Aug 20, 2020
Investigation in the mendelevium - lawrencium family: true or false twins?

The spectroscopy of a mendelevium isotope, 251Md composed of 101 protons and 150 neutrons, reveals a surprise: when it rotates, it behaves exactly like a lawrencium isotope made of 103 protons and 152 neutrons. The experiment carried out at the University of Jyväskylä in Finland required the most advanced tools to study these rare and ephemeral nuclei: filtering and identification of the nuclei, gamma ray and electron detection. Is this completely unexpected similarity the result of chance, or is it related to the properties of strong interaction? The investigation continued with the theoreticians to try to understand this singularity. The results have just been published in the journal Physical Review C.


Mendelevium belongs to the family of actinides: this family of 15 elements of the periodic table, often represented on a somewhat isolated line, most of which have prestigious names such as planets (uranium, neptunium, plutonium), famous scientists (curium, einsteinium, fermium, mendelevium) or related to their discovery place  (americium, berkelium, californium). Regarding Lawrencium, it is the first transactinide: another family with names just as famous (rutherfordium, seaborgium, bohrium, meitnerium, roentgenium, copernicium, etc.). Mendelevium and lawrencium have 101 and 103 protons, respectively. Most actinides and all transactinides are artificial elements: they are not found on Earth even if it is suspected that they can be created in violent stellar phenomena such as a supernovae explosion, neutron stars fusion  or the collapse of a massive star (collapsar).

If they are so rare, it is because they are fragile. Their life hangs by a thread, or rather by a wave (quantum mechanics). The 251Md in which we are interested (101 protons and 150 neutrons) survives about 4 minutes. This is actually a very long time! Neighboring nuclei have a lifetime of a few milliseconds, which makes them even more difficult to study.

These Md and Lr nuclei are also deformed, they have a kiwi-like shape and love to rotate. This is a bonus because we can measure their moment of inertia and have a good idea of their elongation.

That's what we did recently with 251Md. And astonishingly, the 251Md rotational spectrum  resemble the one of 255Lr! They look like twins, and in this case we are talking about twin rotational bands. As we will see, this is completely unexpected and defies nuclear models. Before trying to understand, let's see how we arrived at this point: how we created and observed these nuclei. We will then submit the problems to the theoriticians.


Investigation in the mendelevium - lawrencium family: true or false twins?

Figure 1: "SAGE" detector array at the University of Jyväskylä in Finland to measure gamma rays and electrons. The thallium target is located in the center of the device where the mendelevium-251 nuclei are created.

As we have seen, Md is a rare and unstable nucleus. On Earth, an accelerator must be used to create it, for example by bombarding Calcium-48 nuclei on a Thalium-205 target. When they are created in this collision, in this fusion reaction, the new mendelevium nucleus starts to rotate. This is very convenient because we can study its shape. But it is not that simple. With about 1010 beam particles per second, only about two 251Md nuclei are created per minute. Therefore we have to sort them out very carefully and detect them with great precision and rigor. This is done in Finland with a separator called "RITU", and with the "SAGE" detectors (Silicon And GErmanium, see Figure 1).


To study nuclei, we detect gamma-rays and electrons they emitted. This is indeed how they de-excite, i.e. decrease their rotational frequency before finally coming at rest. After all the sorting procedure, both with the separator and with the whole battery of detectors, we obtain after about ten days of measurement a few thousand interesting events. The gamma-ray spectrum is shown in Figure 2. By looking at this spectrum made up of regularly spaced peaks, the physicist knows immediately that the nucleus is deformed and that it rotates. One can even deduce its rotationnal frequency and its moment of inertia

Investigation in the mendelevium - lawrencium family: true or false twins?

Figure 2: rotationnal spectrum of mendelevium-251 obtained after different selections. The mendelevium-251 regularly spaced peaks are indicated by blue dotted lines. The lawrencium-255 spectrum is not represented, but the peaks position is represented by red stars.

That's where the surprise came: the spectrum looks very similar to that of 255Lr, which has two more protons and two more neutrons. This similarity is quite abnormal. In order to understand, we determined the configuration of the nucleus: how the protons and neutrons behave. We know that nucleons are located on orbitals. Classically their trajectories would look like ellipses. Some tend to give an elongated shape to the nucleus like a kiwi, others a flattened shape like a pumpkin or even a pear, and still others are neutral and prefer the spherical shape. With an odd proton number, we can simplify the problem by considering a rather inert core (the kiwi) around which a proton rotates. A very practical way to determine the characteristics of this proton (how it rotates) is to measure both gamma rays and electrons. In short, a magnetic moment is deduced. However, this measurement is extremely difficult since it is very complicated to measure electrons. There is some background due to the collision, and for a given transition energy, the electron has the choice between about ten possible transitions: the spectrum is very fragmented with a multitude of peaks. Because of this extreme complexity, it is even more complicated to detect both electrons and gamma. The only place in the world where this is possible for very heavy nuclei is precisely the University of Jyväskylä. 251Md is moreover the heaviest nucleus with an odd number of protons for which this type of experiment has been performed.

The electron spectrum is indeed a bit complicated but finally, we can deduce the magnetic moment of the orbital of interest, and thus identify this famous orbital.

As a new surprise, we were unable to simply explain the similarity between 251Md and 255Lr. To obtain the same spectrum, the moment of inertia is necessarily identical. The moment of inertia is somehow the resistance of an object to its rotation: it increases with the mass or with the deformation (it varies according to A5/3 (1+ 0.3 β), where A is the number of nucleons and β the elongation). 255Lr being heavier, it would have to be less deformed to look like 251Md. New disappointment, by analyzing the difference in terms of orbital filling (those who prefer kiwis or pumpkins), the passage from 251Md to 255Lr does not work at all, and even worse, goes in the wrong direction!


So we turned to our theoriticians colleagues of the Institute of Physics of the 2 Infinities of Lyon to try to understand. Their calculations are much more sophisticated than the simplistic approach which consists to assimiate 255Lr to 251Md, to which 4 particles are added. Since it is impossible to formally calculate the state of the 251 constituents of 251Md, the theoriticians use the mean field approximation: it is the potential created by these 251 nucleons in which they evolve. This mean field is very flexible: it adapts to the assembly of protons and neutrons.

And there miracle: it works! Even if, once again, it goes totally against intuition. We went further in trying to understand the source of this similarity. Could it be the nucleons that we add, the detail of the interaction, the pairing correlations (this ability of nucleons to combine in pairs)? The result is not so simple: the ingredients considered one by one explain nothing. However, all things considered, the  calculations confirm the link between the 255Lr and 251Md nuclei: there is a mechanism, totally counter-intuitive, that rearranges all the nucleons to obtain this similarity. The average field worked well!

A small downside to all this: the result depends on the pariring correlations injected into the calculations. We are still unable to favor one parameterization over another, and the calculations do not allow us to perfectly reproduce all the details of the experiment. At this stage, it is suspected that the  251Md and 255Lr twin bands are the result of chance: the result of circumstances that accidentally lead to the same rotational spectrum. Or is it a more general property of very heavy nuclei? To decide, similar cases would have to be observed. The 251Md-255Lr binomial is still unique in this region which is still very poorly known.

Since these nuclei are rare and difficult to create, in order to produce more of them, more intense beams must be used. This is why, among other things, the SPIRAL2 accelerator was built at the GANIL (Grand Accélérateur National d'Ions Lourd) located in Caen. We also saw that a strict filtering and excellent identification was required. The Super-Spectrometer Separator S3 was designed for this purpose. It is scheduled to start up in a few months with some nice experiments in perspective.



R. Briselet et al., In-beam γ-ray and electron spectroscopy of 249,251Md, Phys. Rev. C 102 (2020) 014307

Christophe Theisen


#4857 - Last update : 11/18 2020


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