Escape Widths Research Articles

Non-spin-flip ( 3He, t) charge-exchange and isobaric analog states of actinide nuclei studied at [formula omitted] and 200 MeV

The ( 3He, t) charge-exchange reaction has been studied at θ = 0° and bombarding energies of E( 3 He) = 76.5 MeV and 200 MeV . Spectra were measured using magnetic analysis for target nuclei of 12, 13C, 16O, 19F, 28, 29, 30Si, 90Zr, 117, 120Sn, natTa, natW, 197Au, 208Pb, 230, 232Th, 234, 236, 238U and 244Pu. The measurements at 76.5 MeV concentrated on the isobaric analog states of several actinide nuclei, particularly on their widths and the branching ratios for proton decay. Cross sections, Q-values and total widths were determined for the transitions to the isobaric analog states. Coulomb displacement energies derived from the measured Q-values display the influence of deformed nuclear shapes. Escape widths Γ ↑ and spreading widths Γ ↓ of the isobaric analog states in five actinide nuclei were deduced from the measured proton-decay branching ratios. They were found to be in agreement with predictions which postulate isospin mixing via the Coulomb force with the ( T 0−1)-component of the isovector giant monopole resonance. The measurements at 200 MeV were concerned with transitions to isobaric analog states in both light and heavy nuclei, including several actinide nuclei, but Gamow-Teller resonances and transitions to numerous other states were also observed. The measured cross sections for several transitions to isobaric analog states from 30Si to 208Pb were used to extract the effective interaction V τ for non-spin-flip ( 3He, t) charge exchange at E( 3 He) ≈ 200 MeV . The interaction strength V τ decreases by a factor 0.6 when compared to previously measured values for the energy range E( 3 He) = 65 to 90 MeV . An angular distribution from θ τ = 0° to 16° for the transition to the isobaric analog state in 120Sb measured at E( 3 He) = 200 MeV was found to be in very good agreement with microscopic calculations.

Nucleon escape widths of giant dipole and quadrupole resonances

Direct escape of nucleons from giant resonances is studied in the framework of quasiparticle RPA. Continuum effects are included by the projection operator method. Partial escape widths are calculated for the isoscalar quadrupole and isovector dipole modes in medium and heavy nuclei. Direct escape widths for giant quadrupole resonances are found to be very small. In contrast, giant dipole resonances can have nucleon widths of the order of 100 keV for direct escape.

Proton escape widths of isobaric analog and Gamow-Teller resonances

The proton escape widths associated with the isobaric analog (IAR) and Gamow-Teller (GTR) resonances of 208Bi are calculated making use of Skyrme forces and complex collective states. In the case of the GTR, the theory is in disagreement with the data by more than an order of magnitude. This discrepancy is even more conspicuous in view of the fact that theory describes correctly the observed decay of the IAR and thus the underlying single-particle spectrum.

Nonspectral Dirac random-phase approximation for finite nuclei.

We present a version of the random-phase approximation for the description of nuclear excitations which is a consistent extension of the QHD1 mean-field theory of the ground states of doubly magic nuclei. This approach includes correlations induced by the isoscalar {sigma} and {omega} mesons of QHD1. Our method employs a nonspectral single particle propagator in such a way that we avoid any basis truncation and automatically include the escape widths implied by the theory. Our calculations yield exactly conserved random-phase approximation transition currents as well as correct treatment of spuriosity for 1{sup {minus}}T=0 excitations. Because of the flexibility of our numerical method, we can treat discrete excitations, giant resonances, and the continuum response in general---including quasielastic scattering---in a unified way. We compare our results with experimental ({ital e},{ital e}{prime}) form factors for various discrete excitations in {sup 12}C, {sup 16}O, {sup 40}Ca, and {sup 48}Ca as well as with the quasielastic Coulomb response functions for {sup 12}C and {sup 40}Ca. Agreement with transition charge densities is typically quite good and in some cases superior to comparable nonrelativistic random-phase approximation calculations. Transition current densities are less well described. The question of sum rules in the relativistic random-phase approximation is also addressed.

On the role of anti-bound states in the RPA description of the giant monopole resonance

The limit of the applicability of the resonant random phase approximation method is tested by calculating escape widths in the giant monopole resonance of16O and comparing them to the results of a time dependent Hartree-Fock calculation. Though the widths of the narrows-wave component agree reasonably well, the broadp-wave component shows large disagreement, which cannot be cured by complementing the basis with anti-bound states in the RPA calculation.

Resonant random phase approximation.

Particle-hole excitations are studied in terms of a single-particle representation consisting of bound states and resonant solutions (Gamow resonances) of a ``realistic'' Woods-Saxon potential. Within this representation a particle-hole resonant random phase approximation is developed. Using the resonant random phase approximation the escape widths of the multipole giant resonances in $^{208}\mathrm{Pb}$ are calculated and reasonable agreement with available experimental data is obtained.

Neutron spectroscopic factors in 208Pb from the proton decay of the 208Bi isobaric analog state

Accurate spectroscopic factors for neutron removal from 208Pb, leading to single neutron hole states in 207Pb, are derived from the escape widths of the isobaric analog state of the 208Pb ground state in 208Bi. The accuracy of the analysis, which follows a new procedure, is discussed. Derived lower limits on the occupancies of neutron orbitals in 208Pb are 0.87±0.06 ( p 1 2 , 0.92±0.08 ( p 3 2 , 0.88±0.12 ( f 5 2 ) and a lower limit 0.7 ( f 7 2 ).

Study of the breathing mode of 208Pb through neutron decay.

The neutron decay of the giant monopole resonance region between 13 and 15 MeV in $^{208}\mathrm{Pb}$ is analyzed in terms of collective and statistical doorway states. The direct escape widths of the giant monopole resonance populating the lowest five valence hole states of $^{207}\mathrm{Pb}$ are determined, and compared with the results obtained from complex collective states. This comparison discriminates sharply between different model Hamiltonians which predict similar energies and collectivities for the resonance.

Quantized TDHF for isoscalar giant quadrupole resonances in spherical nuclei

The time-dependent Hartree-Fock theory supplemented with the regularity and single-valuedness quantization condition for the gauge invariant component of the wavefunction is applied to the description of the centroid energy and escape width of isoscalar giant quadrupole resonances in 16O, 40Ca and 110Zr. Calculations are performed using the Skyrme SIII effective interaction. An important role of the finite oscillation amplitude in the mean-field dynamics is emphasized.

The direct neutron decay of giant resonances in 208Pb

The neutron decay of the giant multipole resonance region from 9 to 15 MeV of excitation energy in 208 Pb has been studied. Neutron branching ratios for the decay to the ground state and to the low-lying excited states of 207 Pb were measured as a function of the excitation energy of 208 Pb and compared to Hauser-Feshbach calculations. While the neutron branching ratios from the energy region of the isoscalar giant quadrupole resonance are reproduced by the calculations, the ratios from the energy region of the isoscalar giant monopole resonance show a conspicuous excess with respect to the statistical model predictions. The neutron yield from this energy region was analysed in terms of a multistep model of the compound nucleus which includes collective doorway channels. The total direct escape width as well as the associated direct partial escape widths to the lowest five valence hole states of 207 Pb were determined.

Direct emission of particles from giant resonances: Theoretical approaches

Continuum-RPA calculations can be understood in the time-dependent Hartree-Fock (TDHF) approach as well as in terms of discrete complex RPA states. Numerical calculations show that the TDHF method is efficient for predicting particle decay lifetimes. In the second approach the energy-dependent states have finite widths which are related to direct escape widths. It is stressed that the continuum-RPA response function cannot give these widths when the states are overlapping.

Time-dependent Hartree-Fock calculation of the escape width of the giant monopole resonance in 16O.

The damping of the giant monopole resonance in $^{16}\mathrm{O}$ is calculated within the framework of the time-dependent Hartree-Fock approximation. The strength function contains two peaks, centered at around 25 and 33 MeV, with escape widths of \ensuremath{\sim}11 and \ensuremath{\sim}2 MeV, associated with the 1p(0p${)}^{\mathrm{\ensuremath{-}}1}$ and 1s(0s${)}^{\mathrm{\ensuremath{-}}1}$ configurations, respectively.

Application of Gamow resonances to continuum nuclear spectra.

Neutron and proton Gamow resonances are evaluated in $^{208}\mathrm{Pb}$ and they are used together with bound states as single-particle representation to calculate random phase approximation particle-hole excitations. A good account of the escape width corresponding to the particle-hole giant resonances is obtained.

Underlying structure of continuum response functions in random phase approximation

It is shown that continuum-RPA results can be understood in terms of energy-dependent, complex RPA states. These states have finite widths which are direct escape widths. Calculations have been performed for a simple model of monopole resonance in 40Ca, and the results are compared with those obtained by continuum-RPA and time-dependent Hartree-Fock methods.

Nuclear structure of 208Pb from 207Pb+n resonances.

Resonance structure in the $^{207}\mathrm{Pb}$ + n system has been investigated by measuring the neutron total cross section with high energy resolution and the partial radiative cross sections for transitions to the ground-state and the first-excited state in $^{208}\mathrm{Pb}$. A detailed analysis of resonance parameters was carried out up to a neutron energy of 700 keV. The nuclear level density shows a strong parity dependence. The doorway in the s-wave neutron strength function has been firmly established with an escape width equal to the corresponding widths in the neighboring isotopes. The total magnetic dipole strength detected between the neutron separation energy and 8.0 MeV is B(M1)\ensuremath{\uparrow}=5.8 ${\ensuremath{\mu}}_{\mathrm{N}{}^{2}}$, thus smaller than the lowest theoretical estimate for that region. Above that energy an additional 1 ${\ensuremath{\mu}}_{\mathrm{N}{}^{2}}$ is observed, but more strength may have escaped detection because the sensitivity of the experiment decreases; thus the ``missing'' strength may be partly hidden at these higher energies. Radiative widths for the E1 decay of resonances to the first-excited state of $^{208}\mathrm{Pb}$ show a doorway structure which can be related to the properties of known bound states.

Particle-vibrator coupling model calculation of partial radiative widths for [formula omitted] wave neutron resonance on 28Si

A particle-vibrator coupling model was applied to the calculation of partial radiative widths for the 28 Si p 3 2 wave neutron resonance with large reduced neutron width. The calculation assumed a neutron excitation coupled to one-phonon vibrational states of the 28Si nucleus and neglected the continuum nature of the resonance state wave function in the nuclear external region. The model wave functions were generated from a coupled-channel Schrödinger equation so as to reproduce the observed neutron escape width, neutron binding energies, and spectroscopic factors. Excellent agreement was achieved between the observed and calculated partial radiative widths for the transitions from the 565 keV resonance to the low-lying states of 29Si. As a result, it was confirmed that the core excitation is quite essential to explain the observed partial radiative widths. We emphasize that this resonance can be interpreted as a particle-vibrator doorway state common to the neutron and gamma-ray emission channels, and that a dominant component of the doorway-state wave function belongs to the configuration in which a single quasibound 1 d 3 2 neutron is coupled to the 3 − vibrational state of the 28Si nucleus.

Main parameters of charge-exchange resonance relaxation within the model of interacting and independently damping quasiparticles.

A method for calculating main parameters of Gamow-Teller resonance relaxation, namely total width, proton escape widths, and resonance mixing phase, is formulated within the framework of the model of interacting and independently damping quasiparticles. Calculations of the values indicated are carried out for the set of rigid spherical nuclei with the model parameters taken from independent data.

Total number of stages before compound nuclear reaction and the Fermi energy of the nucleus

The equations of multi-step escape width ( Gamma i up arrow ), damping width ( Gamma i down arrow ) and the interaction-induced transition from ith stage to the (i+l)th stage (Vi) are formulated. On the basis of these equations, the total number of stages before equilibrium and the Fermi energy of the nucleus are discussed.

Test of the Q-space approximation in nuclear response theory

The electric monopole states are solved in TDA with a separable interaction taking into account the continuum. These results are compared with the Q-space approximation, in which the configuration space is discretized by using the harmonic oscillator basis, and the continuum is taken into account via the escape width. The Q-space approximation is found to be very good.

Statistical multistep compound reactions ? with renormalized exciton state densities

The master equation which takes into account angular momentum considerations is used to obtain the emission spectra for statistical multistep compound reactions. Realistic wave functions are used to evaluate the radial integrals appearing in the escape and spreading widths. The renormalized particle hole state density of Akkermans et al. is used in the calculations. The improvements over the one component formulation are discussed.