Calculations of the β-decay half-lives of neutron-deficient nuclei

In this work,β~+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation(QRPA),where neutron-neutron,proton-proton and neutron-proton(np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov(HFB) transformation.In addition to the pairing interaction,the Br¨uckner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions.Calculations are performed for even-even proton-rich isotopes ranging from Z =24 to Z =34.It is found that the np pairing interaction plays a significant role inβ-decay for some nuclei far from stability.Compared with other theoretical calculations,our calculations show good agreement with the available experimental data.Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.     

A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

Emission of helium nuclei in heavy ion interactions at energies ≧ 100 MeV/nucleon

The energy and angular distributions of helium particles emitted in interactions between nuclei in the cosmic radiation and nuclei in photoemulsions at energies ≧ 100 MeV/nucleon have been studied. The data obtained is impossible to interpret on the basis of a statistical decay of excited nuclei. For example, it is found that more than 28% of the helium nuclei are emitted in processes different from simple evaporation. The differential energy distribution of the helium nuclei in the energy interval (40–200) MeV can be represented by the relationN(E)dE=constE ^?a dE, wherea≈1.2. The large spread in angles and energies of the fast helium particles emitted in heavy ion interactions can to a certain degree be understood, if it is assumed that interactions between nucleons and clusters of nucleons occur.     

Pairing with a delta interaction in the energy density nuclear mass formula

The variations of the average pairing strength in the (N, Z) plane are studied with a δ-interaction in the frame of the self-consistent energy density formalism. It is found that the same δ-interaction with constant strength can be used for protons and neutrons in spherical nuclei near the stability line. This interaction is used to study the extrapolation of the average pairing strength to deformed nuclei, to the superheavy region and to the regions of the drip lines. The consequences of the results for the stability of superheavy nuclei and for magic numbers far from the stability region are examined.     

Level-density parameters in the back-shifted Fermi gas model

The parameters a and δ_eff appearing in the back-shifted Fermi gas model are determined for about 3000 nuclei on the basis of modern estimated experimental data and the proposed systematics. For 272 of these nuclei, the parameters are deduced from experimental data on the cumulative numbers of low-lying levels and on mean spacings between S-wave neutron resonances at the neutron binding energy in the nuclei. For 952 nuclei, the parameter δ_eff is calculated by using the cumulative numbers of low-lying levels and values of the parameter a that were obtained via an interpolation from the points corresponding to the aforementioned 272 nuclei. For the remaining nuclei, the parameters a and δ_eff are obtained on the basis of the proposed systematics. An expression is constructed for taking into account the damping of shell effects with increasing excitation energy of nuclei. The results are compared with those from other studies.     

On search and identification of relatively short-lived superheavy nuclei (<Emphasis Type="Italic">Z</Emphasis> ≥ 110) by fossil track studies of meteoritic and lunar olivine crystals

The main goal of the present work is the search for and identification of relatively stable nuclei of superheavy elements (SHE) (Z>110) in galactic matter by fossil track study of nonconducting crystals from the surface of meteorites and rocks from the lunar regolith. Nuclei of SHE are thought to be the products of nucleosynthesis in explosive processes in our Galaxy (supernova r-process nucleosynthesis and, especially, neutron-star formation, etc.). When accelerated to relativistic energies in the Galaxy, they can produce extended trails of damage in nonconducting extraterrestrial crystals. The lifetime of such SHE in galactic cosmic rays will range from 10³ to 10⁷ yr to be registered in extraterrestrial crystals. To search for and to identify the superheavy nuclei in the galactic cosmic rays, it was proposed to use the ability of nonconducting extraterrestrial crystals such as olivines, pyroxenes, and feldspars to detect and to store for many millions of years the trails of damage produced by fast Z≥23 nuclei coming to rest in the crystalline lattice. The track lengths of fast Z≥23 nuclei are directly proportional to Z² of these nuclei. The nuclei of SHE produce, when coming to rest in a crystal volume, tracks that are a factor of 1.6–1.8 longer than the tracks due to cosmic-ray Th and U nuclei. To identify the tracks due to superheavy nuclei, calibrations of the same crystals were performed with accelerated Au, Pb, and U nuclei. For visualization of these tracks inside the crystal volume, proper controlled annealing and chemical etching procedures were developed. Since 1980, fossil tracks due to Th and U nuclei have observed and unambiguously identified (1988) by subsequent calibrations of the olivine crystals with accelerated U, Au, and Pb ions. The number of tracks of Th and U nuclei measured in olivine crystals totaled more than 1600, as compared with the prior 30 events. The other approach to identifying SHE in nature is to search for tracks in phosphate crystals from spontaneous fission of Z ≥ 110 nuclei; these produce two-prong and three-prong fission fragment tracks and differ significantly from the tracks from spontaneous fission of ²³⁸U and ²⁴⁴Pu nuclei. Extraterrestrial phosphate crystals of lunar and meteoritic origin will be investigated. Such SHE nuclei can survive in crystals of extraterrestrial rocks and produce spontaneous fission tracks, if the lifetime is more than 5×10⁷ yr.     

Detecting galactic cosmic ray transuranium nuclei in olivine crystals from meteorites

Results from the experimental search for and identification of tracks from the superheavy and transuranium nuclei of galactic cosmic rays in pallacite olivine crystals, conducted as part of project OLIMPIA [1], are presented. To date, 170 crystals from Marjalahti and Eagle Station pallacites have been processed and 6800 tracks corresponding to nuclei with charges Z > 55 have been found; 45 of these are from nuclei with charges of 88 < Z < 92 and three super-long ones were produced by nuclei with Z > 105. The charge of one of these nuclei is estimated in the first approximation as Z = 119(+10,?6). Our data confirm the hypothesis of islands of stability for natural trans-Fermi nuclei.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

A study of the (α, t) reaction on 19F, 27Al, 51V and 59Co

The angular distributions of tritons from the (α, t) reaction on ¹⁹F, ²⁷Al, ⁵¹V and ⁵⁹Co nuclei corresponding to the (0⁺) ground states and (2⁺) excited states in the final nuclei have been measured in the angular range between 15° and 170° at α-particle energies of 25 MeV. For reactions on ²⁷Al and ⁵¹V nuclei, the differential excitation functions have also been obtained at different angles of outgoing tritons at E_α from 20 to 25 MeV. The experimental angular distributions are analysed by the DWBA approximation on the assumption of a nucleon stripping mechanism. The analyses of the present results and the data obtained earlier for the (α, t) reaction on the 1 p shell nuclei, A ? 30, reveal that the distinguishing feature of the reaction under study is the presence of backward angle peaks in the reaction cross section, which appear to be associated with exchange processes. For the (α, t) reaction on the heavier nuclei (A > 30), the dominant mechanism is nucleon stripping.     

Influence of a monatomic step on the collective behaviour of gold nuclei

The radial distribution of gold nuclei obtained by evaporation in UHV along a monatomic step onto a (100)KCl substrate is measured and analysed in terms of parameters such as the mean density ρ₀ and the mean diameter 〈d〉 of nuclei. Some results of numerical calculations are also given, from which the forces between pairs of nuclei may be evaluated quantitatively.     

A shell-model description of 0+ intruder states in even-even nuclei

Starting from the nuclear shell structure in medium-heavy and heavy nuclei, the excitation energy for low-lying 0⁺ intruder states is studied. Taking as a simplified model two particle-two hole (2p-2h) excitations across closed shells, the effects of the pairing and the proton-neutron (monopole and quadrupole component) residual interaction on the unperturbed energies are calculated. Application to major closed-shell (fZ = 50, Z = 82) and to subshell (Z = 40, Z = 64) regions is performed. We especially concentrate on 0⁺ intruder states in the even-even Pb nuclei.     

Peninsula of neutron stability of nuclei in the neighborhood of neutron magic number N = 126

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.     

The salient features of charge density distributions of medium and heavy even-even nuclei determined from a systematic analysis of elastic electron scattering form factors

All available information on charge distributions of even-even nuclei is analysed systematically. For medium and heavy nuclei five general features of ρ(r) are investigated: (i) The extension for which we discuss several different definitions. The measured extension together with experimental binding energies allows a determination of nuclear compressibility within the framework of the droplet model, the resulting value being K = 165 ± 10 MeV. (ii) The surface thickness. Here too, several definitions are discussed. A close relationship between the surface thickness and binding energies is demonstrated. (iii) The average slope in the inner part of the nucleus. A method is formulated to separate this slope from the oscillations observed. All nuclei show a positive slope of comparable size. (iv) The oscillations on ρ(r). They are related to an abrupt breakdown in the form factor around q = 2.25 fm^?1.This effect seems to be closely related to the fact that ρ(r) is built up out of single particles, details however being unimportant, (v) The high-q components of the form factor are indicative for a scattering mechanism involving pairs of nucleons.     

Microscopic structure of nuclei from scattering through isobaric analogue resonances

Microscopic nuclear structure information that can be reached by proton scattering through isobaric analogue resonances (IAR) is discussed, mainly within the framework of weak-coupling. The concept of isospin for unbound states is examined. A critical evaluation of the methods for extracting nuclear structure information from the experimental results (such as excitation functions, angular distributions, etc.) is given. The mass regions that are studied in detail are the Pb-region and the N = 82 neutron single-closed shell nuclei. Attention is given to the comparison between weak-coupling calculations and experimental results supporting this concept in many nuclei. Level schemes as well as proton partial decay widths and angular distributions have been calculated and compared with the existing data concerning the proton decay of IAR. The concept of generalized neutron particle-hole (GNPH) state is introduced and its occurence extensively discussed within the Pb-region and N = 82 nuclei.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Statistical spectroscopy for nuclei in the fp shell

Nuclei in the fp shell have been studied using the spectral averaging method. This was attempted with a view to provide a rather simple alternative to detailed microscopic calculations. We have considered a decomposition of the overall spectroscopic space (m particles in the fp shell) in terms of a spherical j-orbit, isospin, configuration-isospin and SU(4) isospin subspaces. Centroid energies and widths of these subspaces are evaluated and used to determine binding energies, low-energy spectra and fractional occupancy of j-orbits. We have also examined the extent of Wigner SU(4) symmetry mixing for nuclei in this shell. The ratio of binding energies of isobars suggested by Franzini and Radicati to test the validity of SU(4) symmetry is also evaluated from the calculated binding energies. Comparisons are made with microscopic calculations like the shell model and Hartree-Fock where available. We find that the distribution method is able to determine ground-state energies and spectra of nuclei very well despite the fact that the vector spaces are quite large. The SU(4) symmetry in the ground-state region of these nuclei is strongly mixed largely due to the single particle spin-orbit coupling.     

Response function of superfluid nuclei and low-lying quadrupole vibrations

The response of superfluid spherical nuclei to an external quadrupole field is considered. The mixed (r,λ) representation technique is developed, being the generalization of the coordinate (r) representation for magic nuclei. The transition densities p^tr(r) are shown to possess sharp surface bumps of hydrodynamical nature and pronounced volume quantum components. The shapes of transition densities of 2⁺₂ states in some typical nonmagic nuclei are predicted.     

Topology of “white stars” in the relativistic fragmentation of light nuclei

Experimental observations of the multifragmentation of relativistic light nuclei by means of emulsions are surveyed. Events that belong to the type of “white stars” and in which the dissociation of relativistic nuclei is not accompanied by the production of mesons and target-nucleus fragments are considered. An almost complete suppression of the binary splitting of nuclei to fragments of charge in excess of two, Z > 2, is a feature peculiar to charge topology in the dissociation of Ne, Mg, Si, and S nuclei. An increase in the degree of nuclear fragmentation manifests itself in the growth of the multiplicity of singly and doubly charged fragments (Z = 1, 2) as the charge of the unexcited fragmenting-nucleus part (which is the main part) decreases. Features of the production of systems formed by extremely light nuclei α, d, and t are studied in the dissociation of the stable isotopes of Li, Be, B, C, N, and O to charged fragments. Manifestations of ³He clustering can be observed in “white stars” in the dissociation of neutron-deficient isotopes of Be, B, C, and N.     

Multiquark clusters in nuclei. distributions ofu- andd-quarks

Effects related to the possible admixture of multiquark (mainly 12q) clusters (bags) in nuclei are discussed. In particular the differencies in theu- andd-quark distributions inN≠Znuclei are considered. The quark distribution function is assumed to consist of two components: the nucleon component and the bag one (mainly the 12q-bag). The yields ofπ-mesons and nucleons into the backward hemisphere are governed mainly by the contribution of the bag component. It comes from the available data on theπ ⁺/π ^? andn/p ratios that thed-quarks in the bag component of nuclei withN>Z are “more soft” than theu-quarks in contrast to the situation in the nucleon component. The manifestation of the latter effect in theA-dependence of the ratio of structure functionsR=F _2A(x)/F _2D(x) is also discussed.