Influence of high-spin states on isomeric ratios of nuclear reaction products

The isomeric ratios of some nuclear products of (p, n), (d, 2n), (α, p3n) reactions were analyzed. A comparison of calculation data obtained by using TALYS 1.4 software package with experimental ones shows that the observed significant discrepancies for definite nuclei may be accounted for by the influence of high-spin states on the values of isomeric ratios.     

Discussion of isomeric ratios in (<Emphasis Type="Italic">p,n</Emphasis>) and (<Emphasis Type="Italic">d</Emphasis>, 2<Emphasis Type="Italic">n</Emphasis>) reaction

Isomeric ratios (IR) in the (p, n) and (d, 2n) reactions are considered. The dependence of IR values on the projectile type and energy, the target- and product-nucleus spin, the spin difference between the isomeric and ground states of products, and the product mass number is discussed. The isomeric ratios for 46 product nuclei (from ^44m,gSc to ^127m,gXe) obtained in reactions where target and product nuclei have identical mass numbers were calculated at energies from the reaction threshold to 50 MeV (with a step of ΔE = 1 MeV). The calculations in question were performed with the aid of the TALYS 1.4 code package. The calculated IR values were compared with their experimental counterparts available from the literature (EXFOR database). In the majority of cases, the calculated IR values agree well with the experimental data in question. It is noteworthy that the IR values obtained in (d, 2n) reactions are substantially greater than those in (p, n) reactions.     

New outlook on the possible existence of superheavy elements in nature

A consistent interpretation is given to some previously unexplained phenomena seen in nature in terms of the recently discovered long-lived high-spin super-and hyperdeformed isomeric states. The Po halos seen in mica are interpreted as being due to the existence of such isomeric states in corresponding Po or nearby nuclei that eventually decay by γ or β decay to the ground states of ²¹⁰Po, ²¹⁴Po, and ²¹⁸Po nuclei. The low-energy 4.5-MeV α-particle group observed in several minerals is interpreted as being due to a very enhanced α transition from the third minimum of the potential-energy surface in a superheavy nucleus with atomic number Z=108 (Hs) and atomic mass number around 271 to the corresponding minimum in the daughter.     

Search for neutron resonances in the $$^{178m_2 } Hf$$ isomer and their investigation

Experiments aimed at detecting and investigating neutron resonances in the \(^{178m_2 } Hf\) isomer are described, and the results obtained in these experiments are presented. The investigations in question are of great interest since the structure of this isomer—it is interpreted as the (π7/2⁺, π9/2⁺, ν7/2⁺, ν9/2⁺) configuration—and its high spin of J=16 differ significantly from the structure and spin of nuclei studied previously. The experiments performed at the Kurchatov Institute employed a neutron source based on the FAKEL linear electron accelerator and a multisection detector from NaI(Tl) crystals that was able to ensure a 4π coverage. This equipment made it possible to study gamma-ray cascades in radiative neutron capture versus neutron energy. Despite an extremely small number of isomer nuclei, a low content of the isomer in the target used, and its high radioactivity, resonances were discovered that arise upon neutron capture by a high-spin \(^{178m_2 } Hf\) nucleus. The parameters of these resonances were found. The mean spacing between the revealed resonances is about 1 eV, which is consistent with calculations based on the Fermi gas model. This indicates that the Fermi gas model describes well the density of both low-and high-spin levels. At the same time, the above agreement suggests that, upon the formation of a compound nucleus, the structure of the isomeric state is destroyed completely. On the other hand, glaring discrepancies between experimental data and the predictions of the statistical model were found: gamma transitions from high-spin resonances (J=31/2⁺, 33/2⁺) populate predominantly the low-spin ground state (J=9/2⁺) rather than the high-spin state of the \(^{178m_2 } Hf\) isomer (J=25/2^?); the radiative width is approximately one-third as great as that which is predicted by the statistical model; and the properties of gamma cascades are different for different resonances, this difference being beyond statistical fluctuations. The results of the present investigation make it possible to reveal special features in the behavior of the quantum number K at high excitation energies.     

Der Zerfall des Tb158m

Tb^158m was produced from Tb¹⁵⁹ by (n, 2n) reaction and investigated using scintillation spectrometers. The following results were obtained: half-life\(T_{\tfrac{1}{2}} = (10.5 \pm 0.2)\) sec; energy of the isomeric transitionE _γ =(109.9±1.4) keV; conversion coefficients α _K =56±3; α _L +α _M +?=50±8; α_total=106±10;K/L-ratioK/L=1.3±0.3, yielding the multipole order of the isomeric transition to beM3. Upper limits for the direct beta transitions from the isomeric state to the ground states of the neighbouring even-even nuclei Gd¹⁵⁸ and Dy¹⁵⁸ are 10^?4 and 6·10^?3, respectively.     

Isomeric ratios in reactions induced by gamma rays and fast neutrons in the isotopes of Re,Ir, and Au

Isomeric ratios were measured in the (γ, n) and (n, 2n) reactions leading to the formation of ¹⁸⁴Re, ¹⁹⁰Ir, and ¹⁹⁶Au odd-odd nuclides. The measurements were performed by the activation method implemented for Re, Ir, and Au samples of natural isotopic composition that were irradiated with 14.7-MeV neutrons and bremsstrahlung photons of endpoint energy 22 MeV. Isomeric-and ground-state nuclei formed in these reactions were identified by their x-or γ-ray spectra and by their half-lives. The isomeric ratios were calculated on the basis of the statistical model, and the results were compared with experimental data, where by it was possible to determine parameters that characterize the dependence of the level density on the excitation energy and angular momentum. The effect of the nuclear structure on these parameters is discussed.     

Wirkungsquerschnitte und Isomerenverhältnis für die Reaktionen89Y(α, 3n)90g Nb und89Y(α, 3n)90m Nb

Absolute cross-sections and isomeric cross-section ratios have been measured for the reactions⁸⁹Y(α, 3n)^{90g, 90m} Nb. The energy of the α-particles was varied between 34 and 54 MeV. The experimental isomeric ratios are compared with statistical-model calculations.     

Effect of properties of superheavy nuclei on their production and decay

Properties and stability of superheavy nuclei resulting from hot fusion are discussed. It is shown that the microscopic–macroscopic approach allows obtaining the closed proton shell at Z ≥ 120. Isotopic trends of K-isomeric states in superheavy nuclei are predicted. Evaporation residue cross sections in hot fusion reactions are calculated using the predicted properties of superheavy nuclei. Interruption of α decay chains by spontaneous fission is analyzed. Alpha decay chains through isomeric states are considered. Internal level densities in superheavy nuclei are microscopically calculated.     

The Study of (<Emphasis Type="Italic">n</Emphasis>, 2<Emphasis Type="Italic">n</Emphasis>) Reaction Cross Sections for Ce and Nd Isotopes up to 20 MeV

Neutron cross section calculations for ¹³⁶Ce(n, 2n)¹³⁵Ce, ¹³⁸Ce(n, 2n)¹³⁷Ce, ¹⁴⁰Ce(n, 2n)¹³⁹Ce, ¹⁴²Ce(n, 2n)¹⁴¹Ce, ¹⁴²Nd(n, 2n)¹⁴¹Nd, ¹⁴⁴Nd(n, 2n)¹⁴³Nd, ¹⁴⁶Nd(n, 2n)¹⁴⁵Nd, ¹⁴⁸Nd(n, 2n)¹⁴⁷Nd, and ¹⁵⁰Nd(n, 2n)¹⁴⁹Nd were done in the incident energy range from 10 to 20 MeV. The calculations were performed using three codes TALYS-1.6 for two-component Exciton model, EMPIRE-3.2 Malta for Exciton model, and ALICE/ASH for the Geometry-Dependent Hybrid (GDH) model. The results of model calculations were compared with the available experimental data and also with the evaluated data in the TENDL-2015 (based on the modified TALYS code), ENDF/B-VII.1 libraries. The calculated cross section data were compared with the available experimental data obtained from EXFOR and also compared with semiempirical formulas around 14–15 MeV. The results of model calculation were found to be in good agreement with the experimental data given in literature and semiempirical data around 14–15MeV.     

Cross sections of the photoneutron reaction for <Superscript>141</Superscript>Pr and <Superscript>186</Superscript>W nuclei,estimated from physical criteria of data reliability

Using objective physical criteria for data reliability, cross sections of partial photoneutron reactions (γ, 1n), (γ, 2n) and (γ, 3n) that are free of the shortcomings of neutron multiplicity sorting methods used on beams of quasimonoenergetic annihilation photons are obtained for ¹⁴¹Pr and ¹⁸⁶W nuclei. Evaluation is performed using the experimental–theoretical method (ETM), based on the experimental cross section of neutron yield reaction σ^exp(γ, xn) = σ^exp(γ, 1n) + 2 σ^exp(γ, 2ⁿ) + 3 σexp(γ, 3n) + … and ratios F _i ^theor= σ^theor(γ, in)/σ^theor(γ, xn) calculated within the combined model (CM) of photonuclear reactions, which stipulates that σ^eval(γ, in) = F _i ^theor σ^exp(γ, xn). It is found that for ¹⁴¹Pr and ¹⁸⁶W, ratios F ^exp _i do not contradict the data reliability criteria only at energies up to ~21 and ~22 MeV, respectively. At the same time, there are notable discrepancies between F _i ^theor and F ^exp _i, and thus between the evaluated and experimental cross sections of reactions. It is shown that the discrepancies between the evaluated and experimental cross sections are due to the assumed unreliable experimental distribution of neutrons in the channels with multiplicities 1, 2, and 3.     

Study of <Superscript>179</Superscript>Hf<Superscript><Emphasis Type="Italic">m</Emphasis>2</Superscript> excitation

Isomeric ratios of ¹⁷⁹Hf ^m2,g yields in the (γ, n) reaction and the cross section for the ¹⁷⁹Hf ^m2 population in the (α, p) reaction are measured for the first time at the end-point energies of 15.1 and 17.5 MeV for bremsstrahlung photons and 26 MeV for alpha particles. The results are σ = (1.1 ± 0.11) × 10^?27 cm² for the ¹⁷⁶Lu(α, p)¹⁷⁹Hf ^m2 reaction and Y _m2/Y _g = (6.1 ± 0.3) × 10^?6 and (3.7 ± 0.2) × 10^?6 for the ¹⁸⁰Hf(γ, n)¹⁷⁹Hf ^m22 reaction at Е _ep =15.1 and 17.5 MeV, respectively. The experimental data on the relative ¹⁷⁹Hf ^m2 yield indicate a single-humped shape of the excitation function for the ¹⁸⁰Hf(γ, n)¹⁷⁹Hf ^m2 reaction. Simulation is performed using the TALYS-1.4 and EMPIRE-3.2 codes.     

Isomeric ratios of (γ,p) and (γ,α) reactions on <Superscript>117<Emphasis Type="Italic">m,g</Emphasis></Superscript>In

The isomeric ratios of the (γ,p) and (γ,α) reactions on ^117m,g In have been measured. The ratios Y _m /Y _g was found to be 1.18(9) and 0.23(9), respectively, at a boundary energy of 22 MeV. The statistical character of the reactions under such conditions is shown.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

Intergroup azimuthal correlations of secondary particles in the interaction between <Superscript>56</Superscript>Fe nuclei of momentum 2.5 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon and photoemulsion nuclei

Angular correlations between secondary particles emitted in the interaction between ⁵⁶Fe nuclei of momentum 2.5 GeV/c per nucleon and photoemulsion nuclei were measured. These secondaries are partitioned into four groups: s, g, b, and f. For particles from each pair of the above groups, the average values of the collinearity factor and of the asymmetry parameter, as well as the parameter η of the function α(1+η cos ε) approximating the distribution of azimuthal-angle differences ε, were calculated.     

Special features of the structure of the beta-stability line for nuclei

The mass-number (A) dependence Z _β(A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Z _expt ? Z _β are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously.     

One-nucleon spectroscopy of light nuclei

The capabilities and limitations of the conventional many-particle shell model and modern potential cluster models are discussed. New revaluated and more accurate calculations of one-nucleon spectroscopic characteristics of the light nuclei of 1p shell are presented. In many-particle shell model for nuclei with A = 7, 9, 11, 13, and 15 nucleon partial widths of highly excited states with the isotopic spin T = 3/2 were calculated both for “allowed” and “forbidden” transitions. One-nucleon spectroscopic factors were calculated in threebody multicluster models of ⁶Li{αnp}, ⁸Li{αtn}, and ⁹Be{ααn} nuclei. For isobar-analogue nuclei ⁷Li and ⁷Be, the spectroscopic proton S _p and neutron S _n factors for transitions to the ground and excited states of corresponding residue nuclei of the triplet ⁶Li-⁶He-⁶Be were calculated in the framework of binary potential αtand ατ models. Integral, differential and polarization characteristics of photonuclear processes ⁷Li(γ, n ₀)⁶Li, ⁶He(p, γ_{0 + 1})⁷Li, ⁷Li(γ, p ₀)⁶He, and ⁹Be(γ, p _{0 + 1})⁸Li were calculated in this approach.     

Study of the excitation of high-spin isomers in <Superscript>190</Superscript>Ir and <Superscript>196,198</Superscript>Au in the near-threshold region

The isomeric ratios of the yields for ^190m,g Ir and ^196m,g Au have been measured in the (γ,n) reaction in the near-threshold region at γ-ray energies of 12 and 12.5 MeV. The isomeric ratios for ^198m,g Au have been measured in the (d,p) and (n,γ) reactions. The statistical nature of the (γ,n) and (n,γ) reactions is shown.     

Charge radii and quadrupole-deformation parameters of high-spin isomers

Experimental data on the differences of charge radii of nuclei in the ground and high-spin isomeric states are surveyed. High-resolution laser-spectroscopy methods were used for measurements. The results obtained for the differences of these radii by two methods—from measurements of isomeric shifts of the levels of atoms containing the nuclei being studied and from measurements of their quadrupole moments in both states under the assumption that the differences of the radii are determined by the difference in their quadrupole deformations—were compared. Two-particle isomers in odd—odd nuclei, isomers formed upon the break of one or several nucleon pairs, and isomers featuring the 1i _13/2 configuration of the odd neutron in mercury nuclei were considered. The observed distinctions between the aforementioned differences of charged radii are discussed for isomeric states of different nature.     

Photoneutron reactions in astrophysics

Among key problems in nuclear astrophysics, that of obtaining deeper insight into the mechanism of synthesis of chemical elements is of paramount importance. The majority of heavy elements existing in nature are produced in stars via radiative neutron capture in so-called s- and r processes, which are, respectively, slow and fast, in relation to competing β ^?-decay processes. At the same time, we know 35 neutron-deficient so-called bypassed p-nuclei that lie between ⁷⁴Se and ¹⁹⁶Hg and which cannot originate from the aforementioned s- and r-processes. Their production is possible in (γ, n), (γ, p), or (γ, α) photonuclear reactions. In view of this, data on photoneutron reactions play an important role in predicting and describing processes leading to the production of p-nuclei. Interest in determining cross sections for photoneutron reactions in the threshold energy region, which is of particular importance for astrophysics, has grown substantially in recent years. The use of modern sources of quasimonoenergetic photons obtained in processes of inverse Compton laser-radiation scattering on relativistic electronsmakes it possible to reveal rather interesting special features of respective cross sections, manifestations of pygmy E1 and M1 resonances, or the production of nuclei in isomeric states, on one hand, and to revisit the problem of systematic discrepancies between data on reaction cross sections from experiments of different types, on the other hand. Data obtained on the basis of our new experimental-theoretical approach to evaluating cross sections for partial photoneutron reactions are invoked in considering these problems.