“Features of the population of isomeric states in reactions with weakly bound nuclei”

(a series of works by the team of the G. N. Flerov Laboratory of Nuclear Reactions JINR, recognized with the JINR Encouragement Prize 2019 for contribution to the field of experimental physics).

An isomeric state was discovered by O. Hahn in 1921 in naturally occurring radioactive nuclei (²³⁴Pa formed following the β-decay of ²³⁴U). In 1935 the researchers of the I.V. Kurchatov Laboratory discovered an isomer of the ⁸⁰Br isotope synthesized in the ⁷⁹Br(n, γ) reaction. The first theoretical explanation of this phenomenon was proposed by C. Weizsäcker in 1936.

Isomeric states of nuclei differ from other excited states in that the probability of their transition to any low-lying state is strongly inhibited by the selection rules of spin and parity changes. In particular, high-multipolarity transitions (i.e. transitions with large spin changes) and low-energy transitions are suppressed. Thus, two half-lives are observed when the nucleus undergoes radioactive decay: one involving spin and transition energy changes and allowed by selection rules and the other hindered. More than 100 isomeric states with lifetimes over 1 s are presently known.

The groups of isomers close to magic numbers form the so-called “islands of isomerism”. This phenomenon was qualitatively explained within the nuclear shell model. For odd nuclei in which the number of protons or neutrons is close to magic numbers, the shell model predicted the existence of nuclear levels that are similar in energy but substantially different in spin.

Isomers turned out subsequently to be of several types: shape isomers (decay is forbidden due to the shape mismatch), spin isomers (spin mismatch), and K-isomers (change in spin orientation with respect to the nucleus symmetry axis).

In their works submitted for JINR competition 2019, the authors studied the population of isomers related to “traditional” spin isomers in reactions involving halo, weakly bound, and cluster nuclei. The series of works was performed in collaboration with researchers from the Institute of Nuclear Physics of the Academy of Sciences of the Czech Republic, Řež.

The population probability ratio of ground and isomeric states in the atomic nucleus, defined as σ_m / σ_g and called the isomeric ratio (IR), depends on a number of factors, in particular, transferred angular momentum. Not only does the measurement of IRs in various nuclear reactions provide important information on the structure of the nucleus and the mechanism of its formation, but it also provides insights into the degree of its excitation, including the distribution of nuclear level densities and spins of excited nuclear states.

The production of beams of weakly bound radioactive nuclei opened new avenues for studying the structure and interaction mechanism of these nuclei, which is substantially different from that of stable nuclei: sub-barrier reactions, cluster transfer reactions, a higher probability of population of isomeric states, etc. One of the topics that aroused a great deal of interest among researchers are mechanisms of reactions induced by weakly bound radioactive nuclei characterized by an unusual distribution of proton and neutron densities that markedly affects nuclei interaction. Unlike in reactions with densely packed nuclei(α-particles, etc.), an increase in the mean angular momentum transfer is expected in reactions involving weakly bound and halo nuclei in view of a larger radius of nuclear matter distribution in the projectile nucleus. Compared with the population of isomeric and ground states in nuclei produced in reactions with ordinary, neighbouring stable nuclei, this distribution can in turn affect the population probability of isomeric and ground states of complete and incomplete fusion and transfer reaction products. In such reactions, it seems likely that the population of high-spin isomeric levels will differ from the population probabilities of the given states produced in reactions induced by light stable particles, for example, by protons and ⁴He.

The population of ground and isomeric states in nuclei originating from fusion reactions depends strongly on the excitation energy of the compound nucleus, distribution of angular momentum, and type of particles emitted in the de-excitation of the nucleus that are able to carry away various energies and angular momenta.

In the series of works, a study was conducted on the effect of fusion and transfer reaction mechanisms in collisions of ³He weakly bound and 6He halo nuclei with light and heavy target nuclei upon the excitation of newly formed nuclei, which leads to the population of isomeric and ground states both in residual nuclei and reaction products when transferring single nucleons and clusters to the target and projectile nuclei.

Nuclei were studied near the closed shells Z = 82 and N = 126, which could be produced in reactions with ¹⁹⁴Pt and ¹⁹⁷Au in ground and isomeric states.

The investigations were performed with a ⁶He beam produced at the DRIBs accelerator complex of JINR’s Flerov Laboratory of Nuclear Reactions (FLNR) in Dubna and a ³He beam delivered from the U-120M cyclotron of the Institute of Nuclear Physics of the Czech Republic in Řež. The experiments were carried out using the activation analysis method. Highly efficient germanium detectors were used to measure induced γ-activity. Gamma-ray energy and half-lives characteristic for the process were used for the identification of nuclei with relatively long-lived ground and isomeric states and for the measurement of their formation cross-sections. On the basis of the measured values of typical γ-activity during the decay of the nucleus under consideration, the excitation functions for the formation of these nuclei in ground and isomeric states were measured.

In first experiments with ⁶He and ¹⁹⁷A, the measured cross-sections of fusion and transfer reactions near the Coulomb barrier were shown to be much higher compared to those obtained previously in reactions with α-particles (⁴He). Yields of a number of isotopes produced both in fusion and transfer reactions were observed with a higher probability.

Excitation functions were measured for the production of the ¹⁹⁸Tl and ¹⁹⁶Tl isotopes in the ground and isomeric states via the complete fusion reactions ¹⁹⁷Au (⁶He, 5n 7n) ^198,196Tl.

IRs measured for the ¹⁹⁸Tl and ¹⁹⁶Tl isotopes turned out to be close to the average statistical weight ratio (2J_m + 1) / (2J_g + 1), where J_g and J_m are spins in ground and isomeric states. The IR calculations demonstrated that the imparted angular momentum in reactions with ⁶He was close to that in fusion reactions induced by α-particles at higher energies. The IRs for ¹⁹⁸Tl in the sub-barrier fusion reaction ¹⁹⁷Au (³He, 2n)¹⁹⁸Tl reached 1.1-1.5, which was close to the IR values for ¹⁹⁸Tl produced in the fusion of α-particles with ⁶He at the energy above the Coulomb barrier.

IRs for ¹⁹⁵Hg were measured at a higher ⁶He energy. The nucleus was produced in the ¹⁹⁷Au (⁶He, p7n) ¹⁹⁵Hg fusion reaction accompanied by the emission of neutrons and a charged particle. The IR for this isotope formed in the fusion reaction followed by the evaporation of a proton and seven neutrons also exceeded unity and remained rather unaffected by the increase in the ⁶He energy up to 20 MeV/nucleon.

It was of particular interest to compare the population of ground and isomeric states in nuclei formed in nucleon transfer reactions, which should be more sensitive to angular momentum. The excitation functions were measured for the production of the ¹⁹⁶Au and ¹⁹⁸Au isotopes in ground and isomeric states in the ¹⁹⁷Au + ⁶He reaction accompanied by neutron transfer to the target nucleus or incident particle (stripping and pickup mechanisms). The IRs for ¹⁹⁶Au and ¹⁹⁸Au were shown to be lower than those in complete fusion reactions and exhibited marked differences in behaviour with change of the energy of the bombarding particle. It was found that the IRs for ¹⁹⁶Au were essentially independent of the 6He energy within the energy range under consideration up to 20 MeV/nucleon and fell close to the value of 3 ∙ 10^–1. With increasing ⁶He energy and in the energy range from 20 to 60 MeV, the IRs for ¹⁹⁸Au increase and vary from 10^-3 to 10^-2.

The graph below illustrates the behavior of IRs for various ¹⁹⁷Au + ⁶He reaction channels. It is to be noted that for ¹⁹⁶Au, the dependence of IR on the sup>4He energy is quite different from that for the ¹⁹⁸Au isotope, both being produced in the ¹⁹⁷Au + sup>4He reaction: the IR for ¹⁹⁶Au is seen to increase as the ⁴He energy varies but remains almost unaffected for ¹⁹⁸Au.

The charge-exchange reaction ¹⁹⁷Au (³He, t) ¹⁹⁷Hg was studied using the ³He beam. IRs and cross sections were measured for the ¹⁹⁷Hg isotopes in the ground and isomeric states. The IRs were shown to be fairly low (~ 0.1) and essentially independent of the ³He energy.

Owning to a specially designed and successfully employed technique for irradiating targets and measuring nuclear production cross sections in ground and isomeric states using the unique ⁶He beam emitted by the JINR acceleration complex DRIBs and the ³He beam delivered from the U-120M cyclotron of the Nuclear Physics Institute (Řež, Czech Republic), some interesting results were obtained. They allowed us to determine regularities in the production and behavior of excitation functions of various reaction channels and draw the following conclusions:

1. Production cross sections of the isotopes of Hg, Au, and Tl were measured for the first time in ground and isomeric states in the ¹⁹⁴Pt + ³He and ¹⁹⁷Au + ⁶He reactions using beams of weakly bound nuclei (³He and ⁶He). Excitation functions of various reaction channels were measured (fusion, transfer, and charge exchange reactions).
2. IRs were measured for the first time for the following isotopes:
   
   ¹⁹⁵Hg, ¹⁹⁶Tl, ¹⁹⁸Tl produced in the ¹⁹⁴Pt + ³He
   and ¹⁹⁷Au + ³He (⁶He) fusion reactions;
   
   ¹⁹⁶Au ¹⁹⁸Au formed in transfer reactions with ¹⁹⁷Au using ⁶He and ³He;
   
   ¹⁹⁷Hg produced in the charge exchange reaction ¹⁹⁷Au(³He,t)¹⁹⁷Hg.
3. The IR of fusion reaction products formed with the beams of halo nucleus ⁶He and weakly bound nucleus ³He was shown to be higher than that of nucleon transfer and charge exchange reactions, indicating different population mechanisms of excited states in these reactions. The shift of the IR maximum to lower energies in complete fusion reactions can be attributed to a larger amount of angular momentum added by the ³He and ⁶He nuclei.

The revealed dependence of IRs (in stripping and pickup reactions) and clusters on the energy of the bombarding particle can be explained by the difference in selective population of single-particle and collective states in reactions with beams of weakly bound and stable nuclei.

Thus, reactions with beams of weakly bound radioactive nuclei can be used to populate high-lying states of nuclei, including those at the neutron drip line.

The main results of the work were tested and reported at international conferences: International Conference “Isomers in Nuclear and Interdisciplinary Research” (July 2011, Peterhof, Russia); International conferences on nuclear spectroscopy and the structure of the atomic nucleus: 64 International Conference “NUCLE-2014” (Minsk, Belarus), 65 International Conference “NUCLE-2015” (Peterhof, Russia), 68 International Conference “NUCLE-2018” (Voronezh, Russia ); International symposium: EXON 2016 (September 2016, Kazan); Zakopane Conference on Nuclear Physics “Extremes of the Nuclear Landscape” (September 2018, Zakopane, Poland) and others.

Skobelev N.K., Senior Researcher, FLNR