Phonon–particle coupling effects in odd–even mass differences of semi-magic nuclei

A method to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd–even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the corresponding value of 0.333 MeV for the Skyrme EDF HFB-17, which belongs to a family of Skyrme EDFs with the highest overall accuracy in describing the nuclear masses. Account for the PC corrections induced by the low-laying phonons 2 ₁ ⁺ and 3 ₁ ^- significantly diminishes the deviation of the theory from the data till 0.218 MeV.     

On the maximum in the differential cross sections of the F + H2 reaction in the region of small scattering angles

By means of quantum mechanical simulation of the reaction F + H₂(v = 0; j = 0, 1, 2) → H + HF(v′, j′) on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol, we have analyzed interference of the “partial waves” corresponding to different values of the total angular momentum J. As the vibrational quantum number v′ of the HF(v′, j′) product increases, the interference for the HF forward scattering becomes noticeably more constructive. This is probably the reason for the maximum in the angular distributions of the HF(v′= 3) molecules at small scattering angles that was discovered experimentally by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985) at the same collision energies. We have also determined the intervals of J values most effective for forward scattering of the HF(v′, j′) molecules.     

Dynamics of α-clusters in N = Z nuclei

The systematics for binding energies per α-particle in N = Z nuclei, E _Bα/N _α, are studied up to ¹⁶⁴Pb. It is shown that, although a geometrical model can be used to explain the systematics for light nuclei, the binding energy per α-particle exhibits structures which are due to the well-known shells of the mean field of nucleons in nuclei. The overall dependence of E _Bα/N _α on N _α in N = Z nuclei (for the ground-state masses) can be described in a liquid-drop model of α-particles. Conditions for a phase change with the formation of an α-particle condensate, a dilute Bose gas in excited compound nuclei are discussed for E _Bα/N _α = 0, at the thresholds. This is achieved when the binding energy per nucleon in nuclei is equal to or smaller than in the α-cluster. At somewhat smaller excitation energies the appearance of a Bose gas with a closed-shell core (N = Z, e.g. of ⁴⁰Ca) is proposed within the same concept. The experimental observation of the decay of such condensed α-particle states is proposed with the coherent emission of several correlated α-particles not described by the Hauser-Feshbach approach for compound-nucleus decay. This decay will be observed by the emission of unbound resonances in the form of ⁸Be and ¹²C ^* (0⁺ ₂) clusters.     

Towards a Skyrme–Hartree–Fock–Bogolyubov Mass Formula

In this work, we explain our astrophysical motivations for deriving a mass formula based on HFB calculations with a Skyrme interaction. We give an overview of existing mass formulae and present briefly the last HF+BCS mass formula [1]. The Skyrme force MSk7 [1] is considered in the study of shell effects at N=82, in the neutron-rich region far from stability, within the HFB and HF+BCS theories, and compared with results obtained using the forces SkP^δ and SkP^δρ [2]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Asymmetric nuclear matter and Skyrme potential

The binding energy, symmetry energy, pressure, incompressibility, and the velocity of sound are calculated for asymmetric nuclear matter using Skyrme interaction SkO’. The behavior of these physical quantities is studied for different values of the asymmetry parameter α _τ , the density ρ, and the temperature T. Good agreement is obtained in comparison with previous theoretical estimates and experimental data. The text was submitted by the authors in English.     

π−-meson and nucleon yields from light targets irradiated by deuterium and tritium nuclei beams at energies of 1 GeV/nucleon

In this paper, we present a model of calculation with respect to the interactions of high-energy nuclei with matter. Based on this model, we obtain results on energy and angular spectra of the n- and π⁻-particles produced in collisions of deuterium and tritium nuclei at energiesT _d=1 GeV/nucleon with light targets such as Li, Be. We have also estimated the production yields of neutrons and π⁻-mesons in targets of various radii, as well as mean energies of these these particles. Summarizing, we find that the lithium target of radiusR=10−12 cm for which the energy cost ε_π to produce one π⁻-meson is estimated as 6.7 GeV/π for a d-beam and 5.3 GeV/π for a t-beam is the most preferred pion-production target.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

Determination of low-energy parameters of neutron-proton scattering in the the shape-parameter approximation from present-day experimental data

On the basis of the total cross sections for neutron-proton scattering in the region of laboratory energies below 150 keV, the value of σ₀ = 20.4288(146) b was obtained for the total cross sections for neutron-proton scattering at zero energy. This value is in very good agreement with the experimental cross sections obtained by Houke and Hurst, but it is at odds with Dilg’s experimental cross section. By using the value that we found for σ₀ and the experimental values of the neutron-proton coherent scattering length f, the deuteron binding energy ɛ _t , the deuteron effective radius ρ _t (−ɛ _t , −ɛ _t ), and the total cross section in the region of energies below 5 MeV, the following values were found in the shape-parameter approximation for the low-energy parameters of neutron-proton scattering in the spin-triplet and spin-singlet states: a _t = 5.4114(27) fm, r _0t = 1.7606(35) fm, v _2t = 0.157 fm³, a _s = −23.7154(80) fm, r _0s = 2.706(67) fm, and v _2s = 0.491 fm³.     

Near perpendicular propagation of ion cyclotron modes in a deuterium-hydrogen-oxygen fusion plasma

A dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave has been derived in a fusion plasma that has deuterium as a majority species, hydrogen as a minority species and fully ionized oxygen as an impurity constituent; all being modelled by loss cone distribution functions. The wave has a frequencyω around the deuterium ion gyrofrequency-Ω_D and a wavelength much longer than its Larmor radiusγ _LD(k _⊥ γ _LD<1); the plasma itself being characterized by large ion plasma frequencies (ω _PD ² >Ω _D ² ). Two modes, a low frequency (LF) and a high frequency (HF) mode of opposite electrical energy can propagate in the plasma; the instabilities that arise are thus due to an interaction of modes of opposite energies. We find that while hydrogen tends to destabilize the plasma, the impurity oxygen ions have the reverse effect. Also the plasma is most stable when the ratios of the perpendicular components of oxygen-to-deuterium and hydrogen-to-deuterium temperatures are kept low. Detailed studies of the wave propagation characteristics and energy reveal the close resemblance of a loss cone plasma containing oxygen to a stable Maxwellian plasma in regard to wave stability, propagation and energy.     

Vibrational mode assignments for bundled single-wall carbon nanotubes using Raman spectroscopy at different excitation energies

This study establishes a generic fitting approach to assignment of nanotube chiralities based on radial breathing mode frequencies (ω _RBM) of SWCNTs in as-produced bundles. Four laser lines with energies of 2.62 eV, 2.33 eV, 1.88 eV and 1.58 eV were employed. The observed RBM frequencies, ω _RBM, were plotted as a function of the possible diameters, d, as identified from the so-called Kataura plot and reported values of the parameters A and B, where ω _RBM=A/d+B, assuming that SWCNTs resonant at the respective laser frequencies dominate the spectrum. The refined values of A and B, obtained by the best fit of a linear regression between ω _RBM and 1/d, were found to vary significantly for different laser frequencies. This variation is interpreted in terms of the differences in electronic properties of SWCNTs resonant at different frequencies. The assigned nanotubes match well with those identified in the Kataura plot, falling within a resonant line width of ±0.2 eV of the respective laser lines.     

The Skyrme-TQRPA calculations of electron capture on hot nuclei in pre-supernova environment

We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, ⁵⁶Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT₊ transitions which dominate electron capture at E _e ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.     

Deformation properties of lead isotopes

The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF⁰ Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, ¹⁸⁰Pb and ¹⁸⁴Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF⁰ functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF⁰ functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF⁰ functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A_drip²ⁿ = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A_drip²ⁿ(SKM*) = 272.     

Investigation of the role of the projectile-target orientation angles on the evaporation residue production

The measured yield of evaporation residues in reactions with massive nuclei have been well reproduced by using the partial fusion and quasifission cross sections obtained in the dinuclear-system model. The influence of the orientation angles of the projectile- and target-nucleus symmetry axes relative to the beam direction on the production of the evaporation residues is investigated for the ⁴⁸Ca + ¹⁵⁴Sm reaction as a function of the beam energy. At the low beam energies only the orientation angles close to αP = 30° (projectile) and αP = 0°–15° (target) can contribute to the formation of evaporation residues. At large beam energies (about E _c.m. = 140–180 MeV) the collisions at all values of orientation angles αP and α _T of reactants can contribute to the evaporation residue cross section which ranges between 10–100 mb, while at E _c.m. > 185 MeV the evaporation residue cross section ranges between 0.1–1 mb because the fission barrier for the compound nucleus decreases by increasing its excitation energy and angular momentum.     

Combined model of photonucleon reactions

A combination of the semimicroscopic, exciton, and evaporation models is used to describe photonucleon reactions induced in medium-mass and heavy nuclei by photons of energy below the mesonproduction threshold. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance (GDR) at energies in the range E _γ ≲ 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ≳ 40 MeV. The densities of particle-hole states appearing in the exciton model are calculated on the basis of the Fermi gas model. Our combined model takes into account the multiparticle emission of preequilibrium particles. The influence of isospin conservation and collective phenomena on photonucleon emission by giant dipole resonances is considered. The combined model is used to describe cross sections for photonucleon reactions proceeding on the ^40,48Ca, ⁹⁰Zr, ¹³⁹La, ¹⁴²Nd, and ¹⁸¹Ta nuclei, as well as difference (E _γmax = 85–55 MeV) bremsstrahlung photoneutron spectra for the ⁶³Cu, ¹¹⁵In, ¹¹⁸Sn, ¹⁸¹Ta, ²⁰⁷Pb, ²⁰⁹Bi, and ²³⁵U nuclei and bremsstrahlung photoproton spectra for the ⁹⁰Zr nucleus at the energies of E _γmax = 22, 25, and 34 MeV.     

Atmospheric gamma rays in the energy region 40–1000 GeV

A large stack of lead-emulsion sandwich detector assembly was flown over Hyderabad, India. High energy gamma rays at the float altitude were unambiguously identified from the cascades they induced, and their energies reliably determined by improved methods. From an analysis of 163 gamma rays of energy ≳ 30 GeV, it is found that the differential energy spectrum is represented by the power lawJ _r (E)= 129·4E ^{−2·62±0·12} photons m⁻² sr⁻¹sec⁻¹ GeV⁻¹ at an effective atmospheric depth of 14·3 g cm⁻²; this is the first reliable balloon measurement of atmospheric gamma rays in the energy range 40–1000 GeV. After correcting for the gamma rays radiated by the primary cosmic ray electrons, the production spectrum of gamma rays, resulting from the collisions of cosmic ray nuclei with air nuclei, at the top of the atmosphere isP _r (E, 0)=8·2 × 10⁻⁴ E^2.60±0.09 photons g⁻¹sr⁻¹sec⁻¹ GeV⁻¹. The atmospheric propagation of the electromagnetic component due to the cascade process is also derived from the gamma ray production spectrum.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

Intrinsic frame inverse mass tensor as a function of <Emphasis Type="Italic">β</Emphasis> and <Emphasis Type="Italic">γ</Emphasis> in the Bohr Hamiltonian

Analytical expressions are derived for the components of the intrinsic frame inverse mass tensor of the Bohr Hamiltonian. These expressions contain parameters which are determined by the experimental data on the B(E2)’s and the excitation energies of the low-lying collective states. It is shown that the nondiagonal component of the intrinsic frame mass tensor has a small effect on the collective motion. It is shown also that the values of the B _ββ , B _γγ and the rotational mass coefficientB ₁ differ in the well-deformed nuclei by factor 3 or more.     

Quadrupole strength function and core polarization in drip line nuclei

Using the self-consistent Hartree-Fock calculation plus RPA with Skyrme interactions, the RPA quadrupole strength function is estimated in the coordinate space, including simulataneously both the isoscalar and the isovector correlation. We discuss the result of the isoscalar, the isovector and the electric quadrupole polarization of the Ca-isotopes from the proton drip line towards the neutron drip line. We study also the comparison of the polarizations in the A = 48 mirror nuclei, ₂₈⁴⁸Ni₂₀ and ₂₀⁴⁸Ca₂₈, and the dependence of the polarizations of ₈²⁸O₂₀ on various Skyrme interactions.