Escape Widths Research Articles

Spreading width converted from optical model for α incident scattering

We convert the optical potential in the α + 40Ca elastic scattering, which is determined so as to reproduce the differential cross section precisely, into the spreading width. This spreading width represents the decay width of the α + 40Ca resonance into the more complicated states. The conversion of the optical potential into the spreading width is achieved by the method of the absorbing boundary condition, and it is compared with the escape width of the α emission. The dissociation strength of 44Ti into the α + 40Ca continuum states is calculated to see the effect of the spreading width more clearly. We also estimate the upper value of the decay width into the compound nuclear state, which is a part of the spreading width, on the basis of the formula similar to the strength function originally used in the low-energy neutron scattering.

No-core shell model calculations of the photonuclear cross section of 10B

Results of ab initio no-core, shell model calculations for the photonuclear cross section of 10B are presented using realistic two-nucleon (NN) chiral forces up to next-to-next-to-next-order (N3LO) softened by the similarity renormalization group method (SRG) with \( \lambda= 2.02\) fm-1. The electric-dipole response function is calculated using the Lanczos method, with the effects of the continuum included via neutron escape widths derived from R-matrix theory and using the Lorentz integral transform method. The calculated cross section agrees well with experimental data in terms of structure as well as in absolute peak height, \( \sigma_{\max}=4.85\) mb at photon energy \( \omega= 23.61\) MeV, and integrated cross section 85.36 MeV. mb. We also test the Brink hypothesis by calculating the electric-dipole response for the first nine positive-parity states with \( J \ne 0\) in 10B and verify that dipole excitations built upon the ground and excited states have similar characteristics.

Evaluating emission widths of giant dipole resonances in a Fermi liquid model

In the theory of the finite fermi-systems [1], it was shown that giant resonances in nuclei can be consider as the zero-sound excitations which exhaust the large part of the energy-weighted sum rules. In the framework of [1] the solutions of the zero-sound dispersion equation in the symmetric nuclear matter, \omega_s(k), are considered. The method of calculation of these solutions is based on the analytical structure of the polarization operators \Pi(\omega,k). The solutions of the dispersion equation, which are real at small k, become complex with k increasing when the overlapping of the collective and 1p1h modes starts. The imaginary part of \omega_s(k) is the result of the collective zero-sound excitation decay to the real particle-hole pairs and can be compared with the escape width of resonances. We compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with Re\omega_s(k) and Im\omega_s(k) taken at a definite wave vector k=k_A.

Influence of a polarization operator’s imaginary part on dispersion equation solutions

In this paper the solutions of the zero-sound dispersion equation in the random phase approximation (RPA) are considered. The calculation of the damped zero-sound modes \omega_s(k) (complex frequency of excitation) in the nuclear matter is presented. The method is based on the analytical structure of the polarization operators \Pi(\omega,k). The solutions of two dispersion equations with \Pi(\omega,k) and with Re(\Pi(\omega,k)) are compared. It is shown that in the first case we obtain one-valued smooth solutions without "thumb-like" forms. Considering the giant resonances in the nuclei as zero-sound excitations we compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with \omega_s(k) taken at a definite wave vector k=k_A.

Description of the dipole giant resonance in heavy and superheavy nuclei within Skyrme random-phase approximation

The $E1(T=1)$ isovector dipole giant resonance (GDR) in heavy and superheavy deformed nuclei is analyzed over a sample of 18 rare-earth nuclei, four actinides, and three chains of superheavy elements ($Z=102$, 114, and 120). The basis of the description is the self-consistent separable random-phase approximation (SRPA) using the Skyrme force SLy6. The model well reproduces the experimental data in the rare-earth and actinide regions. The trend of the resonance peak energies follows the estimates from collective models, showing a bias to the volume mode for the rare-earth isotopes and a mix of volume and surface modes for actinides and superheavy elements. The widths of the GDR are mainly determined by the Landau fragmentation, which in turn is found to be strongly influenced by deformation. A deformation splitting of the GDR can contribute to about one-third of the width, and about 1 MeV further broadening can be associated with mechanisms beyond the SRPA description (e.g., escape widths and coupling with complex configurations).

THE ESCAPE WIDTHS AND STRENGTH OF ISOSCALAR GIANT DIPOLE RESONANCE IN 208Pb

The structure of the isoscalar giant dipole resonance (ISDGR) in 208Pb has been investigated by using the continuum Randon Phase Aproximation (RPA). The main properties (strength function and escape widths) of the ISDGR are calculated and compared with recent available experimental data.

Partial escape width for nuclei with neutron excess

In this work, the escape width for nuclei with neutron excess is calculated by continuum Random Phase Approximation (RPA) with a careful treatment on the differences between the densities of neutrons and protons.

Low-energy dipole excitations towards the proton drip-line: Doubly magic 48Ni

The properties of the low-energy dipole response are investigated for the proton-rich doubly magic nucleus 48Ni, in a comparative study of two microscopic models: fully self-consistent relativistic random-phase approximation (RRPA) based on the novel density-dependent meson-exchange interactions, and continuum random-phase approximation (CRPA) using Skyrme-type interactions with the continuum properly included. Both models predict the existence of the low-energy soft mode, i.e., the proton pygmy dipole resonance (PDR), for which the transition densities and RPA amplitudes indicate the dynamics of loosely bound protons vibrating against the rest of the nucleons. The CRPA analysis indicates that the escape width for the proton PDR is rather large, as a result of the coupling to the continuum.

Structure of the isovector dipole resonance in neutron-rich 60 Ca nuclei and direct decay from pygmy resonance

The structure of the isovector dipole resonance in neutron-rich calcium isotope, 60Ca, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation (RPA). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy-dipole resonance (PDR) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant-dipole resonance (GDR) was evaluated, bringing on a detailed discussion about its microscopic structure.

Excitations of the unstable nuclei48Niand49Ni

The isoscalar E1 and E2 resonances in the proton-rich nuclei ^{48,49}Ni and the {f_{7/2}3^-} multiplet in ^{49}Ni have been calculated taking into account the single-particle continuum exactly. The analogous calculations for the mirror nuclei ^{48}Ca and ^{49}Sc are presented. The models used are the continuum RPA for ^{48}Ni, ^{48}Ca and the Odd RPA for ^{49}Ni, ^{49}Sc, the latter has been developed recently and describes both single-particle and collective excitations of an odd nucleus on a common basis. In all four nuclei we obtained a distinct splitting of the isoscalar E1 resonance into 1 h-bar omega and 3 h-bar omega peaks at about 11 MeV and 30 MeV, respectively. The main part of the isoscalar E1 EWSR is exhausted by the 3 h-bar omega resonances. The 1 h-bar omega resonances exhaust about 35% of this EWSR in ^{48,49}Ni and about 22% in ^{48}Ca and ^{49}Sc. All seven {f_{7/2}3^-} multiplet members in ^{49}Ni are calculated to be in the (6-8) MeV energy region and have noticeable escape widths.

Preequilibrium escape widths of giant resonances

In this work we present a calculation of the $2p\ensuremath{-}2h$ preequilibrium escape width of giant resonances for the nuclei ${}^{40}\mathrm{Ca},$ ${}^{90}\mathrm{Zr},$ and ${}^{208}\mathrm{Pb}.$ The problem studied here involves an excited nucleus in the $1p\ensuremath{-}1h$ configuration, evolving to the $2p\ensuremath{-}2h$ configuration with the $1p$ in the continuum. The theoretical approach used for our calculations is based on the statistical multistep compound theory of Feshbach, Kerman, and Koonin (FKK) and on the particle-hole state densities given by Oblo\ifmmode \check{z}\else \v{z}\fi{}insk\'y. Our calculations show that although different state densities supply a similar result for the damping width, the escape width is strongly dependent on the nuclei, on the binding energy of the emitted nucleon, and the excitation energy of the giant resonance.

Quasiparticle-phonon interaction in non-magic nuclei

A general microscopic approach to describe properties of excited states in non-magic nuclei is formulated. It is based on the consistent use of the Green function method in Fermi systems with Cooper pairing. The main attention is paid to even-even nuclei, but for odd nuclei with pairing some important relations are obtained too. The quasiparticle-phonon interaction which is introduced acts also in the particle-particle channel and gives a quasiparticle-phonon contribution to pairing. When applied to the theory of giant multipole resonances, the approach includes all known sources of resonance width, i.e. QRPA configurations (which correspond to Landau damping in magic nuclei), the single-particle con- tinuum (escape width) and more complex configurations (spreading width). The use of the Green function method makes it possible to include consistently the ground-state correlations induced by the more complex configurations. In the approximation of the collective phonon creation amplitude squared, which is considered in detail here, these are the ground-state correlations caused by two-quasiparticle-phonon configurations; effects of these correlations have been found earlier to be noticeable for magic nuclei. Such a unified approach will give a reasonable description of the giant resonances' integral characteristics including their widths and of some more delicate properties like fine structure and decay characteristics. Physical arguments and earlier results of a similar approach for magic nuclei allow to use the known parameters of the Landau-Migdal non-separable interaction for all non-magic nuclei (except the light ones). This means that the theory developed is suitable for realistic predictions of the properties of unknown nuclei including unstable ones. The inclusion of the single-particle continuum allows to consider also nuclei with separation energy near zero.

Structure of the 11/2 − analog state in 91Nb populated by the 90Zr( α,t) reaction

Decay via proton emission of isobaric analog states (IAS's) in 91Nb was studied using the 90Zr( α, t) reaction at E α =180 MeV. This study provides information about the damping mechanism of these states. Decay to the ground state and low-lying phonon states in 90Zr was observed. The experimental data are compared with theoretical predictions wherein the IAS ‘single-particle’ proton escape widths are calculated in a continuum RPA approach. The branching ratios for decay to the phonon states are explained using a simple model.

Microscopic study of Gamow-Teller and spin-dipole states in 208Bi

Gamow-Teller (GT) and spin-dipole (SD) states in 208Bi are studied by using self-consistent Hartree-Fock + Tamm-Dancoff approximation taking into account the coupling to the continuum. Most of SD strength is found at the excitation energy Ex≈ 25MeV with a very broad width, which agrees with recent experimental observations. It is shown that Landau damping effect is responsible for the large width of SD peak, while the escape width is found to be at most 1MeV. We study also electric dipole (E1) transitions between GT and SD states in 208Bi. Main E1 transitions for 0- and 1- states are found near excitation energy expected from Brink's hypothesis in which SD states are considered as E1 resonances built on the GT state. Calculated E1 transition strengths between GT and SD states are compared with the analytic sum rules within one-particle one-hole (1p-1h) configuration space and within both 1p-1h and 2p-2h model space.

Direct proton decay and microscopic structure of the spin-dipole resonance in208Bi

The microscopic structure of the spin-dipole resonance (SDR) at ${E}_{x}=21.1 \mathrm{MeV}$ in ${}^{208}\mathrm{Bi}$ has been investigated in the ${}^{208}\mathrm{Pb}{(}^{3}\mathrm{He}{,t)}^{208}\mathrm{Bi}$ reaction at ${E(}^{3}\mathrm{He})=450 \mathrm{MeV}$ and very forward scattering angles. Protons emitted due to the decay of the SDR were measured in solid-state detectors in coincidence with tritons detected with the high resolution magnetic spectrometer Grand Raiden. The total and partial branching ratios for proton decay from the SDR to the residual neutron-hole states in ${}^{207}\mathrm{Pb}$ have been measured. The deduced escape widths are found to be in good agreement with recent theoretical estimates.

Effects of finite width of excited states on heavy-ion sub-barrier fusion reactions

We discuss the effects of coupling of the relative motion to nuclear collective excitations which have a finite lifetime on heavy-ion fusion reactions at energies near and below the Coulomb barrier. Both spreading and escape widths are explicitly taken into account in the exit doorway model. The coupled-channels equations are numerically solved to show that the finite resonance width always hinders fusion cross sections at subbarrier energies irrespective of the relative importance between the spreading and the escape widths. We also show that the structure of fusion barrier distribution is smeared due to the spreading of the strength of the doorway state.

Isospin Mixing in the Isobaric Analog State Derived from the (p,nIASp̃) Reaction on140Ce,172,174,176Yb, and208Pb

An exclusive coincidence experiment using the $({p,n}_{\mathrm{IAS}}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{p})$ reaction on ${}^{140}\mathrm{Ce}$, ${}^{172,174,176}\mathrm{Yb}$, and ${}^{208}\mathrm{Pb}$ was carried out for the first time by measuring decay protons from the isobaric analog states (IAS). Spreading widths of the IAS are deduced from the escape and total widths. The results show a strong isospin dependence which can be explained by the isospin mixing effect due to the coupling to the ${T}_{0}$ component among three multiplets ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}_{0}\ensuremath{-}1$, ${T}_{0}$, and ${T}_{0}+1$ of isovector monopole states in daughter nuclei. Empirical isospin mixing probabilities are found to be consistent with microscopic sum rule predictions.

Depletion of the2f7/2neutron hole state in207Pb

Spectroscopic factors of six low-lying neutron hole states in ${}^{207}\mathrm{Pb}$ were measured with a $(p,d)$ reaction at 65 MeV. The results are compared with previous $(p,d)$ reaction data as well as recent escape width ones of isobaric analog states in ${}^{208}\mathrm{Bi}$ into the neutron hole states in ${}^{207}\mathrm{Pb}.$ The spectroscopic factor for the ${2f}_{7/2}$ hole state shows a strong quenching (about 50% of the sum-rule limit), which suggests the existence of considerable strengths in higher excitation energy region. The appearance of the fragmentation or quenching in neutron hole strength distribution observed in the $2p\ensuremath{-}1f$ and $3p\ensuremath{-}2f$ shell regions is discussed.

Pairing effects in delayed neutron emission

The energy spectrum of delayed neutrons from the beta decaying odd-mass nuclei is estimated within the quasiparticle Tamm-Dancoff approximation. A complex single particle representation is used in order to describe the neutron escape widths. Qualitative agreement with the energy spectrum of delayed neutrons from beta decaying 137I nucleus is obtained. Sensitive behavior of the neutron spectrum versus the neutron gap parameter is reported.

On the charge-exchange dipole resonance of the ( np−1) type in 208Pb

In connection with the experimental study of the 208Pb( 13C, 13N) 208Tl reaction at small scattering angles, the strength functions and partial neutron escape widths of the monopole and dipole charge-exchange giant resonances of the ( np −1) type in 208Pb are calculated. The angular distribution of the reaction cross-section at small angles is evaluated. It is concluded that the resonance observed at the energy 16.5 MeV is the giant dipole resonance.