Possible mechanisms of fragmentation of 16O nuclei with a momentum of 4.5 GeV/c per nucleon in track emulsions

The angular distributions of doubly charged fragments of ¹⁶O nuclei having a momentum of 4.5 GeV/c per nucleon and interacting with track-emulsion nuclei were studied. The experimental angular distributions of doubly charged fragments of a ¹⁶O nucleus are not described by the statistical model of the fragmentation of nuclei. The possible channels of fragmentation of ¹⁶O nuclei may include ¹⁶O → 2⁸Be → 4α, ¹⁶O → ⁸Be +⁸ Be* → 4α, ¹⁶O → 2⁸Be* → 4α, ¹⁶O → α+¹²C, ¹⁶O → α +¹²C* → α + 3α, ¹⁶O → α +¹²C* → α + pα ⁷Li, ¹⁶O → α +¹²C* → α + 2⁶Li, ¹⁶O → α +¹²C* → α + pt2α, ¹⁶O → Li + B, and ¹⁶O → Li* + B*.     

Constrained variational calculations of closed shell nuclei with the reid potential

Lowest-order constrained variational calculations with harmonic oscillator wave functions are carried out for ⁴He, ¹⁶O, and ⁴⁰Ca nuclei with the Reid potential. The results obtained with this simple method are in very close agreement with those obtained by renormalized Brueckner-Hartree-Fock theory with orthogonalized plane wave intermediate states. The A-dependence of the difference between the experimental and calculated binding energies for A = 2, 3, 4, 16, 40 and ∞ can be explained by a three-body cluster term coming either from a wrong off-energy-shell behavior of the Reid potential or a three-body force. The calculated radii of ¹⁶O and ⁴⁰Ca are ≈ 10% too small, indicating that the Reid potential may not be very realistic.     

A quantal calculation of nucleon transfer contribution in nucleus-nucleus absorptive potential

We present here a model to obtain the quantum-mechanically defined particle-transfer flux in scattering between two heavy nuclei. This flux is calculated from the time-dependent single-particle wave functions in the field of two moving potential pockets. From the calculated flux, we obtain the absorptive potentials for ¹⁶O+⁴⁰Ca and ⁴⁰Ca+⁴⁰Ca, which compare favourably with phenomenological values. In contrast with other similar microscopic calculations, the present results show a weak energy dependence of the absorptive potential as has been observed in phenomenological analyses.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.     

Electric quadrupole and hexadecupole nuclear excitations from the perspectives of electron scattering and modern shell-model theory

Shell-model wave functions obtained from a complete, unified treatment of the structure of the positive parity states in nuclei between ¹⁶O and ⁴⁰Ca are used to calculate the features of inelastic electron scattering to 2+ and 4+ states in this region. These predictions of E2 and E4 form factors, and the corresponding elastic scattering predictions, are compared with the collected experimental data which are available on this topic. The dependence of the calculated results upon alternate models for single-nucleon wave functions and core-polarization transition densities is investigated, as is the consistency between the (e,e′) measurements and the analogous B(E2) measurements.     

Nuclear matter approach to the heavy-ion optical potential

An energy-dependent local potential for heavy-ion (HI) scattering is derived from Reid's softcore interaction using the Brueckner theory. The Bethe-Goldstone equation in momentum space is first solved with the outgoing boundary condition for two colliding systems of nuclear matter with the relative momentum K_r per nucleon. The Fermi distribution is assumed to consist of two spheres without double counting of their intersection separated by the relative momentum K_r. The angle-averaged Pauli projection function is given in the form of a one-dimensional integral. Secondly the optical potential for HI scattering is evaluated using the energy-density formalism. The energy density is calculated for two limiting cases: (i) the sudden approximation in which the spatial distribution of the two HI is described by an antisymmetrized cluster wave function, and (ii) the adiabatic limit represented by an antisymmetrized two-centre wave function. The complex HI potential is defined in terms of the energy density from nuclear matter so that both volume elements in the finite and the infinite systems have the same nucleon and kinetic energy density. This method is applied to the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O, and ⁴⁰Ca + ⁴⁰Ca potentials. The calculated results are compared with phenomenological potentials. Though in principle our approach can generate an imaginary part for the HI potential, the magnitude is too small. Reasons and possible improvements of this point are discussed.     

Time-Dependent Description of Incomplete Fusion of Nuclei and Cluster and Nucleon-Transfer Reactions

A numerical solution of the time-dependent Schrödinger equation is applied in studying the dynamics of incomplete fusion of nuclei and cluster- and nucleon-transfer reactions at energies near the Coulomb barrier. The evolution of wave functions for all nucleons is used to describe multineutron- and multiproton-transfer reactions in ⁴⁰Ca+¹²⁴Sn collisions. The results of the calculations are in satisfactory agreement with experimental data. The evolution of the alpha-cluster wave function in the ¹²C nucleus is used to calculate the incomplete-fusion cross section for the ¹²C+⁵¹V reaction. Agreement with experimental data for the (¹²C, α) and (¹²C, 2α) channels is attained.     

First observation of nuclear rainbow scattering in 16O + 40Ca system

Measurements of the differential cross section of the ¹⁶O + ⁴⁰Ca elastic scattering at the ¹⁶O energy 214 MeV were performed. For the first time, nuclear rainbow scattering in the ¹⁶O + ⁴⁰Ca system was observed. The analysis shows that the 45° minimum in the angular distribution could be identified as an Airy supernumerary one, probably, of the third order. It corresponds to a distance of closest approach of the colliding nuclei less than 3 fm. The text was submitted by the authors in English.     

Exploration of hyperfine interaction between constituent quarks via η productions

The elastic-scattering reaction ³⁶Ar + α was studied using the Thick Target Inverse Kinematics technique. Data were taken at a beam energy of 150 MeV in a reaction chamber filled with ⁴He gas, corresponding to the excitation region of 12–20 MeV in ⁴⁰Ca. Using a simplified R -matrix method of analysis energies, widths and spin assignments were obtained for 137 resonances. The structure is discussed within the concept of α-cluster structure in the quasi-continuum of ⁴⁰Ca and is compared to other nuclei in the same mass region.     

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, ⁶Li) reaction was studied at E_d = 54.25 MeV on the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative S_α were in agreement with those in the (p, pα) reaction at E_p = 100 and 157 MeV. The theoretical calculations of the relative S_α were in better agreement with the experimental data at higher energy than at the lower energies.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

Study of many-nucleon correlations in32S as a model for fragment shell effects in fission

The formation and break-up of substructures is studied in³²S as a calculable microscopic model for analogous long-range many-nucleon correlations in the fission of actinides. The calculations are performed for alpha-cluster wave functions with Volkov and Brink-Boeker interaction allowing forα,¹²C,¹⁶O and²⁰Ne clustering. It turns out that the correlated motion of large magic numbers of nucleons in two groups (¹⁶O+¹⁶O) is energetically favorable already at relatively small deformations. In the second minimum the¹⁶O+¹⁶O substructure occurs with high probability (about 80%). In analogy to these results the “pre-formation” of fragments and “fragment shell” effects occuring in the fission of actinides are explained in terms of probability statements for the formation of the corresponding heavy clusters in the many-body wave function.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Orbital rearrangement in light nuclei

Orbital rearrangement effects due to the removal of a proton are studied. Calculations in the nuclei¹⁶O,²⁰Ne, and⁴⁰Ca are performed using the Yale potential, and the Brink Boeker forceB1. The odd mass nuclei are not restricted to time reversal symmetry which prevents a large overestimation of the rearrangement energies. Although the orbital rearrangement energies are small (<1.5 MeV) utilizing density independent forces one can find larger changes in the wave functions due to the rearrangement as exhibit the discussion of the quadrupole moments and the mass distributions.     

Synthesis of 292116 in the 248Cm + 48Ca reaction

We report on the observation of the first decay event of the new nuclide ²⁹²116 produced in an experiment devoted to the synthesis of Z=116 nuclei in the ²⁴⁸Cm + ⁴⁸Ca reaction. The implantation of a heavy recoil in the focal-plane detector was followed in 46.9 ms by an α particle with E _α=10.56MeV. The energies and decay times of the descendant nuclei are in agreement with those observed in the decay chains of the even-even isotope ²⁸⁸114, previously produced in the ²⁴⁴Pu + ⁴⁸Ca reaction. Thus, the first α decay should be attributed to the parent nuclide ²⁹²116 produced via the evaporation of four neutrons in the complete fusion of ²⁴⁸Cm and ⁴⁸Ca. The experiment is in progress at Flerov Laboratory for Nuclear Reactions (FLNR, JINR, Dubna).     

On pion condensation in finite nuclei

The critical pionic state leading to pion condensation is investigated for finite nuclear systems. The threshold density for light nuclei, including⁴He, is found to be close to that of nuclear matter. For¹⁶O and⁴⁰Ca, the angular momenta of the most critical states areL=0 andL=2.     

Core-excited α-cluster structure in44Ti

With the use of a schematic⁴⁰Ca^*+α model, the low-lying positiveK=O2+ and 2⁺ bands in⁴⁴Ti, which start from the band-head energyE _x =1.90 MeV and 2.88 MeV, respectively, are shown to be well interpreted by an α-cluster structure with an excited⁴⁰Ca core, i.e.,³⁶Ar+α+α structure.     

Elastic deuteron scattering on 12C and 16O nuclei in the alpha-cluster model

On the basis of the dispersive alpha-cluster model for target nuclei and the theory of multiple diffractive scattering, differential cross sections and analyzing powers for the elastic scattering of 400 and 700-MeV deuterons on ¹²C and ¹⁶O target nuclei were calculated in the pointlike-deuteron approximation. In these calculations, the amplitude for incident-deuteron scattering on nuclei was constructed with the aid of amplitudes for dα scattering that were obtained from a fit to data on d ¹⁶O scattering. The same features were calculated on the basis of the diffraction approximation with allowance for the internal deuteron structure by using the amplitudes obtained earlier for nucleon scattering on ¹²C and ¹⁶O nuclei within the same dispersive alpha-clustermodel. The latter made it possible to perform calculations without employing adjustable parameters. The observables calculated on the basis of either approach agree with available experimental data.