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The dances of the Atomic nucleus

The core of matter is much more restless than had been thought and the movement of the subatomic particles no longer fits into the conventional models of Physics

It had become commonplace to imagine the atom as a minute planetary system, in which the nucleus plays the role of the star and the electrons represent the planets. In this model, now seen to be naive, all of the dynamism falls to the electrons, while the nucleus would be an island of tranquility, inhabited by protons and neutrons, motionless as if stuck to each other. The reality couldn’t be more different.

The nucleus is in reality an extremely turbulent structure whose particles move and interact endlessly. In this uninterrupted agitation, there are chaotic movements that challenge any forecast. However, under special conditions, such as those produced by a strong electromagnetic field, there are specific situations of excitation in which the protons and neutrons dance in an organized manner. In one of these conditions, called gigantic resonance, all the particles of the nucleus vibrate coherently at the same time. A trio of researchers from the Physics Institute of the University of São Paulo (USP), in collaboration with specialists of the Federal University of Rio de Janeiro (UFRJ) and of the Aeronautic Technology Institute (ITA), of São José dos Campos, have just completed a theory to explain the intricate dynamics of this phenomenon, which physicists have been attempting to explain since the decade of the 50s.

Natural and exotic
Integrated by the professors Mahir Saleh Hussein, Antonio Fernando de Toledo Piza and Maurício Porto Pato, the team from USP did not limit to equating the collective nuclear oscillations of the elements of nature. Jointly with Dr. Luís Felipe Canto of UFRJ, and Dr. Brett Vern Carlson of ITA, they also explained the strange movements that occur in the nuclei called exotics – produced in laboratories, which have a number of neutrons (particles without an electrical charge) bigger or smaller than the normal and which only last for the tiniest fraction of a second. However, they participate in the fundamental stages of the evolution of the stars, and that’s the importance of their study.

During the thematic project simply called Theoretical Nuclear Physics, from 1997 to the end of lastyear, the researchers published 59 articles in international magazines – nine of them in Physical Review Letters. Now they are diving into a more ambitious undertaking: to extend the developed concepts starting from the atomic nucleus to the synchronized movement of the atoms and molecules. In this more ample field, the attention is centered on two objectives of enormous scientific and technological interest: the so called buckyballs molecules (perfect geodetic structures formed by 60 carbon atoms) and the condensates of Bose-Einstein (atomic gases cooled close to zero absolute).

The great achievement of the team up to this moment has been to produce a theory that encompasses both the simple dance of the nuclear particles during their collective excitation and the chaotic movement that takes place afterwards. The capability to deal with chaos is the main difference between the new picture and the old explanatory model, that only worked well while the energy that produces the coordinated movements of the protons and neutrons is limited to its minimum value, that corresponds to one quantum. A concept created at the beginning of the 20th century to describe the oscillatory movements in micro and macro scales, the quantum is a measure of energy that depends on the frequency of the oscillation of the movement.

There has been research done on the energy level of 1 quantum since the 50s, when the physicists of the project were in primary school. Then, at the beginning of the 90s, a team from the particle accelerator of Gesellschaft für Schwerionenforschung, or Research Society for Heavy Ions (GSI), in Darmstadt, Germany, managed to generate collective excitations with 2 quanta of energy. It was at this point that the old theory fell apart.

To produce the collective excitation in a particle accelerator, it is necessary to accelerate beams of nuclei and then make them collide. The powerful electromagnetic field generated by the approximation of nuclei then acts on the nuclear components. “The photons (particles made from an electromagnetic field) link up with the protons (particles with a positive electric charge) collectively moving them to the same side. Meanwhile, the neutrons make up for this displacement moving in the opposite direction, in order to preserve an important physical concept, the moment or quantity of movement”, says Hussein. Protons to here, neutrons to there, the corpuscles carry out their synchronized dance.

The experimenters from GSI reached the plateau of 2 quanta, the next stage of the coordinated movement, pushing forward the nuclei of very heavy metals, lead, tin, xenon, gold, uranium, with an extremely high acceleration: 900 million electron-volts (MeV) per particle (this is the unit of energy used in Nuclear Physics: the mass of the proton or of the neutron is of approximately 1,000 MeV).
Carried out in a piece of equipment called Land (Large Angle Neutron Detector), that remains at the end of the particle accelerator of GSI, the experiment occurred exactly as was expected, from the qualitative point of view. However, when the quantitative measurements were taken into consideration it was confirmed that the numbers didn’t corroborate the theoretically estimates based on the old atomic model. Toledo Piza explains why: “It so happens that this type of excitation is an extremely fleeting phenomenon. The nuclear particles vibrate only two or three times in conjunction. Afterwards, the energy is dissipated, producing chaotic movements. The sin of the old theory was not to know how to deal with this blatant ingredient.”

When the energy level remained at the mark of 1 quantum, this didn’t have any greater consequences, because the analysts focused in two or three collective vibrations and what came after didn’t come into question: it was like a throw-away residue. When the team from GSI conquered the level of 2 quanta, it became impossibleto brush aside the complexity of the problem.

Noises along the path
This is where things stood when the Brazilian team entered into the scene. Studying deeply, the physicists realized that the nuclear particles systems didn’t respond to the energy jumps as simply as supposed in the earlier model. “Protons and neutrons”, reveals Dr. Hussein “didn’t evolve from the fundamental state which characterizes the nuclei found in nature to the excited state of l quantum and then, in an orderly manner, to the state of 2 quanta. There were noises along the path and the effect of these noises had to be computed, since the second quantum of energy excited particles already entangled in chaotic movement produced by the dissipation of the first.”

In other words, what in the old experiments of 1 quantum would be treated as a throw-away residue now made the difference. With sophisticated mathematical resources, the Brazilian researchers attempted to construct a complete theory, capable of accommodating both the collective oscillations and the chaotic movements. The task was so successful that the German researchers of GSI have been collaborating actively with the team from USP. And at the same time they are preparing for a higher experimental flight: a study of the excitations in the level of quanta 3. “This is not an easy task”, anticipates Dr. Thomas Aumann, one of the GSI researchers who is working in collaboration with the physicists from USP. The higher the energy level, the quicker and noisier the process becomes, which demands from the experimenters a lot of skill and a very special piece of equipment.

The USP model can predict the state of quanta 3, and personally I believe that a vibration of three phonons must really exist”, comments Dr. Aumann. The phonon is equivalent to the quantum, the unit of energy of quantum physics. “As an experimental physicist, nevertheless, I prefer to observe this situation and to compare it with the USP theory.” At the range of quanta 2, all of the elements researched fitted perfectly into the theory of the USP team, except xenon, which, Heaven only knows why, seemed to resist any theoretical norm. “We believe that this is due more to some peculiarity still unknown of the nucleus of the element than to eventual deficiencies of the new model”, ponders Porto Pato.

New project
The group is truly confident of the universality of the new theory, and once the first thematic project was concluded, they began the second, looking to extend the same concepts for other collections of corpuscles – the buckyballs and the condensates of Bose-Einstein. According to the Indian physicist Jagadis Chandra Bose (1858-1937) and the German, naturalized American, Albert Einstein (1879-1955), at temperatures close to absolute zero, the atoms that make determined types of gases condense and all move to occupy a quantum state of less energy, more stable, in which they remain practically still. These condensates were recently obtained by a group of French, German and Italian physicists, who published the fact in the magazine Science of 20th of April.

The USP researchers are studying the possibility of creating hybrid condensates, in which pairs of atoms convert themselves into molecules and vice-versa. “In this case, there could be a collective oscillation of atoms against molecules, analogous to what occurs between the components of the nucleus”, says Toledo Piza. “The interesting fact”, he adds, “is that these systems could be very large, with, for example, 500,000 atoms and reaching the size of a micron, and even then, exhibiting quantum behavior.” Or that is to say, the behavior of sub-atomic particles.

The description of this phenomenon is even more complex than that of nuclear oscillations because, while in the nucleus the number of protons and neutrons remains constant, in the condensed hybrids there is a permanent variation of the quantity of atoms and molecules, since one converts itself into the other.”We are also interested in establishing a link with the experimental physicists of USP in São Carlos, coordinated by professor Vanderlei Bagnato, who have been trying to produce condensates of atoms of two different elements, rubidium and sodium”, says Dr. Hussein.

The prospects for the technological application of these investigations are very promising. For example, the study of cold atoms has already led to an enormous improvement in the measuring of temperature. Thanks to this, the precision with which temperature is determined today is of 1 in 100 quadrillions (the number 1 followed by 17 zeros), which is equivalent to making a mistake of five seconds in the age of the universe.

The worry for the supply of the experimental work is constant. The second part of the research, dedicated to exotic nuclei, is already equivalent to a large push in the experimental physics developed in the country. In order to understand what these nuclei are, it is worth considering the case of lithium. The nuclei of lithium found in nature are made up of three protons and four neutrons. For this reason this element is known as lithium-7, the total number of its nuclear particles. However, through the fragmentation of oxygen, it is possible to make lithium-11, with four extra neutrons.

A strange nucleus
The new nucleus has strange characteristics. Beginning with its size, in spite of being formed from only 11 particles, it is enormous, almost as large as that of lead, composed of 82 protons and 126 neutrons. “This is due to a quantum effect which results in the fact that of the four additional neutrons, only two confine themselves to the small space occupied by the other seven particles of the basic nucleus. The other two begin to move around this core of nine particles, in a halo relatively distant from the center”, explains Porto Pato. Hence the swelling of the nucleus.

However, size is not everything. Equally extravagant is the collective dance of these particles when the nucleus suffers the action of an electromagnetic field. In this case, two ways of vibrating that combine: the three protons move against the six neutrons in the core, and the core as a unit moves against the two neutrons of the halo. The first oscillation is rapid, typical of a relatively rigid body, and the second is slow, as it should with a soft system.

Though they appear more intricate, these compound movements are actually simpler than the collective oscillations produced in the GSI laboratory, since the smooth vibration of the core against the halo has very little energy. “They are states of only one quantum. So, the chaotic movements provoked by the dissipation of energy becomes irrelevant”, comments Dr. Toledo Piza. As a particular case, the oscillations of the exotic nuclei could be perfectly described by the new theory, without it being necessary to use all of the mathematical apparatus that the model contains.

This is a study especially relevant in stellar dynamics. One of the objects of interest, in this case is of boron-8, which has two neutrons less than normal boron-10. “In the Sun, this exotic nucleus decays, producing beryllium-8, which for its part disintegrates into two alpha particles (made up of two protons and two neutrons)”, explains Dr. Hussein. “In the decaying of boron-8, there supposedly occurs the liberation of a neutrino – an elementary particle of the same category (leptons) as the electron – of high energy. With a better understanding of this nucleus, perhaps we can explain why the number of neutrinos detected on the Earth is approximately half of what is expected by the standard model of the solar evolution.”

The applications of the new theory are wide, but this is still not the whole story. The project has already put Brazil in harmony with the international standard in nuclear physics and attracted to USP four post-doctorates: the Englishman Adam Sargeant, the Japanese Manabu Ueda, the Russian Oleg Vorov and the Chinese, nationalized Brazilian, Chi-Yong Lin. Another development was the international congress Collective Excitation of Bose and Fermi Systems, coordinated by members of the team and sponsored by FAPESP during 1998, which had the participation of the physicist Dr. William Phillips, winner of the Nobel Prize for Physics in 1997. With this background, it is understandable the expectation for the next steps of the group, which is now setting their eyes on the collectivity of atoms and molecules.

The theory since ancient times

For at least three centuries man has been advancing in his attempt to uncover the microcosm of matter

The notion of the atom goes back to the most ancient Indian school of philosophy: the Vaisesika system, a name derived from Sanskrit meaning “atomic individuality” which postulated its existence at least 2,800 years ago, and probably inherited this concept from an even more remote past. We received it from Leucipus and his disciple Democritus, Greek philosophers of the 5th century B.C.

The Greek notion of the atom, as the minimal and indivisible fraction of material, passed through a radical transformation in 1897, with the experimental discovery of the electron by the English physicist Joseph John Thomson (1856-1940). Based on this discovery and the fact that the atoms were electrically neutral, Thomson supposed that they contained a second ingredient to counterbalance the charge of the electrons. From this was born his model of the atom as a raisin pudding, the positive charge, distributed evenly, formed the mass of the pudding while the electrons, sprinkled in here and there, were the raisins. A tasty model but which did not resist observation.

This was carried out by the New Zealander Lord Ernest Rutherford (1871-1937) in 1910. The alpha particles (which today we know to be formed by two protons and two neutrons) had just been discovered and Lord Rutherford decided to use these tiny projectiles, liberated in certain radioactive processes, to investigate the intimacy of the atom. Bombarding an extremely fine sheet of gold with a beam of alpha particles, it was discovered that the majority of the projectiles passed through the sheet practically without being deviated, while a few were violently turned back.

It was concluded that the atoms of the sheet structured themselves like minuscule planetary systems. The vast majority of the internal space was empty, passed through without any problems by the alpha particles. The positive charge concentrated itself in a central nucleus, responsible for the repulsion of part of the projectiles. Separated from the positive charge by the vacuum, the electrons orbited around the nucleus, like the planets around the sun.Compatible with the experimental data and easy to be represented graphically, Lord Rutherford’s model had also the virtue of bringing to our spirits the comforting idea that the same standard of organization reproduced itself in the structures of the universe, both in the micro and macro cosmos. However, it held an important defect.

According to classical physics, charges in motion emit electromagnetic radiation, and, in doing so, lose energy. Or in other words that is to say, the electrons in transit should have their speed continually decreasing, and for this reason, orbit closer and closer. In a fraction of a second they would hit the nucleus, no atoms in the universe would survive, and worse of all, we wouldn’t be here to tell the tale. Conservative minds discarded the model, in the name of the good laws of physics. That wasn’t what the young Danish physicist Niels Bohr (1895 – 1962) did, who joined Lord Rutherford’s team at Cambridge University in 1912.

A quantum leap
In a genius’ act , Bohr incorporated into the planetary model of Rutherford the quantum concept of energy, formulated at the beginning of the century by Max Planck (1858-1947). By this concept, energy is not a continuous fluid, as the classical physicists had thought, but a discontinuous flux of “grains”, minimum quantities non-fractional called quanta (Latin plural of quantum). Planck himself didn’t take this idea very seriously and only used it as a mathematical artifact. However, Bohr clang to it and after months of calculations, produced the first quantum model of the atom.

In it, there are precise orbits in which the electron moves without giving off radiation. A change of energy with the environment only occurs when the electron “jumps” from one of these stationary orbits to another. This “quantum leap” is one of the most revolutionary aspects of the new model: without passing through an “intermediary space”, the electron simply disappears from its original orbit to re-appear instantaneously in another.

In 1913, Thomson discovered that a chemical element could have atoms with the same electrical charge and different masses, which were called isotopes. Their existence suggested that besides the negative particles (electrons) and positive particles (protons), the atoms must contain a third type of particle, neutral, but dense. Lord Rutherford called this particle the neutron, but its existence was only experimentally demonstrated in by the Englishman James Chadwick (1891-1974) in 1932. With mass relatively close to the proton, the neutron formed with it the atomic nucleus.

Interactive force
We know today that the nucleus is 10,000 to 100,000 times smaller than the atom. Depending on the number of particles which it contains, its diameter on average can oscillate between 1 x 10-15 and 1×10-14 meters. The active volume is so scanty that we might get the false idea that protons and neutrons are simply squeezed in their interior, incapable of the slightest movement. However, this is not what occurs. They actually have enough available space to develop velocities of the order of 30,000 kilometers per second, a tenth of the speed of light. Also, as occurs with the atom itself, they spread out in a structure with layers that are governed by quantum principals.

Their confinement in such a small region is due to the so called interactive force, which impedes that the nucleus break up through the effect of the electromagnetic repulsion between the protons. The intensity of this force is between 100 and 1,000 times greater than the electromagnetic interaction. However, its reach s extremely limited, not more than 1 x 10-15 m, while the electromagnetic force acts indefinitely.

This interactive force, which in its reduced range of activity is the most powerful force in nature, has other strange peculiarities: it passes from attractive to repulsive when the particles get too near to each other. This allows for the maintaining of a coherent nucleus and, at the same time, avoids that protons and neutrons crash into each other. As matter of fact, physicists believe that it is responsible for the very existence of the protons and the neutrons, since it maintains imprisoned in its interior the even smaller particles which make it up: the quarks, whose existence was postulated during the 60s by the North American Dr. Murray Gell-Mann (1929-).

According to the standard model operative in particle physics, far from being microscopic spheres lacking an internal structure, protons and neutrons are more like minute, but turbulent oceans. In each one of them, three quarks move at very high speed in a cloud formed by gluons, the particle carriers of the interactive force. Within this cloud, fluctuations of energy allow that the pairs of quarks and anti-quarks materialize and de-materialize incessantly, surviving only for a fraction of a second. This uninterrupted flux has already been compared to a tempest in the interior of a drop – an image that expresses well the dynamism of the atomic and sub-atomic worlds where there is no place for rest and permanency.

The project
Nuclear Physics Theory (96/01381-0); Modality: Thematic project; Coordinator: Dr. Mahir Saleh Hussein – Physics Institute of USP; Investment: R$ 26,730.00