A simplified approach to three-body correlations in nuclear matter through a non-zero particle spectrum

Self-consistent nuclear-matter calculations are presented which take into account Dahlblom's results for the contribution to the binding energy due to three-body correlations. We propose a justified parametrization of the single-particle potential for particle states, the energy contribution of which cancels approximately the energy from certain three-body correlations. Indications are given of how to fix this particle-state potential for a given two-body interaction. Two nucleon-nucleon potentials are used: the Reid soft-core potential and a fully momentum-dependent one-boson-exchange potential similar to the form proposed by Ingber and Potenza. The mechanism of the increase in the total wound due to three-body correlations is investigated and reasons are given why this does not prevent the saturation densities from moving to higher values. Due to three-body correlations and with self-consistency on the hole spectrum, the increase in nuclear-matter binding energy is 0.60 MeV/A for the Reid soft-core interaction and 0.68 Mev/A for the OBEP. The saturation momentum is shifted from 1.42 fm^?1 to 1.44 fm^?1 for the Reid potential and from 1.58 fm^?1 to 1.62 fm^?1 for the OBEP.     

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.     

Chiral effective field theory and nuclear forces

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.     

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 non-relativistic quark model for baryons with pion cloud

We incorporate chiral invariance into a non-relativistic scheme for baryon structure in an approximate way, by introducing additional mesonic degrees of freedom. We proceed to calculate static properties for the nucleon and isobar. Using standard few-body techniques we are able to eliminate center-of-mass spurious motion from the wave functions. In our scheme a D-state admixture arises in the nucleon and isobar wave functions. There are parametrizations compatible with sphericity leading to a strong quenching of the effective quark axial coupling constant. Others lead to deformed ground-state baryons with almost no quenching of the weak-coupling constant.     

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.     

Path integral approach to nuclear pairing field

Nuclear pairing field is investigated within the framework of functional integrals. The equations of motion for the quasiparticles are obtained, in the presence of dynamic and static mean fields, using the stationary phase approximation. Small fluctuations of the pairing fields around their mean values are considered. In the limit of static mean fields, the stationary phase contribution to energy together with the leading term of quadratic corrections reproduces the Hartree-Fock-Bogoliubov energy of the quasi-particle vacuum state.     

A quantum model of collective motion in nuclei and its dequantization

Collective coherent states of Perelomov type are denned by acting with unitary operators from a representation of the symplectic group on the ground state of closed-shell nuclei. A dequantization scheme associates with quantum observables classical ones, and with the state space a phase space and a generalized classical dynamics. Applications to the nuclei ⁴He, ¹⁶O and ⁴⁰Ca are derived from microscopic interactions.     

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.     

Nanosecond lifetimes of the low-spin states in the nucleus 147Nd: A particle-rotor model interpretation of the results

Nanosecond lifetimes of several states in ¹⁴⁷Nd have been studied using the reaction ¹⁴⁶Nd(d, pγ)¹⁴⁷Nd with 10 MeV deuterons. The following lifetimes were observed: the $\text{7}\text{2}{}^{\mathrm{?}}$ level at 49.9 keV, 2.5±0.5 ns; the $\text{5}\text{2}{}^{\mathrm{?}}$ level at 127.9 keV, ≦ 0.8 ns; the $\text{9}\text{2}{}^{\mathrm{?}}$ level at 190.3 keV, 1.1±0.3 ns and the $\text{1}\text{2}{}^{\mathrm{?}}$ level at 214.6 keV, 5.8±0.8 ns. The wave functions of the states were constructed using an axial particle-plus-rotor model. The free parameters used are compared to the systematics observed in the neighbouring heavier N = 87 isotones as well as in the N = 89 and 91 isotones. Transition rates within the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ based excitations, separately, are reasonably well reproduced, but the connecting transitions indicate too strong a mixing of the shells in the calculation.     

Two-amplitude model of pion DCX applied to the 18O angular distribution and excitation function

An earlier model developed to fit the DCX excitation function of ¹⁸O has been extended to account for the $\text{T}{}_{\mathrm{\pi }}\text{= 164}\text{MeV}{}^{18}\text{O DCX}$ angular distribution in terms of that for ¹⁶O and a double-isobaric-analog transition.     

A hybrid model approach to the meson and quark theory of nuclear forces and currents

With a particular view to gaining a real understanding of the quark degrees of freedom in nuclei, we propose a simple model for nucleon-nucleon interactions within the framework of the quark cluster theory, which simultaneously incorporates the quark- and gluon-exchange mechanism at short distance and the meson-exchange mechanism at long and intermediate distances. It is shown to reproduce the experimental NN phase shifts and the deuteron properties fairly well. The model is then applied to a study of the electromagnetic properties of the two-baryon system, by putting particular emphasis upon the relation with conventional nuclear theory. The present study shows how the quark degrees of freedom, which should manifest themselves at high momentum transfer, are concealed in the conventional treatment of the two-nucleon problem as long as we observe low momentum transfer phenomena only.     

The applicability of nuclear field theory to shell-model calculations

Previous NFT calculations of the four-particle spectrum reached different conclusions concerning the applicability of the lowest-order Rayleigh-Schroedinger perturbation expansion. In the present paper, we show that the inclusion of second-order diagrams and/or diagonalization procedures yields satisfactory results both for the energies and for the transfer matrix elements even for j-shells as small as the $\text{j =}\text{7}\text{2}$ and $\text{j =}\text{11}\text{2}$ shells.     

Classical many-body model for heavy-ion collisions: (III). Ne-Ne and Ca-Ca calculations

The classical many-body model, previously introduced, has been employed to perform numerical calculations of systems consisting of 20 on 20 and 40 on 40 nucleons. Comparison is made with the 800A MeV data of Nagamiya, et al. Microscopic time development of the system and central compressions are displayed for Ca on Ca. Microscopic comparions with the fireball/firestreak models are presented; although qualitative agreement is found, interesting and expected shortcomings in the latter were seen. In particular, the classical many-body model exhibits shear viscosity and incomplete thermalization.     

Investigation of 36Ar with the 35Cl(p, γ)36Ar reaction: (II). Angular distributions and shell model calculations

The angular distributions of primary and secondary γ-ray transitions at eight resonances in the ³⁵Cl(p,γ)³⁶Ar reaction have been measured with a 60 cm³ Ge(Li) detector. The measurements lead to unambiguous J^gp assignments for 17 states of ³⁶Ar and to J^π limitations for seven other states. A large number of γ-ray multipole mixing ratios were obtained. Many of the resonances are analogues of ³⁶Cl levels. The lifetime of the E_x = 6.36 MeV level has been determined as τ_m = 440 +-150 fs. A simple shell model calculation has been performed to study the odd-parity levels of ³⁶Ar and ³⁶Cl. Coulomb displacement energies have been computed. Spectroscopic factors have been calculated and compared with the experimental data for the ³⁵Cl(d, p)³⁶Cl and ³⁵(τ, d)³⁶ reactions.     

Quasi-linear response theory of statistical heavy-ion collisions: (II). Analysis of the friction tensor and the energy transport

We apply the recently proposed quasi-linear response theory to the study of energy transport in deep inelastic heavy-ion collisions. By solving a master equation, we show how quickly the canonical distribution function becomes a good representation of the intrinsic state in the case of the random intrinsic excitations proposed by Weidenmüller and co-workers. We numerically analyze the properties of the corresponding friction tensor. In addition, we demonstrate that the known fluctuation dissipation theorem in the linear response theory is considerably violated for large part of deep inelastic collisions. We then calculate the double differential cross section for three typical examples. The results agree well with the experimental data if we phenomenologically introduce a time-dependent potential. We remark on the difference of the present calculation from that of the linear response theory. We comment also on the validity of a time-dependent theory, which derives the basic equations from time-independent equations by assuming a one-to-one correspondence between the time and the relative distance.     

Measured lifetimes of states in 197Au and a critical comparison with the weak-coupling core-excitation model

The lifetimes of five excited states in ¹⁹⁷Au up to an excitation energy of 885 keV were measured by the recoil-distance method (RDM). These levels were populated by Coulomb excitation using both 90 MeV ²⁰Ne and 120 MeV ³⁵Cl ion beams. The experimentally determined spectroscopy of the low-lying levels $\text{3}\text{2}{}^{\mathrm{+}}$ (ground state) and $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}^{\mathrm{+}}$, and $\text{7}\text{2}{}^{\mathrm{+}}$ at 77.3, 268.8, 278.9, and 547.5 keV excitation energy, respectively, has been critically compared with the detailed predictions of the de-Shalit weak-coupling core-excitation model. When the model is taken to represent the case of a $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ proton hole coupled to a ¹⁹⁸Hg core, the model parameters obtained are in accord with the criteria implicit for weak core coupling and, at the same time, are in remarkably good agreement with virtually all measured E2 and M1 transition rates.     

A schematic model for monopole and quadrupole pairing in nuclei

A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.     

Effective field theory approach to nuclear matter

Effective field theory provides a systematic approach to hardon physics and few-nucleon systems. It allows one to determine the effective two-, three-, and more-nucleon interactions which are consistent with each other. We present a project to derive bulk properties of nuclei from the effective nucleonic interactions. The text was submitted by the authors in English.     

Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (II). Application to N-4He scattering

A “Coulomb-modified” dispersion relation is applied to low-energy p-⁴He forward elastic scattering. To check the validity of the modification, the results are compared with those deduced from n-⁴He elastic scattering. Completely analogous information is obtained for the two processes. The exchange of three bound nucleons is found to contribute strongly to N-⁴He forward scattering. The corresponding ⁴He-³H-p and ⁴He-³He-n coupling constants are evaluated as R_p = 3.8±0.3 and R_n = 3.0±0.3, respectively. These constants are related to the strength of the asymptotic wave function of nucleons in ⁴He and thus to the tail of the nucleon distribution. A comparison of R_p with the empirical proton distribution in ⁴He as deduced from e-⁴He elastic scattering shows excellent agreement. From R_p and R_n the effective ranges of the singlet ³H-p and ³He-n interactions in the ground state of ⁴He are determined to be equal, in accordance with charge symmetry, and to have a value of r_eff = 1.072±0.006 fm.