Direct-semidirect Model Research Articles

Direct neutron capture cross section on Ge80 and probing shape coexistence in neutron-rich nuclei

Results are presented from the first neutron-transfer measurement on $^{80}\mathrm{Ge}$ using an exotic beam from the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. Newly measured spins and spectroscopic factors of low-lying states of $^{81}\mathrm{Ge}$ are determined, and the neutron capture cross section on $^{80}\mathrm{Ge}$ was calculated in a direct-semidirect model to provide a more realistic ($n,\ensuremath{\gamma}$) reaction rate for $r$-process simulations. Furthermore, a region of shape coexistence around $N\ensuremath{\approx}50$ is confirmed and implications for the magic nature of $^{78}\mathrm{Ni}$ are discussed.

Proton capture to continuum states ofBi209

High resolution spectra from fast proton radiative capture in $^{208}\mathrm{Pb}$ are presented for three energies of the incident protons: 14.8, 15.7, and 16.9 MeV. The collected spectra were analyzed with emphasis on the region of capture to unbound states in order to search for possible structure and to study the competition between two basically different phenomena: the statistical process versus the fluctuation effects in radiative capture to unbound final states. In the energy region of incoming protons considered in our experiment, the statistical processes modeled with a Hauser-Feshbach calculation dominate. The spectra of primary \ensuremath{\gamma} rays, coincident with the low energy one from the decay of the ${f}_{7/2}$ single-particle state, show a prominent structure which is predominantly of ${g}_{9/2}$ character. The calculations of continuum spectra based on the extended direct-semidirect model and the Hauser-Feshbach statistical approach successfully reproduce the experimental data.

High resolution measurement of the 208Pb(p,γ) capture reaction up to Eγ=19 MeV

High-energy γ rays produced by the 208Pb(p,γ) reaction were measured with the AFRODITE germanium detector array. The use of Ge instead of NaI detectors improved the energy resolution by more than a factor of 10 in the γ-ray energy range between 10 and 19 MeV. Proton captures into different single particles states in 209Bi were thus clearly separated, most notably for the i13/2 high-spin state. The measured excitation functions are in very good agreement with the predictions of the direct–semi-direct model, including captures to the i13/2 state, for which the previous agreement had been poor.

Model calculations of the radiative capture process and the Brink–Axel hypothesis

Using the consistent Direct–SemiDirect (DSD) and the improved Preequilibrium (PEQ) exciton model we analyzed the excitation functions for the neutron radiative capture transitions to the isolated single-particle states in 141 Ce and 209 Pb in order to study the energy positions of the peaks belonging to the Brink–Axel Giant Resonances (BA GDR) built on single-particle states. The PEQ calculations of γ transitions to discrete levels have been performed for the first time. The PEQ model peaks appear at energies lower than those of the BA GDRs for about 0.2 MeV for low-spin states, and for about 0.4 MeV for high-spin ones. The DSD model energies are higher than the BA GDR ones for about 0.3 MeV (1 MeV for high-spin states). Both models reproduce the available experimental peak energies within about 0.25 MeV.

Mass and state dependence of the interaction function in the direct-semidirect capture model

In the original direct-semidirect (DSD) model for the radiative capture of nucleons in the region of the giant dipole resonance, the complex particle-vibration coupling function was introduced phenomenologically and the real and imaginary strengths V1 and W1 determined from the comparison of the calculated and rather scarce experimental results. One can, on the other hand, extract an analytical expression for this coupling from the recent formulation of the consistent DSD, in light of which we conclude that the strengths V1 and W1 are both spin and mass dependent. Such dependence has not been known before, while the real and the imaginary parts of the coupling function turn out to be indeed of the volume and the surface peaked shapes, respectively, as used in previous versions of the model. The mass dependence deduced is for the capture to the ground states V1 = 16.8A1/3 MeV for the real and W1 = 16.1A1/3 MeV for the imaginary part.

Fast neutron capture in 206Pb, 165Ho, and 238U as seen through the consistent direct-semidirect model

A recently proposed version of the direct-semidirect capture model is confronted with neutron capture by 206Pb where traditional direct-semidirect theory with phenomenologically introduced complex coupling is incapable of explaining the experimental data. It is shown that the new model predicts the cross sections that are in close agreement with the experimental values also in this case without any change of the model parameters. The new approach is tested on neutron capture by deformed nuclei as well. The results of calculations on integrated cross sections show that both approaches reproduce the experimental data well.

Neutron optical potentials from capture reactions

A new version of the direct-semidirect (DSD) model has been suggested recently. The imaginary part of the form factor is interpreted in terms of consistency requirements for the multipole operators. The calculations of excitation functions and angular distributions of γ-rays from capture reactions show close agreement with experimental values for many different sets of the optical model. Some sets, however, are not so successful. The results of the DSD calculations are sensitive to the optical model wave function in the vicinity of the target nucleus. The elastic scattering of nucleons on the other hand determines the scattering matrix in the asymptotic region of very large radii. In this work we select some global optical model sets which reproduce both elastic scattering and capture reactions well, We believe that such double test of the sets may help in better description of other reactions.

(γ,n)study of the isovector quadrupole resonance in40Ca

The forward-to-backward asymmetry of neutrons emitted in the 40Ca(γ,n0) reaction was measured at photon energies in the range of 27–50 MeV. An energy-dependent asymmetry was observed that is interpreted as evidence of interference between the isovector quadrupole resonance and the giant dipole resonance. Data analysis in terms of semiclassical and direct-semidirect models estimate the isovector quadrupole resonance to be at an excitation energy of 31.0±1.5 MeV, with a width of 16.0±1.5 MeV, and exhausting most of the energy-weighted sum rule for the isovector quadrupole resonance.

Nuclear Dicke states and the direct-semidirect model

Abstract The structure of the doorway state assumed in the direct-semidirect model was addressed by Sokolov and Zelevinsky. Modifications of the model due to the nuclear Dicke state in the presence of two open channels has been considered. The results of calculations for neutron capture to the single particle states in Pb and Ca are presented.

Fast proton capture through a consistent version of the direct-semidirect model

We present the calculations of excitation functions and angular distributions of γ-rays in the proton capture reactions 142 Ce(p, γ) 142 Pr, 208 Pb(p, γ) 209 Bi and the photo-proton reaction 40 Ca(γ, p 0,1 ) 39 K using the recently proposed consistent version of the direct-semidirect (DSD) capture model. The results are in excellent agreement with experimental data.

Fast neutron capture through a consistent version of the direct-semidirect model

Fast neutron capture through a consistent version of the direct-semidirect model

Fluctuation effects in radiative capture to unstable final states: A test via the 89Y(p

We have developed an extended direct-semidirect (DSD) model for fast-nucleon capture to virtual single-particle configurations that subsequently damp into the compound nucleus or (at sufficiently high excitation energies) escape into the continuum. The inclusion of final-state fluctuation effects is an important feature of this model. To test the model we have measured the spectra of gamma rays from approximately 10 MeV to the endpoint in the {sup 89}Y({ital {rvec p}},{gamma}) reaction with 19.6 MeV polarized protons from the TUNL tandem accelerator. Gamma spectra were measured with a pair of 25.4 cm{times}25.4 cm anticoincidence-shielded NaI detectors at angles of 30{degree}, 55{degree}, 90{degree}, 125{degree}, and 150{degree} with respect to the incident beam. The spectra show significant analyzing powers and forward peaking of the angular distributions. These features allow for the discrimination between compounds processes and direct processes. Analyzing powers and fore-aft asymmetries were observed for gamma energies below those associated with direct-semidirect transitions to known bound final states. We have also performed Hauser-Feshbach calculations of the statistical component of the gamma emission, which dominates below approximately 15--16 MeV. The extended DSD model reproduces the spectral shapes and analyzing powers above this energy quite well. There is no evidence in the present reactionmore » that additional mechanisms, such as multistep compound or multistep direct emission, are required.« less

Pre-equilibrium and direct-semi-direct model calculations of nucleon radiative capture excitation functions on heavy nuclei

Excitation functions of activation cross section (cascades over continuum states included) for proton capture in heavy nuclei, namely 52130Te(p, gamma )53131I, 58142Ce(p, gamma )59143Pr, 70176Yb(p, gamma )71177Lu, 83209Bi(p, gamma )84210Po, and integrated cross sections (direct transitions to the bound states) for neutron capture in 3989Y(n, gamma )3990Y, 58140Ce(n, gamma )58141Ce, 82208Pb(n, gamma )82209Pb, were calculated within a preequilibrium-equilibrium exciton model, using the ground-state binding energy of the even nucleon reduced for pairing, as well as within the direct-semidirect capture model. The integrated cross sections calculated within both the approaches agree reasonably well with the available experimental data, though the models differ in many aspects. As the direct-semidirect model does not treat the transitions to the continuum states, only the preequilibrium-equilibrium model is applied to the activation data. It reproduces them rather successfully.

Isovector giant quadrupole resonance observed in 89Y(p

The cross section and vector analyzing power for transitions to the ground and low-lying states in the [sup 89]Y([ital [rvec p]],[gamma])[sup 90]Zr reaction have been studied over the angular range [theta][gamma]=38.8[degree]--130[degree] at [ital E][sub [ital p]]=22.5 MeV and over the energy range [ital E][sub [ital p]]=18.5--28.5 MeV at [theta][sub [gamma]]=90[degree]. Angular distributions for the [gamma][sub 0] and [gamma][sub 1+2+3] transitions (i.e., to the first three strong single-particle excited states) reveal large asymmetries about [theta][sub [gamma]]=90[degree] in both [sigma]([theta]) and [sigma]([theta])[ital A][sub [ital y]]([theta]), suggesting [ital E]1/[ital E]2 interference effects. Legendre polynomial fits to these data yield nonzero coefficients of order [ital k]=3,4, thus confirming interference between the dominant [ital E]1 radiation and opposite parity [ital E]2 radiation. A transition-matrix element analysis of the [gamma][sub 0] angular distribution data, including [ital E]1 and [ital E]2 radiation, suggests a 28% [ital E]2 contribution, while a pure direct capture calculation predicts only 12% [ital E]2 strength. The energy dependence of [ital A][sub [ital y]](90[degree]) for the [gamma][sub 123] data is adequately described using the direct-semidirect model by including isovector quadropole resonances at [ital E][sub GQR]=27.5 MeV, built on each of the three states, with widths of [Gamma][sub GQR]=7.0 MeV and strengths which exhaustmore » 100% of the isovector [ital E]2 energy-weighted sum rule for each state. These results provide strong evidence for collective [ital E]2 strength built on excited states in [sup 90]Zr, approximately at the energy predicted for the isovector giant quadrupole resonance, but are inconclusive concerning the ground-state transition.« less

Proton radiative capture to 13N at beam energies of 40 to 54 MeV

Abstract The reaction 12 C(p,γ) 13 N has been studied for 40 MeV ⩽ E p ⩽ 54 MeV with a large-volume anticoincidence NaI spectrometer. Angular distributions have been measured for excited states up to 11 MeV. We observe transitions to states having a dominant single-particle character and also states with an excited 2 2 12 C core. We compare the data to a direct semi-direct model calculation. There is no evidence for excitation of the second harmonic of the giant dipole resonance. Structure observed near E γ = 24 MeV may be due to 12 C(p,ṕγ).

Radiative capture of polarized neutrons by12C in the energy rangeE n=20?35 MeV

Radiative capture of polarized neutrons by12C was investigated using a scintillating NE-213 target and three NaI detectors. Angular distributions of the capture gamma photons and analyzing powers were measured at laboratory angles of 55°, 90° and 125° and neutron energiesEinn=20 to 35 MeV. Capture photons and recoil nuclei were detected in coincidence, the photons being identified by measuring the time of flight and analyzing the pulse shape in the NaI detectors. In the energy range above the centre of the GDR in13C, a pronounced rise of the forward-backward asymmetry for the12C(n,γ0)13C reaction was observed indicating the presence ofE2 capture interfering with direct and collectiveE1 capture. The direct-semidirect (DSD) model of radiative capture does not give a satisfactory description of the experimental results.

Some suggestions about the research of theE2(T=1) resonance excitation by (n, γ) reaction on cerium

Determining at microscopic level the interaction responsible for the excitation of collective states of140Ce makes it possible to use in a coherent way the direct-semidirect model in the study of the140Ce(\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {n} \), γ) reaction. Computations of differential cross-sections give useful pieces of information about the effects caused by the excitation of the isovector quadrupole giant resonance on the γ-ray emission geometry, closely connected with the polarization state of the incident neutron. Thus, the results supply helpful suggestions on a possible experimental research of theE2(T=1) excitation by means of the radiative capture reaction.

Isovector giant quadrupole resonance in the 40Ca(n, gamma 0) reaction.

The fore-aft asymmetry and the 90\ifmmode^\circ\else\textdegree\fi{} differential cross section in the $^{40}\mathrm{Ca}$(n,${\ensuremath{\gamma}}_{0}$) reaction were measured from ${\mathit{E}}_{\mathit{n}}$=8 to 44 MeV. An energy-dependent asymmetry is observed that is interpreted as the result of the isovector giant quadrupole resonance interfering with background E1 amplitudes. The present data agree with previous low-energy data. At higher incident neutron energies, the present data do not agree with the predictions of a direct-semidirect model calculation based on the low-energy data alone. Calculations using the pure resonance model are in agreement with the data.

Anyonization of lattice Chern-Simons theory: D. Eliezer and G. W. Semenoff. Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

The structure of the doorway state assumed in the direct-semidirect model was addressed by Sokolov and Zelevinsky. Modifications of the model due to the nuclear Dicke state in the presence of two open channels has been considered. The results of calculations for neutron capture to the single particle states in Pb and Ca are presented.

Microscopic approach to M1 radiative capture of nucleons

The microscopic analysis of the excitation mechanism of M1 giant resonance in the 208Pb(n, γ) reaction emphasizes the fundamental role of the nuclear shell structure in determining an effective surface form factor for the nucleon-nucleus interaction. Results of calculations of transition amplitudes obtained with a microscopic radial form factor in the frame of the direct-semidirect model suggest a possible connection between the excitation of the giant M1 resonance and the asymmetries in angular distributions of emitted photons, in spite of the strong statistical contribution to the capture cross section.