe
for priority:
Salpeter
informed
Kinsey93 investigated
rays from
the decay
of Hayakawa
O + e . This
al.
about
the
probability
that
the
7.68MeV
statereactors
deactive isotope is produced in the cooling water of nuclear
via the
cays
into the 4.43MeV state. Hayakawa et al hurried
16
16
ion O + n !andNsubmitted
+ p. Thetheir
halfpaper
lifetime
of the of
isotope
is 7.35 sec. The
to Progress
Theoretical
16
16
y of N is so Physics
high that
it in
can
decay
the first
two levels
Japan
July
1956 into
in which
they made
just of O by
ion of an electron.
Thus,
discovered
which1956.
corresponded to
this claim.
Thethey
journal
published onrays
November
Salpeter
published
his
work
only
in
1957.
Surprisevel at 6.133 ± 0.011MeV and 7.10 ± 0.02MeV. These results were in good
the found
japanese
that: This
(meaning
ment with the ingly
values
byauthors
Chao,claimed
Tollestrup,
Fowler
and Lauritsen94
theirs) rate is 106 times greater than given by Salpeter
136 ± 0.030MeV1952.
andSuch
7.111
± 0.03MeV. To complicate the issue, they did
a great difference is due mainly due to the
iscover rays which
would
the level
6.91MeV. They were
fact that he didcorrespond
not take into to
account
the 12at
C resonance.
ver, able to determine
numbers
the level
J =1 .
They didthe
notquantum
mention that
it wasofSalpeter
whoastold
them about his work and the
12
4.
12
Αα
C+
J=1-
7.115
7.162
J=2+
J=3J=0+
6.917
6.130
6.049
J=0+
16
O
C level.....
16 strucFigure
8.19:ofThe
he situation became complicated once more. The 12 C + ↵ have
a restFigure
14: The
structure
O based
on Ajzenberg
256
CHAPTER
8. HOW
NATURE OVERCOMES ITS O
16
ture
of
the
oxygen
nu-of the relevant
energy of 7.162MeV,
level in the O &nucleus
is 1952. The partial width
Lauritsen
12 Is while
This the
theclosest
Entireenergy
Story?
12 C + ↵ threshold. Thus the carbon plus the alpha combine to form the excited oxygen
at 7.115MeV
not known
because
cleus is1952.
Based
on it is a very
115MeV, that is
to say, just below the threshold of the collidinglevel
particles.
upper tail of the level. On the other hand, as the width of the level is large, the proba
Is this the entire story? No! What about the structure
12 C + ↵ is very small
difficult
measurement.
The
uncertainty
the
level
is
into
and
as
a
matter
of
fact,inwas
never
observed.
use all energy levels
save
the ground
are not
they have a certain Ajzenberg and Lauritsen
of 16 O?
Following
Hoyle,state,
we treated
thestable
reaction
marked byInthe
grey
zone
around
the
level.
The
diffi95
Dyer and Barnes from CalTech attempted to measure the 12 C + ↵. The n
h in energy. The width E is related
to the lifetime t through the relation 19741952.
96 from Münster measured the reaction and discovered that
12
in 1982from
when Kettner
et al.that
culty stems
the fact
the level lies just below
C16+ α16 → O + γ
faster
then what slightly
Dyer and Barnes
from Caltech
a consequence, the most ab
t ⇠ h̄. The 7.115MeV level in O is sufficiently wide to extend
into
energies
above
the found.toAsfeed
the continuum and hence extremely
difficult
in.
the end of helium burning was found to be
16 O
and not
20 Ne
as well established. However, this is not the case. In
97 criticized the analysis and the conclusions of the experiment
Langanke
and Koonin
ccording to the Uncertainty
Principle,
width
of theattempted
level is connected
time
of the
system
in that level.
1974 Dyer and
Barnesthe
from
CalTech
to mea- to the lifethe
very long theoretical analysis of the experimental data. They could not resolve
a nuclear reactionsure
point
of
view
it
means
that
if
the
energy
of
the
colliding
particles
is
within
the
wide
range of the
the 12 C+α reaction. The next attempt was carried
between the Caltech data (Dryer and Barnes) and the Münster data (Kettner et al.)
The experiment
next question
is
where
carbon
iswas
synthesized?
and not just equalout
to in
the1982
prescribed
energy,
the
reaction
can
proceed.
separately. Thus, the Münster
data98
1.5 time higher than that of Calte
when Kettner et al. from Münster measured
washappens
3 timesD.P.,
higher
than
what
stellar
modelers
use. As
and Koonin wrote Su
Or what
if the
carbon
level
were
atLankange
another
eer, M., Wuosmaa,
A.H.,
Betts,
R.R.,
Henderson,
D.J.,
Wilt,
P.,
Zurmuhle,
R.W.,
Balamuth,
Barrow,
S.,
Benton,
16
the reaction and discovered that it is 3 to 5 times faster
, as those found in Münster and Caltech, lead to O rather than 12 C, as the final pr
energy? burning,
wouldand
carbon
still
be
formed?
The
answer
is
Q., Liu, Z., & Miao, Y., Phys. Rev. C, 49, 1751, (1994)
in this way cast a shadow on Hoyle’s argument.
then what Dyer and Barnes from Caltech found. As a
burger, D.E., Phys. Rev., 124, 193, (1961), who used the reaction 10 B + 3 He ! 12 C + p.
consequence, the most abundant specie at the end
of
all & Tanner , Nuclear Phys.,53, 673, (1964), who used
the reaction 10 B + 3 He ! 12 C + p.
helium burning was found to be 16 O and not 20 Ne as
eger, P.A. & Kavanagh, R.W., Nucl.
Phys., 46, 577, (1963), who used the reaction 14 N + 2 D ! 12 C + ↵
the formation of 16 O is faster than its destruction.
ak, H.-B., and 4 co-authors, Phys. Rev. C,12, 1158, (1975)
Langanke
and Koonin
(1983)
criticized
theW.E.,
analysis
eeman, J.M. & Baxter,
A.S., Nature,162,
696,
(1948).
Burcham,
& Freeman, J.M., Phys. Rev. 75, 1756, (1949)
and
the
conclusions
of
the
experimenters
and
repeated
illar, C. H. , Bartholomew, G. A. & Kinsey, B. B., PRL, 81, 150, (1951)
the very
long
theoretical
of theC.experimental
hao, C. Y. ,Tollestrup,
A. V.
, Fowler,
W. A.analysis
& Lauritsen,
C. , Phys. Rev. 79, 108, (1950)
C+α
data. However, they could not resolve the discrepancy
between the Caltech data (Dryer and Barnes) and the
Cau
Münster data (Kettner et al.) and fitted each experiment separately. Thus, the Münster data was 1.5 time
higher than that of Caltech, which in turn was 3 times
higher than what stellar modelers used. As Lankange
and Koonin wrote, such higher values , as those found
Temperature in 1
in Münster and Caltech, lead to 16 O rather than 12 C,
Figure
The measured
capture probability
(in
Figure
8.21: The ratio betwee
The8.20:
measured
capture
probability
(in
units
as the final product of helium burning, and in this way Figure 15:units
of nano-barns) by the Munster (1982) and the
calculated by Kunz et al (2002)
of
nano-barns)
by
the
Munster
(1982)
and
the
KelKellogg (1974) laboratories. The arrow marks the
rate compiled by Caughlan and F
cast a shadow on Hoyles argument. In fig. 15 we show
energy
range at whichThe
the reaction
takemarks
place in thein energy
many calculation of stellar evo
laboratories.
arrow
a comparison between two recent experimental result logg(1974) stars.
The continuous lines are the theoretical fit
is given as a function of the temp
range
at
which
the
reaction
takes
place
in
stars.
The
by Langanke and Koonin 1983 and it includes the
and a theoretical fit. The red arrow shows the energy
e↵ect
of the
resonance.
continuous
lines
are
the
theoretical
fit
by
Langanke
&
range in stars where this reaction takes place. So far
Koonin
1983
and
it
includes
the
effect
of
the
resonance.
Dyer, P. & Barnes, C. A., Nuc. Phys. A233, (1974)
this experimental discrepancy is not sett led.
Ratio of predicted reaction rates
2.4
2.2
12
2
1.8
1.6
1.4
1.2
1
0.8
0
2
4
6
95
96
1
The Crafoord Prize in astronomy and mathematics, biosciences, geosciences or polyarthritis research is awarded by the
Royal Swedish Academy of Sciences annually according to a rotat-
Kettner, K.U. and 8 co-authors, Z. Phys. A, 308, 73, (1982)
97
Langanke, K. & Koonin, S.E., Nuc. Phys. A410, 334, (1983). Ibid. Nuc. Phys., A439, 384, (198
was published when Langanke was still in Munster. The second paper was published after he joined Ko
98
The probability for this reaction to take place at thermal energies (T = 2 ⇥ 108 or 300keV) was giv
350 keV barn (Münster), 240 keV barn (Caltech) and 80 keV barn in standard nucleosynthesis calculat
ing scheme. The prize sum of SEK 4 million makes the Crafoord
one of the worlds largest scientific prizes.
318
Who Discovered the Hoyle Level?
given in fig. 16 for low mass stars and fig. 17 for high
Today, the principle has its own life and the origin
mass stars. We see that ’moving’ the level quite sig- which triggered it is mostly forgotten. In any case the
nificantly changes the dominant stellar mass at which old justification that lead to its inception is not that
carbon is formed but not in a way that would required valid.
258
CHAPTER 8. HOW NATURE
OWN
a revision of our ideas.
TheOVERCOMES
story is told inITS
more
detailBARRIERS
in Shaviv (2011).
10
10000
References
1000
8
100
[1] Ajzenberg, F. & Lauritsen, T., Rev. Mod.
Phys.24, 321, (1952) In 1950
Azjenberg and
M=15Msun
6
Lauritsen had the level at 7.MeV and it is not
clear why the level ?moved? half an MeV upward.
M=1.3Msun
C/O
C/O
10
1
0.1
M=5Msun
4
[2] Beghian, L.E., Halban, H.H., Husain, T., &
M=25Msun
Sanders, L.G., PRL, 90, 1129,
(1953) Submitted
2
April, 1953 and published June 1953.
0.01
0.001
0.0001
-150
-100
-50
0
ΔE-KeV
50
100
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-50
0
50
100
[3] Bethe, H.A. , Rev.
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ΔE-KeV
This
extensive
review
of nuclear physics earned
Figure 16: The C/O ratio obtained in the evolution of
justifiably
the
title
The
Bethes
Bible.
8.22:(1.3M
The C/O
obtained in the
Figure 8.23: The C/O ratio and
obtained
in the
lowFigure
mass stars
andratio
5.0Mand
) upon a hypothetical
doi:10.1103/RevModPhys.9.69
12
evolution
low massof stars
(1.3M and
evolution of high mass stars (15M and 25M )
change
in theof location
the resonance
in 5.0M
C. )
upon a hypothetical change in the location of the
upon
hypothetical
theZeits.
location
of the 76,
[4] aBothe,
W., & change
Becker,inH.,
f. Physik,
12
We did not
the possible decay of the ex- resonance
resonance
in 12discuss
C.
in
C.
421, (1932) doi:10.1007/BF01336726
cited nucleus 12 C∗ to 3α. We can, however, repeat
Hoyle’s argument and argue that the observations im- [5] Cook, C.W., Fowler, W.A., Lauritsen, C.C. &
8.20
C/Othough
ratiopossible
today
- observations
and what
they
imply
Lauritsen,
T., Phys.
Rev.,
107, 508, (1957)
ply that The
this decay,
energetically
and
ER 8. HOW
NATURE
OVERCOMES
ITS
OWN
BARRIERS
doi:10.1103/PhysRev.107.508
should
is very rare
and or
hence
neglected.
Not a take
singleplace,
star without
oxygen
without
carbon was discovered. Detailed observations have shown
C/O
that the abundance ratio C/O varies from star to star. Gradually
it became
clearL.A.,
thatFowler
there &
is Lauritsen,
no
[6] Crane,H.R.,
Delsasso,
10
universal value for the C/O abundance ratio which was the basis
for Phys.
Hoyle’s
analysis1109,
and (1934)
di↵erent stars
C.C.,
Rev.,46,
doi:10.1103/PhysRev.46.1109.2
expose di↵erent ratios. For example, stars with extra high abundance
of carbon do not show extra high
8
abundances of oxygen107 . Examination of the gases ejected from low mass stars shows that when the
[7] Crane,H.R., & Lauritsen,
C.C., Phys. Rev.,45,
metals are more abundance by about
50% the C/O ratio is lower
by about 50%.108 The C/O ratio
M=15Msun
497, 109
(1934)
6
appears to be higher in stars with low abundance of heavy elements.
Finally, the C/O appears to vary
Dyer,
P. & Barnes,
A233, 495,
in low mass stars from 0.2 to 13110 . In short, the picture is [8]
more
complicated
and C.
theA.,
lastNuc.
wordPhys.
has not
4
(1974)
doi:10.1016/0375-9474(74)90470-9
yet been said.
M=25Msun
100
8.21
150
2
The structure of
-100
-50
0
ΔE-KeV
12
[9] Gaerttner, E.R., & Pardue, L.A. , Phys. Rev., 57,
386, Retrospect
(1940) doi:10.1103/PhysRev.57.386
C and the ↵ model:
50
100
[10] Gamow, G., Phys. Rev., 53, 595, (1938)
In 1971
concluded from the nuclear cluster model that 0 our0 state forms a linear chain of three
doi:10.1103/PhysRev.53.595
↵-particles.
Further
indication
(from
bombardment
by electrons), imply that this state has an unusually
ained in the
Figure
8.23:
The
C/O
ratio
and
obtained
in
the
Figure 17:
C/O ratio obtained in the evolution of
112 .The
Guier,
Roberts, J.H. , Phys. Rev. 79,
These
the 25M
probability
of[11]
decay
intoW.H.,
three &
↵ particles.
and 5.0M large
) highradius
evolution
of
high properties
mass stars enhance
(15M and
)
mass stars
(15M
and 25M ) upon a hypothetical
719,
(1950)
doi:10.1103/PhysRev.79.719
113 who
ation of the change
upon
a
hypothetical
change
in
the
location
of
the
This conclusion
was of
supported
in 1997
when
in the location
the resonance
in 12
C. Pichler, Oberhummer, Csoto and Moskowski
12 +
resonance
in
C.
concluded that the 0 level is a genuine three alpha resonance.
If so, oneS.,would
expect
theM.,
level
[12] Hayakawa,
Hayashi,
C., that
Imoto,
& Kikuchi,
would decay directly into three ↵’s and then Salpeter’s equation
for theTheor.
nuclear
statistical
equilibrium
K. Prog.
Physics,
16, 507,
(1956)
may
change.
But thethey
probability
of decay directly into three
alpha appears to be only about 4%.
doi:10.1143/PTP.16.507
13needIna Retrospect
y - observations
and what
imply
8
The reason for this is purely statistical, the phase space of Be + ↵ is that much bigger than the 3↵ mode,
Inwas
1985
Arnet andDetailed
Thielemann
questioned
the
logic of [13] Holloway, M.G., & Moore, B.L., Phys. Rev., 58,
ithout carbon
discovered.
observations
have
shown
in layman
terminology: all possible
modes
of decay
have equal probabilities and the number of ways the
847, (1940) doi:10.1103/PhysRev.58.847
Hoyles
original
argument
as
the
synthesized
carbon
may
om star to
star. can
Gradually
it became
thatlarger
there that
is nothe
8 Be + ↵clear
system
decay into
is much
number of di↵erent ways it can decay into 3↵s.
be
fused
into
heavier
nuclei
or
locked
in
WDs.
Hence,
atio which was the basis for Hoyle’s analysis and di↵erent stars
[14] Hornyak, W.F., Lauritsen, T., Morrison, P. &
107
we
should
re-think
how carbon
synthesized
and it
Bujarrabal,
V. & Cernicharo,
J.,
288,
551,
rs with extra
high
abundance
of carbon
doA&A,
notisshow
extra(1994)
high
Fowler, W.A., Rev. Mod. Phys., 22, 291, (1950)
108
Wang,
W.
&that
Liu,
MNRAS,
669,
(2007)
isejected
not clear
any
remnant
of381,
thethat
Anthropic
Princiof the gases
from
lowX.-W.,
mass
stars shows
when the
doi:10.1103/RevModPhys.22.291
109
Wahlin,
R., and 6 co-authors,
della
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DISCUSSION
TZUMI HACHISU: Is the carbon-burning C/O ratio still uncertain?
GIORA SHAVIV: The reduced width of the 16 O level
is still unknown and there are only guess on its value.
Sp any C/O ratio between 1/4 - to -3/4 is to my mind
plausible.
In 2002 Kunz et al. carried out an extensive theo[23] Öpik, E.J., MSRSL, 1, 131, (1954), Les Processus
retical
analysis based primarily on Kunzs experimental
Nuclaires dans les Astres, Communications
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The result of Kunz et differs significantly
prsentes au cinquime Colloque International
from
Caughlan
& Fowler known tables at low temperdAstrophysique tenu Liege les 10-12 Septembre.
ature which are the relevant temperatures for quiet helium burning. However, it is not the last word on the
[24] Shaviv,G. The Synthesis of the Elements: The
Astrophysical Quest for Nucleosynthesis and What subject.
[22] Öpik E. Proc. Roy. Irish Acad. A54, 49, (1951).
The paper was published over a year after it was
read before the Irish Academy.
320