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Suppose someone gave you an egg and asked you to describe exactly what
was inside. You could crack it open and take a look. But that might destroy
the structure of the interior. A better way might be to give the egg a spin.
A hard-boiled egg, for example, spins differently from a raw one. If you
place a hard-boiled egg on its side and apply a rotational force it is easy
to start the egg spinning. The hard-boiled egg will spin smoothly for a
long time. If you put your hand on the egg for a moment, the egg stops spinning
almost immediately. On the other hand it is hard to get a raw egg spinning,
and if you stop the spinning briefly, it starts up again, almost as though
it has a will of its own. Try it!

By observing the way the egg spins, you can not only distinguish between
a hard-boiled egg and a raw one, but also draw some conclusions about the
fluid properties of the two-component system inside – the yolk and the white.
Such dynamic studies could even allow the careful experimenter to identify
the perfect three-minute egg, with the white fully set and the yolk thickened
but not solid.

Spinning an object gives us a unique perspective of its interior. It
allows us to study the structure of objects that are inaccessible: for example,
those that are too small to see or too far away. Two objects that fit into
this category are atomic nuclei and neutron stars – the massive remnants
of supernova explosions. The two systems, though vastly different in scale,
have more in common than you might think. Neutron stars actu-ally behave
like giant nuclei, and they share some of the same characteristics, as we
shall show later.

One of us (Phil Walker), has been studying the spin of nuclei. Like
the spinning of an egg, with its yolk and white, the rotation of nuclei
offers insights into their fluid properties. When nuclei spin they emit
gamma rays, so I have recently been experimenting with a new gamma-ray detector
array at the Australian National University in Canberra. I have also tested
some current ideas about spinning nuclei at the Nuclear Structure Facility
(soon to be closed down) at the Science and Engineering Research Council’s
Daresbury Laboratory in Cheshire.

Atomic nuclei constitute 99.9 per cent of matter in the known Universe.
Nuclei are made up of protons and neutrons (nucleons) packed tightly together,
and are extremely dense by normal standards: a pinhead-sized piece of pure
nuclear matter would weigh a million tonnes. But tightly packed though they
are, nucleons can slide over each other without any friction. This means
that the nucleus as a whole behaves as a superfluid. Atomic nuclei are the
smallest superfluid objects known to exist in the Universe.

The nucleons also orbit around each other in a well-defined way. Pairs
of nucleons orbit in opposite directions, so if the total number of each
type of nucleon is even, the nucleus as a whole has no net rotation in its
lowest state of energy. We can set the nucleus rotating, without disrupting
the individual orbits of the nucleons, by giving the nucleus a little bit
of energy. But the nucleus as a whole rotates relatively slowly, whereas
the individual nucleons orbit rapidly. To a good approximation, these ‘single-particle’
and collective motions can be described separately. Nevertheless, these
different motions do affect each other in a way that is vital to gaining
an understanding of the nuclear interior.

The rotation of any object is measured in terms of angular momentum,
which depends on the linear momentum (the object’s mass multiplied by its
velocity) and the distance of the object from the centre of rotation. It
is a ‘conservative’ property, that is, one that does not change with time.
The conservation of angular momentum is nicely illustrated by a pirouetting
ice-skater. At first the skater starts spinning slowly, with arms outstretched.
But when the arms are pulled in, there is a dramatic blur of motion. The
angular momentum is conserved, but when the mass becomes concentrated close
to the axis of rotation, in this case the skater’s body, the rate of rotation
increases.

In the submicroscopic world of atomic nuclei, changes in the angular
momentum, or spin, are not smooth. Instead, they come in ‘chunks’ known
as quanta. The size of the quanta are expressed in multiples of cancelled
h (pronounced ‘aitch bar’) which is defined as Planck’s constant, h, divided
by 2 pi. These correspond to the angular momentum of a set of rotational
energy levels that a nucleus can have. Although the value of cancelled h
is very small, it translates into a very fast spin in an atomic nucleus.
For example, the nucleus of tungsten-180, an isotope of tungsten containing
180 nucleons (74 protons and 106 neutrons), with an angular momentum of
2 cancelled h spins at the crazy rate of 10 000 billion revolutions per
microsecond. In contrast, an egg with 2 cancelled h of angular momentum
would take 10 000 billion billion years – or hundreds of billions of times
the age of the Universe – to rotate just once.

To set a nucleus spinning requires a high-energy accelerator . Relatively
light nuclei such as calcium and xenon are collided so that they fuse into
a heavier nucleus such as tungsten. The new nucleus has excess energy from
the collision which is partly taken up by the nucleus spinning. A typical
nucleus can accommodate more than 50 units of angular momentum (50 cancelled
h) before it breaks up. It slows down by radiating gamma rays, each corresponding
to (usually) 2 cancelled h of angular momentum of the nucleus. In such a
case, therefore, 25 gamma rays would be emitted as the nucleus slows to
a halt in about one-billionth of a second. This is a long time on a nuclear
scale, and the nucleus rotates many billions of times before it stops spinning.
This gives us the opportunity to learn about the structure of the nuclear
fluid. Measuring the gamma-ray energies enables physicists to work out how
fast a nucleus is spinning, but more information is required. Not only are
there changes in the motion of nucleons inside a nucleus, but also in the
overall shape of a nucleus.

When nuclei are made to rotate rapidly they take on exotic shapes resembling
rugby balls, pears, peanuts and discs. The shapes of nuclei are not simply
haphazard arrangements of bundles of nucleons. The quantised motions of
the individual nucleons favour a particular shape for a given number of
nucleons (see ‘The shape of nuclear models to come’, ¿ìè¶ÌÊÓƵ, 31 March
1988).

We can obtain further information about the inside of rotating nuclei
by studying their magnetic fields. Because nuclei carry electric charges,
and these charges are in motion within the nuclei, the spinning nuclei act
like little magnets. Measurements of magnetic strength tell physicists how
much of the rotation is due to the charged protons and how much is due to
the uncharged neutrons. For example, if a rotating nucleus had no magnetic
field, this would indicate that all of the rotation must be due to movement
of the uncharged neutrons, rather than movement of the charged protons.

Although spinning nuclei, with their charged protons, do have a magnetic
field, the measured strength of the field is weaker in most nuclei than
would be expected if the neutrons and protons contributed equally to the
spin (or at least in proportion to their numbers). This indicates that it
is the uncharged neutrons that usually have the greatest influence on the
spin characteristics. Theorists have devised models of nuclear behaviour
to describe why this is so. The dominating role of neutrons arises largely
because most nuclei contain more neutrons than protons. The extra neutrons
have to go, on average, into orbits with higher angular momentum. This leads
to a stronger coupling between their single-particle motions and the collective
rotation of the nucleus as a whole.

In 1970, Arne Johnson and colleagues at the Marne Siegbohn Institute
for Physics in Stockholm discovered a kind of nuclear ‘quake’ in rapidly
spinning nuclei. The researchers found that, after the nuclei slowed down
over a few billion revolutions, they then suddenly but briefly speeded up.
This is called ‘backbending’, because it produces a characteristic zigzag
trace of the gamma-ray pattern on the recording chart, as the gamma-ray
trace appears to fold over on itself. Backbending appears to be a common
feature in nuclei with differing numbers of protons and neutrons.

Backbending represents a tremendous upheaval, a major redistribution
of spin within the nucleus. The process is in many ways like a phase transition
such as freezing or melting. But whereas the phase transition from liquid
water to solid ice involves a slowing down of the motion of the molecules,
during backbending the interior of the nucleus appears to begin flowing
like a superfluid, as pairs of protons and pairs of neutrons join up. But
how the phase change takes place is a mystery, and it remains a challenge
to find definitive experimental evidence. Now one of us (Phil Walker), working
with George Dracoulis and his team in Canberra has revealed some new clues
from the backbending in nuclei of tungsten-179. This work allows us to pinpoint,
for the first time, the phase boundary between the normal and superfluid
nuclear state.

There are two rival theories to account for backbending. In 1960, well
before backbending had been observed experimentally, Ben Mottelson and J.
G. Valatin of the Niels Bohr Institute in Copenhagen predicted that, as
nuclei spin faster, they would undergo a ‘pairing collapse’, a type of phase
transition in which the orbiting pairs of nucleons uncouple. They draw an
analogy between the rotation of nuclei and the effect of a magnetic field
on a superconductor. In a superconducting material, pairs of electrons spin
in opposite directions, so their magnetic moments cancel each other; a strong
magnetic field can disturb this pairing. In a nucleus, the pairs of nucleons
are affected by the rotation of the nucleus. In both phenomena the disturbance
does not destroy the pairing, until it reaches a critical level, at which
point the pairs suddenly undergo a phase transition.

In a spinning nucleus the superfluid phase flips to a normal fluid above
a critical rotational frequency. Similarly a superconducting material becomes
a normal conductor above a critical value of the magnetic field. But one
important difference between superfluid nuclei and superconducting materials
is that nuclei contain only a small number of nucleons (179 in tungsten-179),
whereas superconductors are regarded as having an infinite number of electrons.
In theory, only infinite systems undergo phase transitions. Nevertheless,
you can apply a generalised concept of phase transitions to systems, such
as nuclei, which have a finite number of particles.

The pairing collapse theory has been challenged by the ‘rotational alignment
model’ championed by Frank Stephens at the Lawrence Berkeley Laboratory
in California. He points out that the most rapidly spinning nucleons will
be the ones most affected by the rotation of the whole nucleus. The spinning
nucleons are affected by the nuclear rotation in the same way as the rotation
of the Earth affects atmospheric movements through the Coriolis force –
bending winds into swirls of cyclones and anticyclones. Nuclei experience
much stronger effects and can swing the nucleons around completely, so that
they rotate in the same direction as the nucleus. The Coriolis force is
strongest on the fastest-spinning nucleons. As these fast-spinning nucleons
align, the rest of the nucleus will slow down a bit so as to conserve the
total angular momentum, and so reach a lower energy state (see Figure 1).

But nucleons like to be paired up, and this inhibits the onset of rotational
alignment. Imagine a nucleus gradually spinning faster and faster. Suddenly,
a single pair of nucleons uncouples. According to the rotational alignment
model, it is this process that causes backbending. This model accounts very
well for the significant differences between nuclei with different numbers
of neutrons and protons, but it does not address the problem of the phase
transition and whether rotational alignment itself could trigger the total
collapse of pairing.

Mark Riley, working at the University of Liverpool, recently produced
convincing evidence to show that, at higher spins, nucleons are not paired.
But the actual phase transitions, when the particles unpair, remain difficult
to pinpoint.

In Australia, we used a new array of gamma-ray detectors called CAESAR
coupled to a heavy-ion accelerator to study the phase transitions of tungsten-179.
Using specially designed timing techniques, we could pick out, with exceptional
sensitivity, nuclear states that survive for as little as a few billionths
of a second. In this way we identified a new form of nuclear rotation, with
the rotationally aligned neutrons coupled up the wrong way round – at least
according to existing theories. When backbending occurs in tungsten-179,
it not only involves the rotational alignment of a pair of neutrons, but
also apparently a drastic loss of neutron pairing. As nuclei rotate over
a range of different speeds, superfluid protons can coexist with normal
fluid neutrons in the same nucleus. This type of evidence allows us to recognise
the phase boundary between normal and superfluid neutrons in tungsten-179.
At the rotation rates that we were studying, the protons in tungsten-179
remain in their superfluid state.

To assess the rival theories I have recently performed a follow-up experiment
at Daresbury in collaboration with physicists from the Universities of Surrey,
Manchester and Liverpool and the Niels Bohr Institute. We projected a beam
of the rare isotope calcium-48 into a target of solidified xenon-136. The
fusion of these exotic nuclei produced isotopes of tungsten with a high
spin, some of which emit gamma rays while they are still slowing down from
the collision. Because the accelerator at Daresbury is larger than that
at Canberra we could measure half-lives one-thousandth as long as those
previously studied. This puts the new ideas to the test, but it will be
some months yet before the data from the new experiment are analysed and
interpreted.

Now, let’s look at those much larger nuclei – neutron stars, and pulsars
in particular. There are some interesting comparisons between pulsars and
the spinning nuclei we have generated in the laboratory. Pulsars are small,
spinning neutron stars, about 20 kilometres across, and are shrouded in
a strong magnetic field. They are the largest superfluid objects known in
the Universe. As a pulsar spins, each revolution provides a flash of radiation
(usually at radio wavelengths) which is detectable on Earth. These cosmic
beacons flash about once a second.

Astronomers have noted that as the rotational energy of a pulsar is
used up and radiated into space, the rate of spin gradually slows down.
But in the early spring of 1969, they saw something unexpected. The rotation
of the pulsar Vela suddenly speeded up. It looked as if the star had been
rocked by a cosmic giant – in astrophys-ical terms, there had been a ‘glitch’.
At first, scientists thought that the hard crust of the star had fractured
suddenly while cooling, and as a result the star had become a little smaller.
In order to conserve its angular momentum, the star, like the pirouetting
ice-skater, had to spin a bit faster.

However, further observations indicated that the mechanism behind pulsar
glitches may be more complicated than first imagined. A glitch seemed to
involve the movement of vortex – the sort of flow we see when we let the
bath water out – in the superfluid interior of the neutron star. These vortex
are tiny, not much bigger than atomic nuclei. They become attached or ‘pinned’
to the nuclei of atoms in the near-solid crust of the pulsar. Every so often,
a large number of the vortex break free simultaneously. This speeds up the
rate of rotation of the star and causes the glitch.

Observations of the Crab pulsar, a relic of a supernova explosion in
the year 1054 which was recorded by Chinese astronomers, are now providing
new insights into the nature of glitches. In the Crab pulsar, glitches happen
around once every five years, which works out at once every few billion
revolutions. In 1989 Andrew Lyne and colleagues, working at the Jodrell
Bank radio telescope centre in Cheshire, were fortunate to be observing
the Crab pulsar during the few minutes when there was a sudden glitch. Now,
almost two years later, the Crab pulsar is still recovering from the shock,
and theories about the vortex motion in the superfluid interior are still
under scrutiny.

We can compare glitching in pulsars with backbending in nuclei. In each
case, as the rotating nuclear matter slows down, superfluid effects cause
a sudden, though temporary, increase in rotation rate (see Figure 2). Although
the scales on the two graphs are very different, in each case the perturbation
happens after a few billion revolutions. The perturbations themselves give
unique information about the interiors of the rotating objects that are
otherwise remarkably stable.

Phil Walker is a lecturer in the department of physics at the University
of Surrey. Nina Morgan is a science writer specialising in earth and physical
sciences.

* * *

HOW TO MAKE A NUCLEUS SPIN

Atomic nuclei are, by normal standards, inaccessible objects, surrounded
by a protective screen of electrons. It is difficult to push them together
because they are positively charged and so repel one another. Accelerators
make atoms travel so fast that when they collide with another atom their
electrons are pushed clean out of the way, giving the nuclei a chance to
interact. Given enough speed, nuclei fuse together and make a new, heavier
element. Unless the collision was exactly head-on, the resulting fused nucleus
will be spinning around. As the spinning slows, gamma rays are emitted.
By measuring the energies of the gamma rays, physicists can learn about
the spinning nuclei.

Several types of accelerator can be used to fuse nuclei together. Electrostatic
Van de Graaff accelerators have a high-voltage terminal which provides about
10 million volts, which is enough to fuse light nuclei. To investigate the
full range of elements more than 25 million volts are needed. The accelerator
at the Australian National University, which operates at about 14 million
volts, is called a ‘tandem’ Van de Graaff, because it accelerates nuclei
in two stages. First, negative ions are injected and attracted to a positively
charged high-voltage terminal in the middle of the accelerator tower. Inside
the terminal, electrons are stripped off the ions, by passing them through
a very thin carbon foil. The ions, now positively charged, are repelled
from the terminal with enough energy for their nuclei to fuse with target
nuclei. The target could take the form of a thin metal foil, for example,
installed in the path of the accelerated ions.

Gamma-ray detection has developed rapidly over the past few years, following
the lead of Peter Twin from the University of Liverpool, who developed the
first arrays of composite detectors in the early 1980s, working with Bent
Herskind of the Niels Bohr Institute. Each composite detector consists of
a germanium crystal surrounded by scintil-lators, such as bismuth ger-manate.
The electronics are arranged to veto the recording of gamma rays which scatter
between the germanium crystals and the scintillator, vastly improving the
quality of the signal. Dracoulis’s CAESAR array in Australia is composed
of six separate detecting systems, each with a crystal of germanium at its
heart weighing 1 kilogram, and cooled with liquid nitrogen. The array that
is coupled to the 20-million-volt accelerator at Daresbury has 16 gamma-ray
detecting systems. Next year, an Anglo-French array called Eurogam, with
45 detecting systems, will be in operation at Daresbury. The greater sensitivity
of the larger arrays gives a more detailed and accurate view of nuclei.