Calculated masses of heaviest nuclei

Masses of heaviest nuclei are calculated within a macroscopic-microscopic approach. Even-even, odd-A, and odd-odd nuclides are considered. A large region of nuclei with proton and neutron numbers of Z=82–128 and N=126–192, respectively, is analyzed. The results are compared with those of other macroscopic-microscopic and of recent microscopic Hartree-Fock-BCS calculations. Alpha-decay energies are also given.     

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.     

Effect of Nucleon Pairing in the Spectra of <Emphasis Type="Italic">N</Emphasis> = 50 Isotones

The emergence of the pairing effect of identical nucleons in the j = 9/2 state in low-lying excited states of nuclei near ⁹⁰Zr (N = 50, Z = 40) is discussed. Multiplets of states with seniority s ≥ 2, the splitting of which is determined by the proton pairing energy, are clearly visible in the nuclear spectra for a chain of N = 50 isotones. A comparison of the spectra of ground state multiplets, calculated in the δ-interaction approximation, with experimental data and results from other theoretical calculations shows this approach can be used to describe the structure of spectra and level positions with high J values.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.     

New magic nuclei and conditions of their formation

The systematic studies of the arrangement features of single-particle nucleon subshells in even-even ^90,92,94,96Zr isotopes and behavior of some known “magicity parameters” in isotopes and isotones neighboring the ⁹⁶Zr nucleus have led to the interpretation of ⁹⁶Zr as a new doubly magic nucleus. Analysis of the structure of nucleon shells in the ⁹⁶Zr nucleus revealed a feature, which consisted in that near the Fermi energy it had filled proton (π1f _5/2) and neutron (v2d _5/2) subshells with an identical and large total momentum j = 5/2, which was called the j-j coupling. Above the π1f _5/2 shell, there is another filled shell (π2p _1/2) with two j = 1/2 protons. Applied to other filled shells, this empirical rule allowed revealing several new nontraditional magic nuclei: ⁹⁶Sr (Z = 38, N = 58), π1f _5/2, v2d _5/2, and v3s _1/2 subshells; ⁵⁴Ca (Z = 20, N = 34), π2p _3/2, v1d _3/2, and v2p _1/2 subshells; a pair of ³⁰Si (Z = 14, N = 16) and ³⁰S (Z = 16, N = 14) nuclei, π1d _5/2, v1d _5/2, and (π/v)2s _1/2 subshells; and a pair of ¹⁴C (Z = 6, N = 8) and ¹⁴O (Z = 8, N = 6) nuclei, 1p _3/2, v1p _3/2, and v2p _1/2 subshells. The existence of the magic nuclei ^52,54Ca is widely discussed in the literature, the possibility of the existence of the other nuclei found is confirmed by the systematics of the behavior of the “magicity” parameters. The fact that shells with some nucleon numbers different from the classical magic numbers are closed may be due to the manifestation of a new type of interaction between nuclear protons and neutrons occupying certain subshells.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

New neutron magic number <Emphasis Type="Italic">N</Emphasis> = 16 for neutron-rich nuclei

A survey of experimental results obtained at GANIL (Caen, France) on the study of the properties of very neutron-rich nuclei (Z=6–20, A=20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N=16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behavior of the two-neutron separation energies S_2n derived from mass measurements gives very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between the 2s_1/2 and 1d_3/2 orbitals. This fact, strongly supported by the instability of C, N, and O isotopes with N>16, confirms the magic character of N=16 for the region from carbon up to neon, while the shell closure at N=20 tends to disappear for Z≤13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using in-beam γ-ray spectroscopy are also reported.     

Die Kernradiusänderung beim Einbau eines Protons

The change of therms radius of the nuclear charge distribution on addition of one proton is derived for 25 nuclides between ₁₉ ³⁹ K and ₈₂ ²⁰⁸ Pb. For this purpose, results of the muonic 2p-1s transition energies are used together with the optical isotope shifts. The uncertainties of the procedure are discussed. Corresponding results from elastic electron scattering are included for three pairs of nuclides. — For heavy nuclei, the average increase in radius per proton exceeds considerably that per neutron, as expected. Although the individual values are associated with rather large errors, shell effects seem to be noticeable atZ=28 andZ=50.     

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.     

Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X^±Y^±Z^? consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X^±Y^±Z^? with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X^±X^±Z^?. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X^±X^±Z^?, which are stable at any particle masses, asymmetric trions X^±X^±Z^? possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t⁺d⁺p^? and t⁺d⁺d^? combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.     

Azimuthal anisotropy of the emission of fragments and relativistic particles in collisions between iron nuclei of momentum 2.5 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon and photoemulsion nuclei

The azimuthal anisotropy of the emission of fragments and relativistic particles in collisions between ⁵⁶Fe nuclei of momentum 2.5 GeV/c per nucleon and photoemulsion nuclei is measured. For semicentral collisions at impact-parameter values in the range 0.12 ≤ b/b_max ≤ 0.70, charged fragments and relativistic particles are predominantly emitted in the direction orthogonal to the nuclear-reaction plane. The azimuthal-asymmetry parameter P₂ for fragments whose charge numbers are Z = 1, 2 and Z ≥ 3 takes values of, respectively, ?0.192±0.057, ?0.28±0.07, and ?0.39±0.12. Evaporated b particles have an isotropic azimuthal distribution.     

Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

Special features of the <Emphasis Type="Italic">K</Emphasis> = 0 channel in nuclear fission

The opinion that the K = 0 fission channel is completely closed if the spin J and the parity π of the nucleus undergoing fission do not satisfy the condition (?1) ^J = π is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and π values such that they satisfy the condition (?1) ^J = π. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.     

Nucleon-content effect on the fission lifetime of excited nuclei

It was shown previously that the fission lifetime of a nucleus excited to about 100 MeV depends strongly and nonmonotonically on the initial value of its angular momentum L ₀. This result was obtained on the basis of a refined version of the combined dynamical and statistical model. The present study is devoted to a theoretical analysis of the dependence of the fission time on the nucleonic composition of the nucleus involved. The respective calculations were performed within the same model. The dependence of the average fission time 〈t _f 〉 on the initial fissility parameter (Z ²/A)₀ appears to be of a resonance type and is similar to its dependence on L ₀. This dependence of the average fission time on (Z ²/A)₀ stems both from statistical calculations and from a dynamical simulation of the fission mode with allowance for friction. The conditions under which the average fission time reaches a maximum are specified. The dependence of the average fission time on (Z ²/A)₀ remains nonmonotonic in the fusion-fission reaction as well, in which case the distribution of compound nuclei with respect to the initial angular momentum is broad.     

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.