Escape From A Nuclear Football

February 25, 1998

Radioactivity has been known for over 100 years, but it continues to bring new surprises. Radioactivity occurs when a nucleus--the core of an atom--spontaneously spews out one or more particles. The various kinds of radioactivity can provide different types of information about a nucleus. For many decades, physicists thought that radioactivity came in but a few garden varieties, known as alpha, beta, and gamma decay. Only recently have they realized that it can occur in many forms.

3. PROTON RADIOACTIVITY First detected in 1970, proton radioactivity is an extremely rare form of radioactive decay. In proton radioactivity, a nucleus simply gets rid of a single proton. Although this form of radioactivity was originally discovered in the relatively light cobalt-53 nucleus, it has mainly been observed in proton-rich isotopes of elements heavier than tin.

4. NEW INSIGHTS INTO THIS RARE PHENOMENON Working at Argonne National Laboratory in Illinois, a multinational research team has measured the rates of proton radioactivity in two isotopes--holmium-141 (containing 67 protons) and europium-131 (possessing 63 protons). To be published in the March 2, 1998 issue of the journal Physical Review Letters, their results differ significantly from the predictions of the standard theory of proton radioactivity, which assumes that the nucleus has a spherical shape. The results only make sense if the researchers consider that the nucleus has a highly deformed shape that resembles a football. This research provides insights into how the deformed shape of a nucleus can affect its radioactivity rates.

5. THE PROTON DRIPLINE Whether a nucleus is stable or radioactive depends on the relative number of neutrons and protons it contains. If a nucleus has approximately the same number of neutrons and protons, it tends to be stable. If they are very unequal, the nucleus tends to be unstable, and undergoes radioactivity very readily.

Physicists map the inventory of known nuclei on a chart of nuclides. On this chart, the horizontal axis represents the number of neutrons a nucleus contains and the vertical axis shows the number of protons it possesses. The region of stable nuclei is roughly found on a diagonal line, where the neutron number approximately equals proton number. Below this diagonal is a jagged line called the "neutron dripline" and above this diagonal is another jagged line called the "proton dripline." In general, proton radioactivity has been observed only for nuclei mapped above the proton dripline and containing between 51 and 83 protons (elements antimony through bismuth).

6. SPHERICAL NUCLEI For nuclei mapped above the proton dripline containing between 69 and 81 protons (elements thulium through thallium), the rates of proton radioactivity are predicted well by a conventional model that assumes a spherically shaped nucleus. The theory works well on the nuclei in this region because they are believed to be have a near-spherical shape.

7. THE BUGROV-KADMENSKII MODEL For nuclei beyond the proton dripline having between 51 and 67 protons (elements antimony through holmium), the spherical model breaks down. Nuclei in this region are believed to exist only in a highly deformed shape closer to a football. Such a deformed nucleus arises when the outermost protons and neutrons move with respect to the innermost protons and neutrons.

Researchers first noticed the breakdown of the spherical model when studying proton radioactivity in iodine-109 (53 protons) and cesium-113 (55 protons). In the late 1980s, physicists V.P. Bugrov and S.G. Kadmenskii of Voronezh State University in Russia came up with a model which considers the radioactivity rate for a nucleus that is deformed. Their model yields the correct radioactivity rates for the moderately deformed iodine and cesium isotopes.

8. HIGHLY DEFORMED NUCLEI In the present research, the researchers took the approach of the Bugrov-Kadmenskii model and applied it to study proton radioactivity in holmium-141 and europium-131. These nuclei are believed to be highly deformed, even more so than the iodine-109 and cesium-113 nuclei that were previously studied.

Incidentally, these highly deformed nuclei are not quite as distorted as the "superdeformed" nuclei that have also been previously studied. Whereas superdeformed nuclei are roughly twice as long as they are wide, highly deformed nuclei have a length-to-width ratio of approximately 1.5.

9. HOW DOES PROTON RADIOACTIVITY OCCUR? For this radioactive process to occur, the proton must first escape the nucleus. The proton experiences the strong interaction, the force which normally holds together the protons and neutrons in the nucleus. However, if a nucleus is inherently unstable, it seeks a lower-energy, more stable configuration, and in the case of proton radioactivity, the strong force supplies energy to a proton to allow it to escape. This makes proton radioactivity different from another radioactive process known as beta decay, in which the decay rate is governed by another fundamental force known as the weak interaction.

In its attempt to escape the nucleus, the proton encounters a repulsive force, known as the "Coulomb barrier," formed by the repulsive positive charges of all of the other protons in the nucleus. The Coulomb barrier makes it difficult both for protons to leave the nucleus and for protons to enter it. In the holmium-141 and europium-131 nuclei, a proton may attempt to escape the nucleus 10^21 or 10^22 times per second, but smash repeatedly against the Coulomb barrier.

On top of that, the proton may have something else stacked against it: angular momentum. Roughly speaking, a proton's angular momentum describes how much "spin" it has, like a figure skater revolving around a fixed point on the ice. The higher the proton's angular momentum, the harder it is for it to escape.

10. PROTON TUNNELING According to the laws of classical physics, a proton cannot leave the nucleus unless it has enough energy to surmount the Coulomb barrier. In the holmium-141 and europium-131 nuclei, a proton does not have enough energy. But according to quantum theory, this proton can sort of teleport itself to a location outside the nucleus thanks to a process known as "tunneling."

Quantum theory says that all objects--including protons--don't always act like solid particles. Under the right conditions, protons can act like a wave that spreads out into space. Roughly speaking, this wave is related to the possible positions where the proton can be found. If the wave extends out far enough, the proton has a chance of existing at a point beyond the clutches of the Coulomb barrier. Therefore, the proton has a chance of escaping the nucleus. This tunneling process is the basis of proton radioactivity--and another form of radioactivity known as alpha decay.

11. TUNNELING THROUGH A DEFORMED BARRIER By studying proton radioactivity in holmium-141 and europium-131, the physicists were studying proton tunneling in a deformed nucleus. The tunneling rates for these nuclei are expected to be different than for those in a spherical nucleus. Furthermore, the researchers preferred to study proton radioactivity rather than a process such as alpha decay, in which they would have to worry about the alpha particle (consisting of 2 protons and 2 neutrons) first forming in the nucleus and then escaping. With proton radioactivity, the researchers just had to worry about the proton leaving the nucleus.

12. THE EXPERIMENT Using the ATLAS accelerator at Argonne National Laboratory in Illinois, the researchers bombarded a molybdenum target with an iron beam at energies of around 300 MeV. In about one in a million cases, iron and molybdenum nuclei fused together to form an erbium nucleus. Possessing a great deal of energy, these erbium nuclei acted like hot drops of liquid, in which they would quickly evaporate particles. Approximately one in a million of these erbium nuclei would evaporate one proton and 4 neutrons to become a holmium-141 nucleus--the isotope they wanted to study. The holmium-141 nuclei and the other reaction products travelled in the direction of the iron beam.

These nuclei then entered the Argonne fragment mass analyzer (FMA), a device which first separated the reaction products from the unused iron beam. Then they were directed to a device known a double-sided silicon strip detector. The nuclei implanted themselves at specific regions of the detector depending on their mass. This detector contains horizontal strips on one side and vertical strips on another side which give information on the positions of the nuclei. The holmium-141 nuclei would occupy a specific position in the detector because they all had the same mass. The researchers could then monitor the holmium-141 nuclei to see how long it took for them to emit a proton.

The researchers repeated this approach to study proton radioactivity in europium-131. In those studies the researchers created that isotope by colliding a calcium beam with a ruthenium target at energies of around 200 MeV.

13. EXPERIMENTAL RESULTS For these nuclei, the researchers were able to measure a property known as half-life, which describes the amount of time it takes for half of a collection of these nuclei to undergo proton radioactivity. They also measured the energy of the protons emitted from the nuclei. Combining the measurements of half-life and proton energy with a theoretical model allowed the researchers to obtain information on the lowest-energy (ground) state of a highly deformed nucleus above the proton dripline--something that was impossible to do before. For example, they were able to ascertain the angular momentum of the holmium-141 nucleus in its ground state. Previous experiments have actually determined the lowest-energy state of other highly deformed nuclei, but not for those mapped above the proton dripline, in which the nucleus wants to get rid of a proton even in its lowest-energy state, only to be inhibited by the Coulomb barrier.

14. AGREEMENT WITH THE BUGROV-KADMENSKII MODEL The researchers found that their data agrees pretty well with a theory that employs the Bugrov-Kadmenskii model when the nuclei are highly deformed. The researchers plan to perform complementary studies with the detector Gammasphere, which will further probe the deformed shapes of these nuclei by studying the gamma rays that can be emitted by these nuclei as they get rid of their energy.

By finding proton radioactivity in holmium-141 and europium-131, and showing that they fit a model in which they are assumed to be highly deformed, the researchers suggest that other nuclei mapped above the proton drip line between antimony and holmium may exist in a highly deformed state.

American Institute of Physics

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