Microscopic calculations for the 8Li system

A microscopic multi-channel cluster model calculation for the ⁸Li scattering system has been performed. Diagonal phase shifts, channel coupling strengths, and eigenphases are presented. For comparison, the ⁸Li bound and quasibound states have been investigated by a refined resonating group calculation. The results of both types of calculations are in excellent agreement. In the energy region up to the ⁵He-t threshold the calculated S-matrix elements, the energy eigenvalues, and the overlaps of the normalized functions with the eigenvectors explain the origin of the experimentally detected levels and moreover give predictions for the existence of additional levels.     

Microscopic approach to the antiproton-nucleus optical potential

By using the self-energy of an antiproton evaluated in nuclear matter, the antiproton effective interaction with a bound nucleon is derived and is found to have a drastic density dependence. The p?-nucleus optical potential constructed by folding the effective interaction well reproduces experimental data on the p?-nucleus absorption cross section as well as on the complex level shift of p?-atoms. In addition, it is pointed out that the strong spin-orbit interaction spreads each doublet and considerably affects the lower complex level shift.     

Microscopic description of low-energy neutron scattering by nuclei

The Bloch and Gillet shell-model formalism extended to continuum states is applied to lowenergy neutron scattering by nuclei. It is shown that complete antisymmetrization leads in the r-representation to corrective terms which yield important corrections to the scattering lengths. Calculations are performed within a model restricted configuration space for the target nuclei ¹²C, ¹³C, ¹⁶O, ¹⁷O and ⁴⁰Ca. We predict values for the spin-dependent scattering amplitude for ¹³C and ¹⁷O. The antisymmetrization problem in the case of a large configuration mixing is studied for the ¹⁹F target nucleus. The resonant effects of the compound nucleus are then very important and the results become very sensitive to the configuration space and the interaction parameters.     

Energy surfaces,collective potentials and collective inertia parameters

The Hill-Wheeler equation is used to derive a collective Hamiltonian from an energy surface. Two simple ansatz are proposed for the collective Hamiltonian, which is then calculated explicitly in a hierarchy of approximations. The consistency of the method is verified in an illustrative example.     

The structure of 4He and phase-shift equivalent potentials

The Hartree-Fock and Brueckner theories are applied to the nucleus ⁴He. A truncated finite space of single-particle oscillator states is used, and different choices of the particle spectrum in Brueckner theory are considered. Results for the total binding energies and wound integrals are presented for the Reid soft-core potential and sets of phase-shift equivalent potentials generated from the Reid potential by a rank-one unitary transformation. The relation of the results to the position of the Emery singularities is investigated.     

Microscopic nuclear collective motion studied by classical equations of motion

The time-dependent variation principle is used to obtain generally non-canonical equations of motion from any class of quantum states which are parameterized by a set of continuous complex quantities. A class of states is presented whose associated classical dynamics is described by the five collective quadrupole degrees of freedom. Information about the classical dynamics of the system can be obtained from the non-canonical equations by finding physically interesting quantities which are coordinate independent and which characterize the low-energy collective motion. Approximate collective hamiltonians, of either a Bohr-Mottelson or an IBM type, can be found by insisting that the interesting physical quantities which describe the low-energy classical behavior of the many-body system are the same as those describing the classical behavior of the system given by the collective hamiltonian. The method is applied to two simple schematic models, one vibrational and one rotational, and IBM hamiltonians are obtained.     

Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from ¹⁶O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2?ω basis space and find that the triplet of 2p2h states (4⁺, 2⁺, 0⁺) around 11 MeV excitation is quite well described by this model, as may be a 1⁺ state which is observed for the first time by proton scattering from ¹⁶O.     

The breakup of 16O into He: An event-by-event study of nucleus-nucleus collisions at 75, 175 and 2000 MeV/A

We present an event-by-event study of the breakup of the ¹⁶O in ¹⁶O + emulsion nucleus interactions at 75, 175 and 2000 MeV/A. The events are categorized according to their multiplicity of projectile He nuclei. The multiplicity depends on the degree of target destruction. Although the fragmentation model describes the gross features of inclusive He spectra, an event-by-event study reveals deviations from the model. The momenta of the He nuclei, emitted from the projectile, depend on helium multiplicity and the breakup properties of the target nucleus. The probability that the ¹⁶O projectile breaks up into multiple He fragments is larger at 75 MeV/A than at 2000 MeV/A. At 75 MeV/A the mean velocity of projectile He is on the average 0.06c below the projectile velocity. This recoil velocity depends on the target nucleus destruction also for the most peripheral collisions.     

Microscopic form factor for DWBA analysis of light-ion induced three-nucleon transfer reactions

A modified zero-range distorted-wave Born approximation calculation was performed for the (p, α) reactions. The form factor is calculated by a first method, which is an extension of the Bayman and Kallio method to extract the relative l = 0 part of two-nucleon shell-model wave functions. The method includes some of the range effects so that one can predict the absolute magnitudes of the cross sections. A second method in finite range involves the ³He cluster expansion of the α-particle where the known (³He, α) transfer normalization may be used to estimate the absolute cross sections. The ¹¹⁸Sn(p, α)¹¹⁵In reactions are analyzed using the hole-vibration coupling model for ¹¹⁵In. The shapes of the experimental cross sections and the analyzing powers can be fitted by the calculations but the magnitudes of the cross sections are predicted to be too small.     

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

Microscopic approach to calculating cross sections and optical potentials for nucleus-nucleus interaction at intermediate energies

Nucleus-nucleus scattering is considered in the high-energy approximation and on the basis of Glauber-Sitenko microscopic theory in the optical limit. Analytic expressions for eikonal phase shifts are given for the case of Fermi-type realistic potentials and nuclear-density distributions. The effect of taking into account the distortions of the trajectories of the nuclei involved and the nuclear-density dependence of nucleon-nucleon forces on the total reactions cross sections is illustrated. The sensitivity of the reaction cross sections to the choice of model for the ⁶He projectile nucleus, which involves a neutron halo, is explored. Semimicroscopic optical potentials are introduced in order to describe differential cross sections for elastic scattering. The results of the present calculations are compared with available experimental data.     

Microscopic and macroscopic DWBA analysis of the reactions 28Si(α, d)30P, 32S(d, α)30P and 32S(α, d)34Cl studied at Eα = 50MeV and Ed = 40MeV

The reactions ²⁸Si(α, d)³⁰P, ³²S(d, α)³⁰P and ³²S(α, d)³⁴Cl have been studied at E_α = 50 MeVand E_d = 40 MeV. The angular distributions have been analysed in terms of the single-step, zero-range DWBA with microscopic as well as macroscopic form factors. By requiring an almost identical shape in the microscopic and macroscopic radial form factors for all L-values with L ? 6 the size parameters of the Woods-Saxon well in which the transferred cluster is bound to the nucleus were determined as r₀ = 1.15 fmanda = 0.76 fm. Despite the differences between the two approaches with these parameters the shape of the microscopic angular distribution is well reproduced and the corresponding strengths agree to within 25%. The method has been applied to the three reactions and relative two-nucleon spectroscopic factors have been deduced. A comparison is made with the results of two shell-model calculations.     

Nuclear-rainbow scattering and nucleus-nucleus potentials at short distances

The elastic scattering of strongly bound nuclei at energies of 10 to 70 MeV per nucleon shows the phenomenon of “rainbow scattering.” A nuclear rainbow appears because of deflection to negative angles. This process involves a strong overlap of nuclear densities, with values of up to twice the saturation density of nuclear matter. The ¹⁶O+¹⁶O system is studied with a high precision over a wide energy range from 7 to 70 MeV per nucleon in several laboratories. Primary Airy maxima and higher order Airy structures are observed. At all energies, excellent fits are obtained with deep potentials as deduced from the double-folding model involving a nucleon-nucleon interaction weakly dependent on the density. It is shown that Pauli blocking expected at low energies is strongly reduced if the local momenta are calculated self-consistently. Systematics confirms a refractive origin of large-angle scattering, at low energies inclusive. Thus, nuclear-rainbow scattering yields unique information about the properties of cold nuclear matter at higher densities.     

Microscopic theory of photon production in proton-nucleus and nucleus-nucleus collisions

The production of energetic photons in medium-energy proton and heavy-ion induced reactions is studied on the basis of incoherent nucleon-nucleon collisions. For this purpose we first evaluate covariantly the photon production from proton-neutron collisions in a vector (ω) and scalar meson (σ) exchange model with coupling constants given by the M2Y G-matrix in the nonrelativistic limit. We furthermore follow the proton-neutron collisional history by means of a phase-space simulation based on the Boltzmann-Uehling-Uhlenbeck approach for proton-nucleus and nucleus-nucleus collisions adding up incoherently the yields from each individual collision. The satisfactory agreement we obtain in comparison with experimental data allows to conclude that energetic photons predominantly arise from proton-neutron bremsstrahlung during the early stage of the collision.     

Phase-function method for velocity-dependent potentials

We have adapted the phase-function method for studying on- and off-shell properties of velocity-dependent potentials. The main result presented in this paper is an ansatz for the interpolatingT-matrix function (on- or off- the energy-shell as the case may). Based on this ansatz we have presented an efficient method for computing the off-shell extension function which plays a role in the theories of three particle system. We have demonstrated this by means of a model calculation.     

Lifetimes and g-factors of the 6− and 7− isomers in 66Ga and 68Ga

The 6^? and 7^? isomeric states in ⁶⁶Ga and ⁶⁸Ga at 1440.9 and 1229.6 keV, respectively, have been populated with the (¹³C, 2np) and (¹⁵N, n2p) reactions on natural Fe. The half-lives of these states have been measured to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(6}{}^{\mathrm{?}}\text{,}{}^{66}\text{Ga}\text{) = 57.3 ± 1.2}\text{ns}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(7}{}^{\mathrm{?}}\text{,}{}^{68}\text{Ga}\text{) = 64 ± 2}\text{ns}$. Using previous data on the hyperfine field of Ga in Fe, the g-factors of these states have been determined by means of the TDPAD method. The results are $\text{g(6}{}^{\mathrm{?}}\text{,}{}^{66}\text{Ga}\text{) = 0.129 ± 0.003}$ and $\text{g(7}{}^{\mathrm{?}}\text{,}{}^{68}\text{Ga}\text{) = 0.105 ± 0.003}$. These values are in very good agreement with the independent particle model if one assumes the and configurations and uses the empirical proton and neutron g-factors from odd-A neighboring nuclei instead of the Schmidt values. The large disagreements with experiment when Schmidt values are used show that core polarization effects are important in these nuclei.