Abnormal nuclear matter and pion condensation

The possibility of nuclear matter undergoing a combined phase transition into abnormal matter and a pion condensate is investigated. Various lagrangians for the meson (σ and π_i) fields, based on the σ-models, are used in mean-field approximation, and the entire system (mesons + nucleons) is treated fully relativistically. Equilibrium conditions of nuclear matter are obtained with NN repulsion, parametrized by the excluded volume approximation. It turns out that the formation of abnormal matter depends crucially on the choice of the σ-model lagrangian and considerably less on the additional pion condensate.     

Functional approach to nuclear field theory: A schematic model with pairing and particle-hole forces

Path integral techniques in collective variables are applied to a schematic model with monopole pairing and particle-hole forces. The single-particle and collective excitation modes of the system for various kinds of phase transitions are discussed. We formulate a modified perturbation theory (loop expansion) from which, finally, nuclear field theory (NFT) is obtained. The NFT Lagrangian is strictly derived. The graphical rules of the NFT expansion come out automatically.     

Probabilities of muon induced nuclear reactions involving charged particle emission

The probabilities for the reactions (μ^?, p), (μ^?, pn), (μ^?, p2n), (μ^?, p3n) and (μ^?, α) were measured by activation experiments on 18 elements from Na to Bi. The results suggest the following systematics : (i) the probability W of each type of reaction depends on the atomic number of the target and can be described by W = aexp( -bV), where V is the Coulomb barrier of the compound nucleus for the ejected charged particle; (ii) the factor b is the same for all (μ^?, pxn) reactions and not very different for (μ^?, α) reactions; (iii) the relative probabilities for (μ^?, pxn) reactions for a given target vary as 1 :6 :4 :4 for x = 0, 1, 2, 3. The experimental results are compared with a theoretical estimate of the reaction probability and with the corresponding 14 MeV neutron induced reactions.     

Three-body forces in nuclear matter from intermediate Δ-states in three-nucleon clusters

Those three-body force contributions in nuclear matter usually generated through a πN scattering amplitude dominated by the Δ(1236) resonance, are here treated as a three-nucleon cluster, in which one of the nucleons becomes, in an intermediate state, a Δ-resonance. All exchange diagrams are calculated and found to significantly reduce the energy per particle from the direct graph. This is contrary to earlier estimates of the exchanges, using more approximate approaches. The resulting attractive contribution is rather small, −1.1 MeV at κ_F = 1.4 fm⁻¹, but the roughly linear density dependence has a crucial effect on the saturation properties. The sensitivity of the results to the correlations used, and to the two-body force spin structure, is displayed. The energy per particle from clusters with three intermediate Δ-resonances is also estimated.     

On the self-consistency requirement in the low density expansion of the optical potential in nuclear matter

We critically discuss the choice of the auxiliary potential U which is introduced in the low density expansion of the mass operator M(k, w). This choice is related to the analytical properties of M(k, w) in the complex w-plane and we take due account of momentum conservation in the intermediate states appearing in the diagrams associated with M(k, w). We also provide a computation of the one-hole line, rearrangement and renormalization contributions to the optical potential, of the hole state spectral function and of the momentum distribution in nuclear matter. We use a real auxiliary potential which is self-consistent up to the order considered here, i.e. which takes into account the rearrangement and the renormalization corrections. Rearrangement is treated rigorously. The dependence of the obtained results on the choice of the nucleon-nucleon interaction, namely the Hamman-Ho Kim one in our calculation, is discussed.     

A density-matrix approach to critical phenomena

A density-matrix approach to the constrained Hartree-Fock problem is proposed as an alternative to Kümmel's maximum overlap method for the study of critical phenomena, with reference to two different quasi-spin models. Excellent results are obtained.     

Non-linear density dependence of the Δ-self-energy in nuclear matter and its implications in pionic atoms

The $\text{Δ(}\text{3}\text{2}\text{,}\text{3}\text{2}$) self-energy in a nuclear medium is shown to be highly non-linear in density, when proper care is taken of the virtual meson propagation in the medium and retardation effects. As a consequence the p-wave absorptive potential for pionic atoms diverges appreciably from the standard ρ² form. A fit to the existing data on pionic atoms is carried out with the new functional of the density and turns out to be as good as those with the ρ² functional. The successful fits with such different density functionals are due to a very narrow range of nuclear effective densities felt by the pion in the observed pionic atoms. The influence of these effects in related problems is discussed along with the suggestion to widen the range of nuclear densities felt by the pions by looking at other nuclear phenomena.     

A numerical study of resonance contributions to nuclear sum rules

The modified form of the nuclear sum rule which was proposed by Berggren is applied to a simple solvable problem and it is demonstrated, within the confines of that problem, that the continuum contribution to the sum rule is often dominated by the contribution from a few resonances, just as Berggren had anticipated. It is further shown that the bound, virtual and resonant states of the Hamiltonian considered form a complete set of states in terms of which the internal region of space can be expanded.     

A study of the Li(π, pp)He reaction within the three-body problem

The differential cross section for the ⁶Li(π⁺, pp)⁴He reaction for symmetrical coplanar kinematics has been calculated at the incident pion energy E_π = 70 MeV within the three-body problem + 2N taking into account the Pauli exclusion principle in each N subsystem. Three-body distortions in the final state have been taken into account in the eikonal approximation. The treatment is based on the superposition of the single-particle and two-particle mechanisms of absorption leading to the rescattering of the π- and ρ-mesons through the Δ-isobar. The analytical character of the adopted wave function for the ⁶Li nucleus (the multidimensional gaussian basis) makes it possible to ascertain clearly that the reaction amplitude of the type under study is insensitive to short-range NN correlations both in the initial and final states. The calculated momentum distribution of recoil -particles is in good agreement with the experimental data available, but the experimental accuracy should be improved in order to see the contribution of a specific three-body part of the ⁶Li wave function orthogonal to the ad channel. Some problems to be solved in future are discussed.     

Dependence of nuclear deorientation on nuclear spin for recoils in vacuum

Time-integral measurements have been made of the vacuum deorientation of the 2⁺ and 4⁺ states in ¹⁵⁰Sm and the 6⁺ and 8⁺ states in ¹⁵⁶Gd Coulomb-excited by 133 MeV ³⁵Cl ions. The ¹⁵⁰Sm results were deduced from γ-ray angular distributions measured in coincidence with backscattered ³⁵Cl ions. In the ¹⁵⁶Gd measurements, a fixed counter array and a sandwich target were used to measure directly the differences between the γ-ray angular distributions from nuclei recoiling in vacuum and the unperturbed γ-ray angular distributions from nuclei stopped in a thick ¹⁵⁶Gd target. The measured deorientation time constants in ps are τ₂(2⁺) = 27±4; τ₂(4⁺) = 14±4; τ₂(6⁺) = 24±3; τ₂(8⁺) = 23⁺¹⁰_?6; τ₄(2⁺) = 12±2; τ₄(4⁺) = 5±3; τ₄(6⁺) = 7.6±2.5. The 8⁺ data were analyzed assuming τ₂/τ₄ = $\text{10}\text{3}$ as predicted by the Abragam-Pound theory for $\text{I ≧ 4}$ essentially independently of the degree of quadrupole admixture. The other results are consistent with this except for the 2⁺ level which shows some quadrupole effect. The present results, which show strong deorientation of high spin levels, are in contrast to earlier work on neutron deficient Er isotopes. In light of our findings we suggest that the failure to observe deorientation in the high spin states in Er is primarily due to anomalously low g-factors associated with the backbending observed in these nuclei.     

A microscopic description of nuclear molecules: Application to the 12C + 12C system

The interaction energy between two oblate ¹²C ions is calculated by means of the constrained Hartree-Fock method. The influence of the mutual orientation of the ions is investigated by considering two extreme configurations: an axial symmetric one where the two ions approach each with their symmetry axes aligned with the collision axis and a triaxial one where the axes of the fragments are perpendicular to the collision line. The corresponding potentials V₁ and V₂ display very distinct features. In particular the minima of the potentials occur for quite different interdistances. A method is devised for constructing from V₁ and V₂ the potentials and coupling factors between two ions rotating with definite angular momentum. Using these quantities in a coupled channel calculation, we explain the gross features of the elastic, single 2⁺ inelastic and double inelastic cross sections. The same calculation yields good agreement with the fusion data.     

Modifications of single-particle properties in nuclear matter induced by three-body forces

Within the self-consistent Green’s function formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.     

Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon–nucleon potential, within the framework of self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle–particle and hole–hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.     

The rôle of particle transfer in large-angle scattering of 1p-shell nuclei

The scattering of different 1p shell heavy ions on nuclei of the same species has been measured in the whole angular range up to 174°. Various pairs of interacting nuclei have been selected according to the different complexities of their properties which can influence the scattering through higher-order processes to different degrees. In general, the observed rise of the cross section in the backward region is satisfactorily described as a single-step transfer reaction. Second-order processes and compound-nucleus contributions are of no practical importance for the explanation of the elastic scattering data. The performed analysis, however, leaves some features in the experimental angular distributions not fully and satisfactorily understood.     

The boundary condition approach to nucleon-nucleon potentials and the calculation of the T- and K-matrices

It has been shown that the off-shell T- and K-matrices can be obtained by means of boundary conditions imposed upon the off-shell wave function only. When there is a potential outside the boundary condition radius the method proposed permits to deduce in a rather simple way a renormalized Lippmann-Schwinger equation. The S-components of the T- and K-matrices are considered in detail using a potential of the exponential type in the exterior region. For such types of potentials a rather effective method for factorizing the K-matrix is given. Parameter fits to the ¹S₀ and ³S₁ phases are presented.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Charged particle emission following the absorption of stopped π− in 12C, 59Co and 197Au

Energy spectra of charged particles (p, d, t, ³He, α) emitted following the absorption of stopped π^? in ¹²C, ⁵⁹Co and ¹⁹⁷Au have been measured. The results are compared with results from neutron spectroscopy and discussed in the context of the quasi-deuteron model of π^? absorption.     

Total nuclear photoabsorption cross sections in the region 150 < A < 190

The curves of the total gamma-absorption cross sections (σ_tot) in the E1 giant resonance energy range for the nuclei ¹⁵⁴Sm, ¹⁵⁶Gd, ¹⁶⁵Ho, ¹⁶⁸Er, ¹⁷⁴Yb, ¹⁷⁸Hf, ¹⁸⁰Hf, ¹⁸¹Ta, ¹⁸²W, ¹⁸⁴W, ¹⁸⁶W and ¹⁹⁷Au have been measured using the absorption method. Parameters of the Lorentz curves fitting the measured cross sections σ_tot are given. Quadrupole moments (Q₀) and nuclear deformation parameters (β) were obtained.For deformed nuclei in the ～ 155 < A < ～ 180 region a violation of the correlation between giant resonance widths (Γ) and nuclear deformation parameters was found. Γ₁ and Γ₂, the widths of the resonances corresponding to vibrations of nucleons along and across the nuclear deformation axis, were observed to decrease with the increase of A which could be accounted for by the presence of an N = 108 subshell.     

High-spin states in 24Mg and upper limits for particle spectroscopy of high spins by heavy-ion compound reactions

High-spin states in ²⁴Mg have been investigated by the reaction ¹⁰B(¹⁶O, d)²⁴Mg up to $\text{E}{}^1\text{≈ 24}\text{MeV}$. High-spin states with $\text{I ≧ 9}$ have been identified at $\text{E}{}^1\text{= 19.20, 20.26, 20.8, 21.6, 23.1,}\text{and}\text{23.5}\text{MeV}$. The 10⁺ yrast state in ²⁴Mg is probably located at 20.26 MeV. The upper limits with respect to spin and excitation energy of the applicability of heavy-ion compound reactions for particle spectroscopy of high-spin states are discussed. The main limitations result from the increasing continuum and from a decrease of the high-spin selectivity when the final spins approach the critical angular momentum for compound-nucleus formation. It will be shown that the difficulty in the analysis of the experiments arising from the decreasing probability of finding isolated yrast states at high excitation energies, i.e. from the increasing level density, can be overcome in such experiments. The decrease in the high-spin selectivity of the total cross section is compensated for spins up to J_max by the fact that the shape of the angular distributions depends on the final spin for states with I ～ J_max. This is caused by the decreasing alignment of the final nucleus with decreasing values of |I ? J_max| and can be used for high-spin spectroscopy.