Random Phase Approximation Calculations Research Articles

The compression modes in atomic nuclei and their relevance for the nuclear equation of state

Accurate assessment of the value of the incompressibility coefficient, K∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K∞ from experimental data is highlighted.

Finite amplitude method for the solution of the random-phase approximation

We propose a practical method to solve the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing finite amplitude of single-particle wave functions. The method only requires calculations of the single-particle Hamiltonian constructed with independent bra and ket states. Using the present method, the RPA calculation becomes possible with a little extension of a numerical code of the static HF calculation. We demonstrate usefulness and accuracy of the present method performing test calculations for isoscalar responses in deformed 20Ne.

Critical assessment of mean field models based on effective interactions

Mean field schemes, from simple Hartree—Fock plus random phase approximation calculations of the ground and excited states to more sophisticated approaches which include pairing as well, have been popular for quite a long time. In these models, the input is an effective interaction. We still lack a precise link between this interaction and a more fundamental theory; however, there have been various new recent attempts to correlate empirical pieces of evidence about nuclear (and neutron) matter, or experimental results, with the properties of the effective interactions. In this contribution, we claim that, while we have indeed made some progress in our understanding of certain features of the interactions, we are still missing a clue about its proper density dependence and about its isovector properties.

Evidence for direct neutron decay of the isoscalar giant dipole resonances inZr90,Sn116, andPb208

The direct and statistical neutron decay of the isoscalar giant dipole resonance was studied in Zr-90, Sn-116, and Pb-208 using the (alpha,alpha(')n) reaction at a bombarding energy of 200 MeV. The spectra of fast decay neutrons populating valence hole-states of the Z,N-1 nuclei were analyzed, and estimates for the branching ratios were determined. The results were compared to recent continuum random-phase approximation calculations.

Nuclear collective excitations using correlated realistic interactions: The role of explicit random-phase approximation correlations

We examine to what extent correlated realistic nucleon-nucleon interactions, derived within the unitary correlation operator method (UCOM), can describe nuclear collective motion in the framework of first-order random-phase approximation (RPA). To this end we employ the correlated Argonne V18 interaction in calculations within the so-called ''Extended'' RPA (ERPA) and investigate the response of closed-shell nuclei. The ERPA is a renormalized RPA version which considers explicitly the depletion of the Fermi sea due to long-range correlations and thus allows us to examine how these affect the excitation spectra. It is found that the effect on the properties of giant resonances is rather small. Compared to the standard RPA, where excitations are built on top of the uncorrelated Hartree-Fock (HF) ground state, their centroid energies decrease by up to 1 MeV, approximately, in the isovector channel. The isoscalar response is less affected in general. Thus, the disagreement between our previous UCOM-based RPA calculations and the experimental data are to be attributed to other effects, namely to residual three-body terms in the Hamiltonian and to higher-order configurations. Single-particle energies and occupation probabilities obtained within the ERPA are compared with corresponding HF and perturbation-theory results and are discussed as well. The ERPA formalism ismore » presented in detail.« less

The spreading width calculation of giant resonances with a semi-microscopic approach

We have proposed a semi-microscopic approach to calculate the two particles - two holes (2p - 2h) spreading width of giant resonances. Our proposal has been based in a hybrid method that implements the statistical multistep compound theory of Feshbach, Kerman and Koonin (FKK), widely and successful used in nuclear reactions mechanisms, in order to include relevant informations about the microscopic structure obtained by the Random Phase Approximation (RPA) calculations. This method is an approximative calculation to avoid the intrinsic numerical difficulties of those microscopic calculations that incorporate more complex structure than one particle - one hole (1p - 1h) excitations. Unlike the reaction context, the residual interaction was adjusted in RPA calculation to reproduce the lowest energy levels of the studied nuclei. The feasibility and the efficiency of the approach has been tested in giant dipole resonances in 208Pb and neutron-rich calcium isotopes, 48Ca and 60Ca.

The neutrino response of low-density neutron matter from the virial expansion

Abstract We generalize our virial approach to study spin-polarized neutron matter and the consistent neutrino response at low densities. In the long-wavelength limit, the virial expansion makes model-independent predictions for the density and spin response, based only on nucleon–nucleon scattering data. Our results for the neutrino response provide constraints for random-phase approximation or other model calculations, and we compare the virial vector and axial response to response functions used in supernova simulations. The virial expansion is suitable to describe matter near the supernova neutrinosphere, and this work extends the virial equation of state to predict neutrino interactions in neutron matter.

Wave-vector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: Support for nonempirical density functionals

We report a three-dimensional wave-vector analysis of the jellium exchange-correlation (xc) surface energy in the random-phase approximation (RPA). The RPA accurately describes long-range xc effects which are challenging for semilocal approximations, since it includes the universal small-wave-vector behavior derived by Langreth and Perdew. We use these rigorous RPA calculations for jellium slabs to test RPA versions of nonempirical semilocal density-functional approximations for the xc energy. The local spin density approximation displays canceling errors in the small- and intermediate-wave-vector regions. The Perdew-Burke-Ernzerhof generalized gradient approximation improves the analysis for intermediate wave vectors, but remains too low for small wave vectors (implying too-low jellium xc surface energies). The nonempirical metageneralized gradient approximation of Tao, Perdew, Staroverov, and Scuseria gives a realistic wave-vector analysis, even for small wave vectors or long-range effects. We also study the effects of slab thickness and of short-range corrections to the RPA.

Mixed representation RPA calculation for negative-parity excitations built on superdeformed states in the 40Ca and neutron-rich sulfur regions

Low-lying negative-parity excitations on superdeformed states in the 40Ca and neutron-rich sulfur regions were calculated using fully self-consistent random phase approximation calculations with Skyrme interaction.

Precession mode on high-K configurations: non-collective axially-symmetric limit of wobbling motion

The precession mode, the rotational excitation built on the high-K isomeric state, in comparison with the recently identified wobbling mode has been studied. The random-phase-approximation (RPA) formalism, which has been developed for the nuclear wobbling motion, is invoked and the precession phonon is obtained by the non-collective axially symmetric limit of the formalism. The excitation energies and the electromagnetic properties of the precession bands in 178W are calculated, and it is found that the results of RPA calculations well correspond to those of the rotor model; the correspondence can be understood by an adiabatic approximation to the RPA phonon. As a by-product, it is also found that the problem of too small out-of-band B(E2) in our previous RPA wobbling calculations can be solved by a suitable choice of the triaxial deformation which corresponds to the one used in the rotor model.

Role of boundary conditions in dynamic studies of nuclear giant resonances and collisions

Absorbing boundary conditions are often employed in time-dependent mean-field calculations to cope with the problem of emitted particles which would otherwise return back onto the system and falsify the dynamical evolution. We scrutinize two widely used methods, imaginary potentials and gradual attenuation by a mask function. To that end, we consider breathing oscillations of a nucleus computed on a radial one-dimensional grid in coordinate space. The most critical test case is the computation of resonance spectra in the (linear) domain of small amplitude motion. Absorbing bounds turn out to provide a reliable alternative to fully fledged continuum random phase approximation (RPA) calculations, although rather large absorbing bounds are required to simulate reliably well continuum conditions. We also investigate the computation of observables in the nonlinear domain. This regime turns out to be less demanding. Smaller absorbing margin suffice to achieve the wanted absorption effect.

Effects of self-consistency violation in Hartree-Fock RPA calculations for nuclear giant resonances revisited

We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock (HF) based random phase approximation (RPA) calculations of the centroid energy $E_{cen}$ of isoscalar and isovector giant resonances of multi-polarities $L=0-3$ in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (ph) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find that the shifts in the value of $E_{cen}$ due to self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in $E_{cen}$.

β-decay half-lives and β-delayed neutron emission probabilities for neutron rich nuclei close to theN=82r-process path

{beta}-delayed neutron emission branchings (or upper limits) for neutron rich {sup 116-120}Rh, {sup 120-122}Pd, and {sup 124}Ag have been measured. These branching ratios serve as direct inputs to astrophysical rapid neutron capture process models and affect the final abundances calculated in these models. In addition, half-lives for neutron rich {sup 114-115}Tc, {sup 114-118}Ru, {sup 116-121}Rh, and {sup 119-124}Pd near the proposed path of the r-process have also been measured. The results agree with theoretical quasiparticle random-phase approximation calculations within model uncertainties; the only exception is the delayed neutron branching in the decay of {sup 120}Rh, which is found to be much smaller than predicted.

Microphase and Macrophase Separation in Multicomponent A/B/A−C Polymer Blends with Attractive and Repulsive Interactions

A balanced A-C diblock copolymer surfactant was used to organize mixtures of immiscible A and B homopolymers. The C block of the copolymer exhibits repulsive and attractive interactions with the A and B homopolymers, respectively, leading to rich phase behavior. Experimental results indicate the existence of a microphase-separated state at low temperatures, a homogeneous phase at intermediate temperatures, and macrophase separation at high temperatures. It is unusual for a microphase-separated blend to exhibit a homogeneous phase prior to macrophase separation. In this study, component A was saturated polybutadiene with 89% 1,2-addition, component B was polyisobutylene, block A of the diblock copolymer was chemically equivalent to component A, and block C of the diblock copolymer was saturated polybutadiene with 63% 1,2-addition. We use a combination of Flory-Huggins theory (FHT), self-consistent field theory (SCFT) and the random-phase approximation (RPA) to understand the origin of our observations. All of the parameters needed for the SCFT, FHT, and RPA calculations were obtained from independent measurements. The measured length scale of the periodic concentration fluctuations in the homogeneous state and the domain spacing of the microphase-separated blends were in close agreement with RPA and SCFT, respectively. The transition temperatures between phases predicted with theory were in reasonable agreement with the experimental measurements.

N=14Shell Closure inO22Viewed through a Neutron Sensitive Probe

To investigate the behavior of the N = 14 neutron gap far from stability with a neutron-sensitive probe, proton elastic and 2(1)+ inelastic scattering angular distributions for the neutron-rich nucleus 22O were measured using the MUr à STrip detector array at the Grand Accélérateur National d'Ions Lourds facility. A deformation parameter beta(p,p') = 0.26 +/- 0.04 is obtained for the 2(1)+ state, much lower than in 20O, showing a weak neutron contribution to this state. A microscopic analysis was performed using matter and transition densities generated by continuum Skyrme-Hartree-Fock-Bogoliubov and quasiparticle random phase approximation calculations, respectively. The ratio of neutron to proton contributions to the 2(1)+ state is found close to the N/Z ratio, demonstrating a strong N = 14 shell closure in the vicinity of the neutron drip line.

Continuum effects for many-body correlations in nuclei close to the neutron drip line

Continuum effects for pairing correlations and low-frequency vibrational excitations in nuclei close to the neutron drip line are investigated by use of the coordinate space Hartree-Fock-Bogoliubov and quasiparticle random-phase approximation calculations. It is shown that quasiparticle states with small orbital angular momentum $\ensuremath{\ell}$ acquire significant changes of the spatial structure by the pairing correlations and the coupling to continuum states, and they cause the spatially extended distribution of the pairing density that enhances the pairing energy. By a similar mechanism, the spatially extended structure of the two-quasiparticle states among low-$\ensuremath{\ell}$ neutrons is realized, and it brings about the strong transition strength of the low-frequency vibrational excitations around the neutron drip line.

Fabrication of closely spaced, independently contacted electron-hole bilayers in GaAs-AlGaAs heterostructures

We describe a technique to fabricate closely spaced electron-hole bilayers in GaAs-AlGaAs heterostructures. Our technique incorporates a method for making shallow contacts to a low density (<1011cm−2) two-dimensional electron gas (2DEG) that do not require annealing. Four terminal measurements on both layers (25nm apart) are possible. Measurements show a hole mobility μh>105cm2V−1s−1 and an electron mobility μe>106cm2V−1s−1 at 1.5K. Preliminary drag measurements made down to T=300mK indicate an enhancement of coulomb interaction over the values obtained from a static random phase approximation (RPA) calculation.

Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force

Theoretical results for giant resonances in the three doubly magic exotic nuclei 78Ni, 100Sn and 132Sn are obtained from Hartree-Fock (HF) plus Random Phase Approximation (RPA) calculations using the D1S parameterization of the Gogny two-body effective interaction. Special attention is paid to full consistency between the HF field and the RPA particle-hole residual interaction. The results for the exotic nuclei, on average, appear similar to those of stable ones, especially for quadrupole and octupole states. More exotic systems have to be studied in order to confirm such a trend. The low energy of the monopole resonance in 78Ni suggests that the compression modulus in this neutron-rich nucleus is lower than the one of stable ones.

132Te and single-particle density-dependent pairing

132Te has been studied through β- decay of 132Sb radioactive beam at HRIBF leading to a significantly revised level scheme. A number of newly identified, likely 2+ states allows for a test of recent quasiparticle random phase approximation calculations with a density-dependent pairing force. In addition, the removal of a previously proposed 3− state allows for a simple shell model interpretation of the low-lying negative-parity states.

Photo-double detachment from the F− ion

The correlated process of photodetaching two electrons from the F− ion following the absorption of a single photon has been investigated over an energy range 20–62 eV. In the experiment, a beam of photons from the Advanced Light Source was collinearly merged with a counter-propagating beam of F− ions from a sputter ion source. The F+ ions produced in the interaction region were detected, and the normalized signal was used to monitor the relative cross section for the double-detachment reaction. An absolute scale for the cross section was established by measuring the spatial overlap of the two beams and by determining the efficiency for collection and detection of the F+ ions. The measured cross section is compared with R-matrix and random phase approximation calculations. These calculations show that the Auger decay of the 2s2p6 core-excited state of the F atom plays a minor role in the production of F+ ions and that double detachment is likely to be dominated by simultaneous correlated ejection of two valence electrons at energies well above threshold.