Muon addition to nitrogen,oxygen and other atoms: Considerations for level crossing resonance studies

The purpose of this note is to examine the conditions under which muon level crossing resonance with quadrupolar nuclei may be used to characterise the elusive diamagnetic fraction which is formed when positive muons are stopped in various media and associated chemically with the host molecules. A potential difficulty is identified for nuclei having integral spin, which may explain why cross polarisation to¹⁴N has not yet been detected. The general suitability of nuclei with half-integral spin (I≥3/2) is illustrated with the case of¹⁷O, and suggestions are made for future studies with other nuclei, including species such as molecular ions and defect complexes (muon-impurity pairs).     

Relativistic mean-field study on proton skins and proton halos in exotic nuclei

We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei ^26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of ²⁵Al and ²⁶P and found that the isovector potential from the p meson has an important effect on the differences.     

Proton-neutron interaction near closed shells

Odd-odd nuclei around double shell closures are a direct source of information on the proton-neutron interaction between valence nucleons. We have performed shell-model calculations for doubly odd nuclei close to ²⁰⁸Pb, ¹³²Sn, and ¹⁰⁰Sn using realistic effective interactions derived from the CD-Bonn nucleon-nucleon potential. The calculated results are compared with the available experimental data, attention being focused on particle-hole and particle-particle multiplets. While good agreement is obtained for all the nuclei considered, a detailed analysis of the matrix elements of the effective interaction shows that a stronger core-polarization contribution seems to be needed in the particle-particle case.     

Synthesis of heavy and superheavy elements by reactions of massive nuclei

By comparing theoretical and experimental excitation functions of evaporation residues resulting from the same compound nucleus or heavy and superheavy nuclei, it is possible to understand the effect of the entrance channel and the shell structure of reacting nuclei on the fusion mechanism. The competition of complete fusion with the quasifission process is strongly related to the intrinsic fusion barrier B _fus ^* and the quasifission barrier B _qf as well as the size of the well in the nucleus-nucleus potential. In our calculations of the excitation functions for capture, fusion, and evaporation residues, we use the relevant variables such as mass asymmetry of nuclei in the entrance channel, potential energy surface, driving potential, spin distribution, and surviving probability of compound nucleus that are responsible for the mechanism of the fusion-fission process. As a result, we obtain a beam energy window for the capture of the nuclei before the system fuses and the Γ_n/Γ_f ratio at each step along the deexcitation cascade of the compound nucleus. Calculations performed in the framework of the model taking into account the nuclear shell effect and shape of colliding nuclei allow us to reach useful conclusions about the mechanism of the fusion-fission process and the production of the evaporation residues. We analyze the ⁴⁰Ar + ¹⁷⁶Hf, ⁸⁶Kr + ¹³⁰Xe, and ¹²⁴Sn + ⁹²Zr reactions leading to ²¹⁶Th*; the ³²S + ¹⁸²W and ⁶⁰Ni + ¹⁵⁴Sm reactions leading to ²¹⁴Th*; the ⁴⁸Ca + ²⁴⁸Cm reaction leading to the ²⁹⁶116 compound nucleus; and the ⁴⁸Ca + ²⁴⁹Cf reaction leading to the ²⁹⁷118 compound nucleus.     

Shell-model structure of exotic nuclei beyond <Superscript>132</Superscript>Sn

We report on a study of exotic nuclei around doubly magic ¹³²Sn in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the bare potential is renormalized by constructing a smooth low-momentum potential, V_low-k, that is used directly as input for the calculation of the effective interaction. In this paper we focus attention on the nuclei ¹³⁴Sn and ¹³⁵Sb which, with an N/Z ratio of 1.68 and 1.65, respectively, are at present the most exotic nuclei beyond ¹³²Sn for which information exists on excited states. Comparison shows that the calculated results for both nuclei are in very good agreement with the experimental data. We present our predictions of the hitherto unknown spectrum of ¹³⁶Sn.     

A Systematic Study on 1neutron and 2neutron Halo Nuclei Using Coulomb and Nuclear Proximity Potential

The halo-structure of a nucleus is analyzed on the basis of potential energy consideration and separation energy calculations and thereby characterized a nucleus as a halo nucleus. The separation energy analysis showed that ¹¹Be, ¹⁴B, ^{15, 17, 19}C, ²²N, ²³O, ^{24, 26}F, and ²⁹Ne are 1n-halo nuclei since the 1n separation energy S(n) is the lowest and ^{6, 8}He, ¹¹Li, ¹⁴Be, ¹⁷B, ²²C, and ²⁹F are 2n-halo candidates as 2n separation energy S(2n) is the lowest. The potential energy calculations are consistent with the predictions based on separation energy calculations except for ¹²Be, ¹⁹B, and ²⁷F which can be considered as 2n-halo candidates by potential energy consideration. Also, a discrepancy is noticed in the case of the proposed 2n-halo ⁸He and ¹⁷B nuclei. Further, the possibility of emitting halo nucleus via heavy particle decay of heavy nuclei, within the range 82?≤?Z?≤?102, has been studied using the Coulomb and proximity potential model (CPPM). It is observed that the probability of emission of a halo nucleus is lower than that of a normal cluster Nevertheless, there is a finite chance of emission of a halo nucleus in the decay of a heavy nucleus.     

Fluorine NMR in Zirconium,Hafnium and Thorium Tetrafluorides and f-Orbital Contribution to Interatomic Bonds

Previously¹ we have observed a ¹⁹ NMR asymmetric line in polycrystalline ThF₄ in the 6–9 kOe fields, which was ascribed to the anisotropy of the ¹⁹F nuclei screening constant. However, the accepted interpretation in the case of a powder sample is not the only possible one, since in the presence of chemically or structurally non-equivalent fluorine atom groups spectrum asymmetry may also arise on account of the difference in the nuclei magnetic screening constants due to non-equivalent positions. This dilemma in the case of polycrystalline samples may be solved only when recording spectra in the highest fields. Non-equivalence of the nuclei may lead, to a split of the NMR spectrum into components, corresponding to the various positions. When spectrum asymmetry is due to the anisotropy of the screening constant, field strength rise may but lead to an increase of the total spectrum width, its shape remaining unaltered.     

Coulomb-assisted hybrid bound states of ∑− in medium nuclei populated by K− absorption at rest

To seek for a possible way to determine ∑⁻-nuclear interactions even in the case of a shallow nuclear potential and/or a strong ∑-Λ conversion, theoretical discussions are given on the formation of Coulomb-assisted hybrid bound states of ∑⁻ in nuclei, where the short-range strongly absorptive potential coexists with the long-range Coulomb potential. Bound states of hybrid character of medium widths are predicted, which can well be populated in (stopped K⁻, π⁺) reactions.     

Role of thermal fluctuations in the damping of the giant dipole resonance of spherical and deformed nuclei: 90Zr and 164Er

We study the damping width of the giant dipole resonance (GDR) built on the ground state and on excited states of ⁹⁰Zr, which is spherical at zero spin and temperature, and ¹⁶⁴Er which is deformed. Neither of these nuclei changes appreciably their equilibrium shape when excited. Nonetheless, fluctuations due to finite temperature produce a marked increase in the width of the GDR of ⁹⁰Zr, leaving essentially unchanged that of ¹⁶⁴Er. This is because in the case of deformed nuclei thermal fluctuations imply the sampling of both larger and smaller deformations around the equilibrium shape, while spherical nuclei can only feel larger distortions. In spite of the stability of the GDR of ¹⁶⁴Er, the angular distribution of the associated γ-rays is strongly affected by the temperature.     

Multichannel nuclear reactions involving light neutron-rich nuclei: Microscopic approach

The influence of the Pauli exclusion principle on the relative motion of light neutron-rich nuclei in their collision is investigated within the microscopicmethod using as an example ¹¹Be + n and ¹⁰Be + ² n nuclear reactions, as well as ³ n + n and ² n + ² n reactions. Antisymmetrization effects related to the kinetic and potential energy of the relative motion of colliding nuclei are analyzed. The influence of the Pauli exclusion principle on the kinetic energy of the relative motion of the ¹¹Be nucleus and a neutron is shown to result in their attraction. The same phenomenon is observed for the case of the ³ n + n cluster system. The strength of such attraction is high enough to ensure the existence of a bound state in the ¹²Be nucleus and a low-energy resonance in the tetraneutron. The conclusion is drawn that, for a resonance state in the ⁴ n system to exist, the value of the oscillator length must be large enough. It is shown also that increasing the oscillator length results in depression of the cluster-cluster potential. The text was submitted by the authors in English.     

Reactions involving loosely bound cluster nuclei: Heavy ions and new technologies

Experimental results on excitation functions for complete-fusion and transfer reactions in the interaction of ⁶He and ^6,8,9Li nuclei with various target nuclei are presented. Data on fusion-reaction cross sections in the case of ⁶He differ strongly from the predictions of the statistical model. A strong enhancement of the cross section at barrier energies is observed for this reaction channel. Also, an increase in the cross sections for neutron-transfer reactions (in the case of ⁶He and ^8,9Li beams) and deuteron-transfer reactions (in the case of ⁶Li) is observed in the deep-subbarrier energy region. The results are discussed from the point of view of the effect of the cluster structure of nuclei on the probability of interaction at barrier energies. The results of employing heavy-ion beams in new technologies are presented.     

Allowance for the shell structure of colliding nuclei in the fusion-fission process

The motion of two nuclei toward each other in fusion-fission reactions is considered. The state of the system of interacting nuclei is specified in terms of three collective coordinates (parameters). These are the distance between the centers of mass of the nuclei and the deformation parameter for each of them (the nose-to-nose orientation of the nuclei is assumed). The evolution of collective degrees of freedom of the system is described by Langevin equations. The energies of the Coulomb and nuclear (Gross-Kalinovsky potential) interactions of nuclei are taken into account in the potential energy of the system along with the deformation energy of each nucleus with allowance for shell effects. The motion of nuclei toward each other are calculated for two reaction types: reactions involving nuclei that are deformed (₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄²⁰⁰Po) and those that are spherical (₈₂²⁰⁸Pb + ₈¹⁸O → ₉₀²²⁶Th) in the ground state. It is shown that the shell structure of interacting nuclei affects not only the fusion process as a whole (fusionbarrier height and initial-reaction-energy dependence of the probability that the nuclei involved touch each other) but also the processes occurring in each nucleus individually (shape of the nuclei and their excitation energies at the point of touching).     

Theoretical studies of proton capture reactions in A～25 proton-rich nuclei

The direct proton capture and resonance proton capture properties of stellar reactions 22Mg(p,γ)23Al and 26Si(p,γ)27P are studied by employing a mean-field potential obtained from the Skyrme-Hartree-Fock(SHF) model.Calculations with the SHF potential reproduce well the loosely-bound structure of the ground states as well as the widths of the resonant states in these nuclei.With the obtained potential we estimate the reaction rates of direct proton capture and resonance proton capture to nuclei 23Al and 27P....     

On the total binding energy of spherical nuclei

The total binding energy of nuclei is determined by means of many-body field theory. The problem is then reduced to finding the energy-dependent average potential (mass operator) and solving the single-particle equations of motion. Such a potential can be established phenomenologically by using data on low excitations and reactions knocking out nucleons from deep “hole” levels. Calculations of the total binding energy of the nuclei ¹⁶O, ⁴⁰Ca and ⁵⁸Ni with this potential are in satisfactory agreement with experiment.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

α-Decay half-lives, α-capture cross sections, and α-nucleous interaction

The expression for the α-nuclear potential was found. This potential describes the α-decay half-lives for the ground states of nuclei and the α-particle capture cross sections for ⁴⁰Ca, ⁴⁴Ca, ⁵⁹Co, ²⁰⁸Pb, and ²⁰⁹Bi nuclei well. The potential was used to calculate the probabilities of α-transitions from the ground states of parent nuclei to different excited states of daughter nuclei. Simple analytical relations for calculating α-decay half-lives for transitions between the ground states of nuclei are determined.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Formation of heavy and superheavy elements by reactions with massive nuclei

The effects of the entrance channel and shell structure on the experimental evaporation residues have been studied by analyzing the ³²S + ¹⁸²W, ⁴⁸Ti + ¹⁶⁶Er and ⁶⁰Ni + ¹⁵⁴Sm reactions leading to ²¹⁴Th^*; the ⁴⁰Ar + ¹⁸¹Ta reaction leading to ²²¹Pa^*; the ⁴⁸Ca + ²⁴³Am, ²⁴⁸Cm, ²⁴⁹Cf reactions leading to the ²⁹¹115, ²⁹⁶116 and ²⁹⁷118 superheavy compound nuclei, respectively. The fusion mechanism and the formation of evaporation residues of heavy and superheavy nuclei have been studied. In calculations of the excitation functions for capture, fusion and evaporation residues we used such characteristics as mass asymmetry of nuclei in the entrance channel, binding energies and shape of colliding nuclei, potential energy surface, driving potential, partial-fusion cross-sections and survival probability of the compound nucleus, ratio at each step along the de-excitation cascade of the compound nucleus. The calculations have allowed us to make useful conclusions about the mechanism of the fusion-fission process, which is in competition with the quasifission process, and the production of the evaporation residues.Received: 22 April 2003, Revised: 26 June 2003, Published online: 18 December 2003PACS: 25.70.Gh Compound nucleus - 25.70.-z Low and intermediate energy heavy-ion reactions - 27.80. + w - 27.90. + b      

Mass-surface predictions near the doubly magic nuclide 78Ni

The mass surface of nuclei close to the doubly magic nuclide ⁷⁸Ni is calculated by two methods. The first relies on the multiparticle shell model based on an effective interaction and a mean nuclear potential. The second employs the concept of so-called “magic crosses” and enables us to determine the masses of odd-odd nuclei close to ⁷⁸Ni by using similarity of the shell structure and neutron-proton interaction in the region of nuclei under consideration and in the region of heavy magic nuclides. The energies of the separation of one and two neutrons from nuclei close to ⁷⁸Ni and the energies of the β decay of these nuclei—recall that these quantities of astrophysical interest—are presented.     

Medium effects in ΛK~+ pair production by 2.83 GeV protons on nuclei

We study ΛK~+ pair production in the interaction of protons of 2.83 GeV kinetic energy with C, Cu,Ag, and Au target nuclei in the framework of the nuclear spectral function approach for incoherent primary proton–nucleon and secondary pion–nucleon production processes, and processes associated with the creation of intermediate Σ~0K~+ pairs. The approach accounts for the initial proton and final Λ hyperon absorption, final K~+ meson distortion in nuclei, target nucleon binding, and Fermi motion, as well as nuclear mean-field potential effects on these processes.We calculate the Λ momentum dependence of the absolute ΛK~+ yield from the target nuclei considered, in the kinematical conditions of the ANKE experiment, performed at COSY, within the different scenarios for the Λ-nucleus effective scalar potential. We show that the above observable is appreciably sensitive to this potential in the low-momentum region. Therefore, direct comparison of the results of our calculations with the data from the ANKE-at-COSY experiment can help to determine the above potential at finite momenta. We also demonstrate that the two-step pion–nucleon production channels dominate in the low-momentum ΛK~+ production in the chosen kinematics and, therefore, they have to be taken into account in the analysis of these data.