Isomers of superheavy elements can be much more stable than assumed so far

Alpha decay scheme of sister nuclei 270Ds and 270Cn which illustrates transitions between analogous states (highlighted in red). The length of the transition line is connected to stability of a state. The longer the line, the shorter the lifetime, meaning a faster decay. Different lengths of the lines explain high stability of isomeric state in 270Ds (short line – long lifetime) and low stability of 270Cn (long line – short lifetime).

Work of a team of theoreticians from NCBJ and University of Zielona Góra points, that some isomeric states of superheavy elements can have half lives measured in seconds, so tens of thousands times longer than half lives of their very unstable ground states. Should such exotic nuclear states be produced experimentally, they will be stable enough to research their chemical properities.

The Mendeleev periodic table currently consists of 118 elements, but only as much as 80 has stable isotopes. Nuclei of unstable isotopes sooner or later undergo the process of decay. In some cases the half-life is very long, measured in millions of years, in other cases this time is less than a millionth of a second. All isotopes of the most heavy elements are not stable. Mean lifetime of less than a second can’t allow, with current technology, determine chemical properties of an element, especially the group in the periodic table.

Atomic nuclei are systems made of protons and neutrons, which interact with each other in a manner, which we can currently describe only approximately. In the most heavy elements the number of nucleons – protons and neutrons – can reach 300. In the macroscopic world, which we know from our everyday surroundings, complex systems can be susceptible to fluctuations, for example they can oscillate or rotate, while their individual components are still bound to each other. In the world of complex systems such as atomic nuclei, which are governed by the laws of quantum physics, fluctuations are possible as well, and they correspond to transitions of the system into excited state. The main difference – and in fact the essence of the world on quantum scale – is that the energies and other parameters of quantum excited states cannot change freely. Instead, only precisely portioned changes are allowed, meaning they are quantized.

A nucleus in an excited state has the energy higher than the energy of the ground state and in general quickly (in the order of one trillionth of a second) returns back to the state with lower energy, giving the energy of the excitation away in the form of gamma radiation. However, some nuclei have such excited states, that last for a considerably longer time – they are called isomers. One of the signs of the change in their internal excitation can be a change of spin, which is the quantum analogy to angular momentum, which expresses „the speed of rotation of individual elements in a system”. Nuclei in isomeric states create atoms with the same chemical properties as nuclei in ground state.

In 2001, scientists from GSI Institute in Germany discovered an isomer of the isotope of the element called darmstadtium with mass number equal to 270. As it turns out, it decays with emission of alpha particle, like most superheavy elements, but its mean lifetime is approx. 60 times longer than the same isotope in ground state. Isomers existing longer than the ground state are known for lighter nuclei as well. But decay of this isomer of darmstadtium through alpha particle emission means, that typical electromagnetic (gamma) decay is less probable for this nucleus. The natural question is, are there other isomers of superheavy elements, that can have longer mean lifetimes in comparison with their ground states.

A team of Polish physicists made an attempt of assessing the effects responsible for forbidding the alpha decay. Scientists, conducting calculations and estimations, sought for nuclei of superheavy elements, for which alpha decay would be the most forbidden. We can assume, that such nuclei are the best candidates for long-lived isomers.

„Purely experimental identification of the structure of an excited state is basically impossible” – explains Professor Michał Kowal, head of NCBJ Theoretical Physics Division. „For now it is speculated, that the observed stability of isomer of darmstadtium-270m is caused by excitation of a neutron pair. Our calculations suggest, that proton excitations, rather than neutron, are responsible for this stability.”

Excited states, which we are discussing, can be imagined as systems, in which a number of nucleons – for example two protons, two neutrons or both of these pairs simultaneously – are not in their basic position, but rather they circulate around the core of a nucleus in the same direction. In some nuclei such excited state can have total spin of value up to 19 or 20 Planck constants. The dominant decay channel of such nuclei is alpha decay, essentially emission of helium nucleus, which is made of two protons and two neutrons. The decay of nuclei from isomeric states can lead to the ground state or some of the intermediate excited states of the child (final) nuclei. „Currently nobody can accurately calculate mean lifetime of an isomer considering alpha decay” – adds Professor Kowal. „However, we do know, that forbidding of the alpha decay is connected to at least three causes: difference in structure or spin of the initial and final state and energy difference of these states. Alpha decay to child nucleus in ground state requires change of spin in the order of twenty Planck constants. This is plenty! The centrifuge barrier connected with this change is huge and blocks the decay practically completely. Moreover, because of totally different structure of initial and final state, the decay is additionally strongly forbidden. Those two effects cause the decay to ground state of the final nucleus to be incredibly improbable. On the other hand, decay to a nucleus in an excited state with spin similar to the initial isomeric nucleus happens with large probability only when that state has equally low excitation energy compared to the excitation energy of the emitting nucleus. In some cases of the nuclei that we are researching this is not the case, so we suspect, that alpha decay is strongly forbidden for those initial states, and in consequence, isomeric state will be long-lived.”

Work of Polish physicists was published in Physical Review C and was presented during annual summer conferences on nuclear physics. „We were analysing exotic states in the heaviest nuclei with even numbers of protons and neutrons” – says Professor Janusz Skalski (NCBJ). „We have described the forbidden mechanism and pointed at the candidate for long-lived nuclear states. The calculations and estimations we conducted show, that long-lived isomeric states with the structure of simultaneous excitation of two pairs – protons and neutrons, should exist in four darmstadtium isotopes. We do not expect such long-lived isomeric configurations to occur in isotopes of elements with atomic numbers Z=106, 108 and 112.”

„The expected alpha decay of diproton states is highly forbidden for basically all darmstadtium nuclei” – adds Dr Piotr Jachimowicz (University of Zielona Góra). „The lifetimes we estimated for these isomers are hundreds or even thousands of milliseconds, which is three to five orders of magnitude longer than their ground states.”

So far the results are only theoretical estimations. However, scientists believe, that in a short time it will be possible to experimentally verify their predictions. „It is entirely possible, that similar states were already created in past experiments, but nobody noticed them, because the measurements were prepared for much shorter lifetimes.” – explains Professor Kowal. „Currently there shouldn’t be any significant problems with adequate measurements. A few laboratories in the world have adequate equipment. Perhaps such experiment will be possible in Warsaw in a few years, if only the project of buying new cyclotron for Heavy Ion Laboratory in University of Warsaw will be executed. If our predictions concerning stability of these isomers are validated, they will open new possibilities for researching chemistry of superheavy elements.”

Source article: „Hindered α decays of heaviest high-K isomers”, Piotr Jachimowicz (University of Zielona Góra), Michał Kowal and Janusz Skalski (NCBJ), Physical Review C 98, 014320 (2018)

Different lengths of the lines explain high stability of isomeric state in 270Ds (short line – long lifetime) and low stability of 270Cn (long line – short lifetime).