Continuum Random Phase Approximation Research Articles

Nuclear compressibility and the isoscalar monopole resonance in a relativistic continuum random phase approximation.

The distribution of isoscalar monopole strength is calculated in $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ using the Dirac-Hartree random phase approximation. The resulting strength has a wide distribution and the average energy is lower than one would expect from the high compressibility coefficient in nuclear matter inherent in the relativistic theories. The distribution of the monopole strength has several peaks but only the highest peak in $^{40}\mathrm{Ca}$ can reliably be related to the ``breathing'' mode and thus to the nuclear compressibility.

Comparison of inelastic neutrino and antineutrino scattering on nuclei.

Based on calculations performed with the continuum random phase approximation model we compare neutrino- and antineutrino-induced reactions on several target nuclei. We find that neutrinos and antineutrinos excite parts of the isovector giant dipole resonance differently, with scattering on $^{16}\mathrm{O}$ showing the most noticeable deviations.

Random-phase approximation calculations of the nuclear response in the continuum using a finite-range interaction

A formulation of the continuum random-phase approximation (CRPA) equations with a finite-range particle-hole (ph) interaction is presented. The resulting equations can be applied to the calculation of RPA wave functions not only in the continuum, but also in the bound region. These CRPA equations, which are inhomogeneous coupled-channel integro-differential equations with a large dimension and thus difficult to solve, are modified so that the Lanczos method can be applied to solve them relatively easily. As examples we apply our method to the 3 − bound state and the giant quadrupole resonance (GQR) in 16O and 40Ca. A nuclear matter G-matrix is used for the ph interaction. Since treating the continuum exactly introduces in effect an infinitely large shell-model space, the ph correlations induced by the G-matrix interaction are too strong, not only for the bound collective states but also for collective states in the continuum. Renormalizing the exchange ph matrix elements allows one to fit the experimental data in both the bound and continuum part of the excitation spectrum in a consistent manner. For both the low-lying and continuum region the ring approximation is shown to be a good approximation for dealing with the exchange part of the ph matrix elements that are responsible for the ground-state correlations.

Use of the (e,e'n) reaction to study the giant multipole resonances in 116Sn.

The giant multipole resonances in $^{116}\mathrm{Sn}$ have been studied using the (e,e'n) reaction. Data were taken at effective momentum transfers of 0.37, 0.45, and 0.55 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ and a multipole analysis of the data was performed. The inferred multipole strength functions identify the E2 and E0 resonances as distinct peaks at 12.2 and 17.9 MeV, respectively. The energy-weighted sum-rule strengths for the E2 and E0 resonances, obtained using a Lorentzian fit to the data, are 34\ifmmode\pm\else\textpm\fi{}13% and 93\ifmmode\pm\else\textpm\fi{}37%. When compared with results from alpha scattering and pion scattering the sum-rule strengths exhibit approximate agreement, but the E0 strength identified in this measurement lies at higher excitation energy, consistent with the trend observed in heavier nuclei. The (e,e'n) data are compared with a continuum random phase approximation (RPA) calculation of the E2 and E0 strengths, and with an open-shell RPA calculation of the E2 strength. Both calculations disagree with the data in the region of the E2 resonance.

Aspects of the final-state interaction and long-range correlations in quasi-elastic (e, e′p) and (e, e′n) reactions

We present quasi-elastic (e, e′p) and (e, e′n) cross sections as obtained within a self-consistent Hartree-Fock (HF) and continuum random-phase approximation (RPA) model. A Skyrme type interaction is used, for which the momentum-dependence is studied in detail. Calculations are performed for the nuclei 12C and 16O in parallel and perpendicular kinematics. We investigate in how far a HF-RPA reaction model can account for the final-state interaction (FSI) in (e, e′p) and (e, e′n) processes in a realistic way. Furthermore, the effect of the RPA correlations on the cross sections is discussed. We confront the results of our calculations with the available 12C data.

Continuum random-phase-approximation study of direct decay of giant monopole resonances in90Zr and208Pb

Using a method recently developed by us, continuum random-phase approximation calculations are performed for the direct decay of giant monopole resonances in90Zr and208Pb, including spreading effects via the imaginary part of the optical potential for the particle excited by the external monopole field. The calculated results are discussed and compared with experimental data.

On the separation between the longitudinal and transverse strength in quasi-elastic (e, e′p) reactions

The ratio of the transverse to longitudinal (e, e′p) strength in the quasi-elastic peak is investigated within a non-relativistic Hartree-Fock (HF) and continuum random-phase approximation (RPA) reaction model. Calculations are performed for proton knockout from different orbitals in 12C and 40Ca. Each single-particle state is found to show a particular behaviour in the transverse to longitudinal ratio. Comparison with experimental data indicates that a beneficial role can be attributed to the RPA correlations.

Excitation of spin-isospin modes in the quasifree scattering region

Nuclear spin longitudinal and transverse response functions in the isovector channel are calculated by the continuum random-phase approximation with the orthogonality condition. This method treats the nucleus as of finite size and with a continuum single-particle spectrum. It can include an imaginary potential for the particle states. The corresponding longitudinal and transverse cross sections for $^{40}(\mathit{p}$,p') at ${E}_{p}$=500 MeV are calculated by distorted-wave impulse approximation fully quantum mechanically which is beyond the previous analyses by the Glauber approximation. The results are compared with the longitudinal-transverse response ratio extracted from the polarization transfer observables of the Los Alamos experiment. Large effects of the finiteness of the nucleus are seen especially in the longitudinal response. Effects of the distortion diminish the softening and hardening due to nuclear correlation, but the enhancement and quenching still remain. These effects cooperatively reduce the ratio.

Nucleon emission induced by polarized electrons at low momentum transfer

The use of coincidence experiments with polarized electrons, ( e , e'x), in the study of the structure and decay of the giant multipole resonances is discussed. In plane wave Born approximation the ( e , e'x) cross section is expressed as a sum of five structure functions, one more than in the case of coincidence experiments with unpolarized electrons (e, e'x). The differences between the fifth response function and the other four is discussed in detail. Results are presented for a numerical study of the decay of the giant resonances of 16O and 40Ca, performed within the framework of the continuum random phase approximation. The angular distributions of the fifth response function are shown to be strongly dependent upon the specific nature of the decaying waves of the emitted nucleon.

A model for particle emission induced by electron scattering

A model for the description of particle emission after electro-excitation of a nucleus is developed. The coupling between the individual decay channels is treated within the framework of the continuum random-phase approximation. The interference terms between charge and current operators as well as the interference term between the two different transverse components of the current operator are included in the calculation. The model is applied to the proton decay of 16O. The sensitivity of the angular distribution of the emitted particle to the presence of weak multipole strengths is analysed and signatures for monopole strength are discussed. Coincidence experiments are shown to be a selective tool to excite bound states embedded in the continuum. Quasi-free knock-out is found to start immediately above the giant-dipole-resonance region.

Electric quadrupole photoneutron reactions inO16

Photoneutron energy spectra from the $^{16}\mathrm{O}(\ensuremath{\gamma},{\mathrm{n}}_{0})^{15}\mathrm{O}$ reaction were measured as functions of laboratory angle over a range of excitation energies from 30 to 35 MeV. Angular distribution Legendre-polynomial coefficients were extracted up to third order as functions of excitation energy. Nonzero values of the coefficients ${a}_{1} (+0.25\ifmmode\pm\else\textpm\fi{}0.02)$ and ${a}_{3} (\ensuremath{-}0.2\ifmmode\pm\else\textpm\fi{}0.02)$ were observed over the energy region explored, indicating interference between states of opposite parity. These values can be accounted for in a simple model incorporating electric quadrupole absorption strength decaying via the ground-state photoneutron channel. When combined with the previously-determined amplitude ratio for the $E1$ $p\ensuremath{\rightarrow}s$ and $p\ensuremath{\rightarrow}d$ single-particle transitions, the present results suggest that about 4% of the isovector energy-weighted sum rule is found in the ($\ensuremath{\gamma}$,${\mathrm{n}}_{0}$) channel in the energy range studied. The value of the ($\ensuremath{\gamma}$,${\mathrm{n}}_{0}$) cross section was found to vary from 1.5\ifmmode\pm\else\textpm\fi{}0.1 mb at ${E}_{x}=30$ MeV to 0.8\ifmmode\pm\else\textpm\fi{}0.1 mb at 35 MeV. The average magnitude of the $E2$ contribution to this cross section was estimated to be 0.05\ifmmode\pm\else\textpm\fi{}0.02 mb. This is in reasonable agreement with a recent continuum randomphase approximation shell model calculation, but is in disagreement with a previous measurement.

Theoretical analysis of proton decay of electro-excited carbon

A theoretical model for the microscopic description of electron-induced coincidence experiments is developed, which includes final-state interactions within the continuum random-phase approximation. Charge and current interference effects on the angular distributions of the emitted particle are included. The analysis of the recent 12C(e, e′p) data by Calarco et al. exhibits clear effects due to the presence of monopole strength, even though no concentrated monopole resonance is present in the theory.

Compression mode strength inPb208

Compression modes are characterized as volume oscillations of the nucleus which do not contribute to the photonuclear sum rule but show up as concentrated strength in, e.g., inelastic hadronic scattering. Comparison of the nuclear response to different operators in the frame of a continuum random phase approximation is the theoretical technique used to search for such compression modes. Sharply concentrated strength is found only for the breathing mode and the isoscalar dipole mode. Large widths are expected for the isovector monopole, the isovector dipole compression mode, and the isoscalar quadrupole compression mode. For those modes whose escape width corresponds to a large fraction of the total width, one suggests the possibility of detecting them in coincidence experiments by observation of the decaying particle.NUCLEAR STRUCTURE $^{208}\mathrm{Pb}$; calculated compression mode sum rule strength. Random phase method, Landau-Migdal interaction.

Treatment of nucleon scattering in the continuum random-phase approximation

Treatment of nucleon scattering in the continuum random-phase approximation