Semidirect Capture Research Articles

Editorial: Biographical Memoirs , Volume 68

Editorial: <i>Biographical Memoirs</i> , Volume 68

Anthony Milner Lane. 27 July 1928—9 February 2011

Tony Lane came from humble beginnings to become one of the world's leading theoretical nuclear physicists. His career in the Theoretical Physics Division at the Atomic Energy Research Establishment (AERE) at Harwell was characterized by his outstanding successes in explaining experimental nuclear data. He pioneered the understanding of the important nucleon capture reactions by introducing new mechanisms of direct and semi-direct capture and, together with colleagues, he greatly advanced knowledge of nuclear analogue states, and the role of isospin in nuclear physics. With R. G. Thomas, he wrote a comprehensive review of R-matrix theory, applied to analyse resonances in nuclear reactions, which became one of the most cited papers in physics. His book Nuclear theory gave a good account of the use of pairing force theory in nuclear physics, and its application to nuclear collective motion.

EMPIRE: A code for nuclear astrophysics

The nuclear reaction code EMPIRE is presented as a useful tool for nuclear astrophysics. EMPIRE combines a variety of the reaction models with a comprehensive library of input parameters providing a diversity of options for the user. With exclusion of the direct- semidirect capture all reaction mechanisms relevant to the nuclear astrophysics energy range of interest are implemented in the code. Comparison to experimental data show consistent agreement for all relevant channels.

Coupled-Channel Models of Direct-Semidirect Capture via Giant-Dipole Resonances

Semidirect capture, a two-step process that excites a giant-dipole resonance followed by its radiative de-excitation, is a dominant process near giant-dipole resonances, that is, for incoming neutron energies within 5–20 MeV. At lower energies such processes may affect neutron capture rates that are relevant to astrophysical nucleosynthesis models. We implement a semidirect capture model in the coupled-channel reaction code Fresco and validate it by comparing the cross section for direct-semidirect capture 208Pb(n,γ)209Pb to experimental data. We also investigate the effect of low-energy electric dipole strength in the pygmy resonance. We use a conventional single-particle direct-semidirect capture code Cupido for comparison. Furthermore, we present and discuss our results for direct-semidirect capture reaction 130Sn(n,γ)131Sn, the cross section of which is known to have a significant effect on nucleosynthesis models.

Direct and semi-direct capture in low-energy (n,γ) reactions of neutron-rich tin isotopes and its implications forr-process nucleosynthesis

The direct and semi-direct (DSD) components of the neutron capture cross sections are calculated for a series of tin isotopes by employing a single-particle potential (SPP) that gives a good reproduction of the known single-particle energies (SPEs) over a wide mass region. The results are compared with the Hauser-Feshbach (HF) contribution in the energy region of astrophysical interest. The calculated result shows that the HF component drops off rapidly for isotope $^{132}\mathrm{Sn}$ and toward more neutron-rich ones, whereas the DSD component decreases only smoothly and eventually becomes dominant. This result is consistent with those of previous studies, but the dependence of the DSD cross section on the target mass number is a feature of the present SPP that gives a smooth variation of SPEs. As a consequence, the direct portion of the DSD component gives the largest contribution to the total ($n,\ensuremath{\gamma}$) cross section for neutron-rich isotopes below a few MeV. Therefore, the direct capture process modifies the astrophysical ($n,\ensuremath{\gamma}$) reaction rates to a great extent. The semi-direct component, however, gives a negligible contribution to the astrophysical reaction rates, but its impact is significant above several MeV. The reason for the difference in isotopic dependence between the HF and DSD components is discussed, and its implication for $r$-process nucleosynthesis is given.

Giant dipole resonance on the15.1MeVstate inC12studied viaB11(p,γ)C12reaction

The radiative proton capture cross section to the $15.1\phantom{\rule{0.3em}{0ex}}\text{MeV}$ $T=1$ state in $^{12}\mathrm{C}$ has been measured in the reaction $^{11}\mathrm{B}(p,\ensuremath{\gamma})^{12}\mathrm{C}$ at the proton energies of $7.2\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and $17--24\phantom{\rule{0.3em}{0ex}}\text{MeV}$ in $1\phantom{\rule{0.3em}{0ex}}\text{MeV}$ steps. The capture $\ensuremath{\gamma}$ ray was detected in coincidence with the $15.1\phantom{\rule{0.3em}{0ex}}\text{MeV}$ $\ensuremath{\gamma}$ ray arising from the subsequent decay of the $T=1$ state to the ground state. The measured cross sections, for ${E}_{p}=17--24\phantom{\rule{0.3em}{0ex}}\text{MeV}$, are much larger than the direct capture model prediction whereas the agreement with the model is good at ${E}_{p}=7.2\phantom{\rule{0.3em}{0ex}}\text{MeV}$. A semidirect capture model, including the excitation of the giant dipole resonance on the $15.1\phantom{\rule{0.3em}{0ex}}\text{MeV}$ state, reasonably explains the data. The energy and the width of the resonance are extracted.

Direct neutron capture in light nuclei

The consistent direct-semidirect capture model (CDSD) is applied to the keV energy region where the direct process is dominant. We study the influence of the correction of the form of the direct term due to a difference ΔV in the potentials used to describe the scattering and the bound single-particle state of the captured neutron. The sensitivity of the cross sections on the semidirect capture mechanism in this energy regiion is examined as well. We consider the 12C(n,γ) and 16O(n,γ) processes which are of astrophysical interest in the energy region of the incoming neutrons between 10 keV to 0.6 MeV where good experimental data exist. It is shown that both corrections are negligible for capture to the states where s-waves are not involved. For s-wave capture to the p-orbits the ΔV correction of the direct term is important. The data do not support the contribution of the semidirect term as described by the model in the energy region studied.

Interference effect of doorway states in a radiative capture reaction.

This work investigates the interference in radiative nucleon capture reactions between the giant resonances and the doorway configurations mixed in compound nucleus levels. A unified formalism has been established by which it is possible to study the interference among the four parts in the capture amplitude: the potential capture, valence capture, semidirect capture, and fine resonance capture stemming from doorway configurations. The $^{12}\mathrm{C}$(p,${\ensuremath{\gamma}}_{0}$) data in the excitation energy region of 10--30 MeV in $^{13}\mathrm{N}$ were analyzed by means of this formalism with an emphasis on investigating the dips and peaks superimposed on the pigmy resonance. These structures are interpreted as destructive or constructive interferences in doorway configurations. Parameters for both the giant resonances and fine levels were extracted by fitting the measured data. We extend the study to discuss the potential of observing similar interferences in the reactions $^{12}\mathrm{C}$(n,${\ensuremath{\gamma}}_{0}$) and $^{12}\mathrm{C}$(p,${\ensuremath{\gamma}}_{\mathit{n}}$${)}^{13}$${\mathrm{N}}^{\mathrm{*}}$, leading to excited states of the final nucleus.

On the distortions of direct-semi-direct model predictions for nucleon radiative capture

The nucleon-nucleus interaction, responsible for the semidirect radiative capture process, is expressed in terms of finite-range nuclear forces having a Gaussian dependence on nucleon-nucleon distance, in order to deduce, in the frame of the shell model, a particle-vibration coupling form satisfying a range-independent normalization condition. Calculations, carried out for the40Ca(n, γ) reaction with this microscopic coupling form, containing essential two-body contributions, make it possible to evaluate the distortions of the direct-semi-direct model predictions, produced by the phenomenological approach used till now, and to test model sensitivity to the range of nuclear forces.

Virtual excitation of the GDR mode in the subbarrier23Na(p, ?)24Mg reaction

Differential cross sections for nonresonant radiative capture of low energy protons (E p = 1,348 keV and 1,370 keV) by23Na nuclei exhibit features pointing to the virtual excitation of the giant dipole resonance (GDR) mode. Theoretical analysis carried out within the framework of the direct — semidirect capture model reveals an enhanced coupling of the GDR with the incident protonf-wave consistent with the microscopic structure of the GDR in thes-d shell nuclei.

Proton capture byN15above the giant dipole resonance

The proton capture cross sections to the ground and excited states of /sup 16/O have been measured at several angles in the proton energy interval between 18 and 40 MeV. The ground state angular distribution, which shows a significant E1-E2 interference effect above 40 MeV, results in reasonable agreement with semidirect capture calculations. Transitions to final bound and unbound 1p-1h states in /sup 16/O having a dominant 1p/sub 1/2//sup -1/ hole have also been measured. Resonances built on these residual states have been systematically observed above E/sub p/ = 20 MeV; the possible interpretation of these states as giant dipole resonances built on excited states is discussed.

Investigation of the 31P( [formula omitted], γ) 32P reaction

The circular polarization has been measured of 16 γ-rays produced by the capture of polarized thermal neutrons in 31P. The results, fitted together with those from previous γ-γ angular correlation measurements, determine the channel spin mixing parameter α for four primary transitions and the mixing ratio δ for one primary and eight secondary transitions. On the assumption that the reaction proceeds by means of direct capture, the α-values obtained prove that the J π = 1 − states in 32P at 4.04 and 4.88 MeV have very pure s 1 2 p 3 2 character, and that at 5.78 MeV pure s 1 2 p 1 2 character. For the E x = 4.66 and 5.35 MeV levels J π = 2 − has been determined. The 31P(n, γ) 32P reaction provides an example of violation of the sum rule for primary intensities Σ ± √ α(1 − α) I γ = 0. This cannot be explained by a semi-direct capture contribution to primary M1 transitions but only by missing 2p 1 2 strength.

Investigation of the electric quadrupole strength in 13N using the [formula omitted] reaction

Cross sections for the 12 C( p , γ 0) 13 N reaction have been measured from E p = 10 MeV to 17 MeV in the laboratory system by bombarding an enriched carbon-12 target with a beam of polarized protons. A 25 cm diameter × 25 cm Nal(Tl) detector with a plastic anti-coincidence shield was used to detect the gamma rays. The total E2 capture cross sections were of the order of 0.2 μb and no resonance effects were observed. The amount of the E2 energy-weighted sum rule depleted in this energy range is (8.5 ± 3.3)%. Calculations based on a direct semi-direct capture model provide a good description of the experimental results by including only direct E2 capture and direct plus collective El capture.

Analysis of E1 and E2 radiative α-capture and giant multipole resonances

Experimental data on E1 and E2 radiative α-capture are analyzed by taking account of direct and semidirect processes as well as the compound process. Observed excitation functions for these reactions are reasonably well reproduced assuming the reactions take place mainly through giant multipole resonances. It is shown that the compound process dominates in the lower energy region especially for E1 capture whereas in the higher energy region direct and semidirect captures are the major processes especially for E2 capture. Several interesting results are obtained on α-particle spectroscopic factors of target ground states and on spreading widths and isospin-mixing coefficients of the giant multipole resonance states. The data are shown to be consistent with the existence of the isoscalar giant quadrupole resonances. The applicability of direct and semidirect capture theories to α-capture is examined.

Radiative capture of fast neutrons by 40Ca

The radiative capture cross section for the reaction 40Ca(n, γ) 41Ca has been measured for the neutron energy range of 6.8–18.2 MeV. A NaI(Tl) anti-Compton spectrometer, a pulsed neutron beam, and time-of-flight techniques were utilized. The γ-ray spectra show strong transitions to the 1 f 7 2 ground state and a relatively high intensity of unresolved γ-rays to a group of levels at about 2 MeV, where two 3 2 − states are known to carry the 2 p 3 2 strength, and to levels around 4 MeV, which is the centroid energy of the 2 p 1 2 strength. Absolute cross sections were determined for these γ-ray transitions as well as the integrated cross section for transitions to bound states of 41Ca. Only the cross section for the transition to the f 7 2 ground state of 41Ca shows the resonance behavior predicted by the semidirect (collective) capture theory, but the agreement between the theoretical and measured f 7 2 cross sections is not satisfactory. The measured cross sections for the other γ-ray peaks are almost constant with neutron energy below about 15 MeV, in sharp contrast to the cross sections predicted by the semidirect theory for p 3 2 and p 1 2 transitions.

Isospin effects in fast neutron radiative capture

The effect of isospin splitting of the giant dipole resonance of the final nucleus on neutron capture cross sections in N = Z nuclei is discussed. The 40Ca(n, γ) ground-state transition is taken as an example. The suggested modification of the semi-direct capture model gives an improved description of the energy dependence of the 40Ca(n, γ 0) cross section.

Different coupling interactions in semi-direct capture of 14 MeV neutrons by Si, Sr, Ce and208Pb

Gamma-ray spectra following the capture of 14 MeV neutrons by Si, Sr, Ce and208Pb are compared with the predictions of semi-direct theory. All the values for the input parameters are taken from experimental data independent of the γ-ray experimental spectra examined. It is found that for nuclei in different mass regions the volume form of the coupling interaction is more adequate than the surface form to account for the available experimental data.

Gamma-Ray Spectra from the Interaction of 14-MeV Neutrons with Copper, Zirconium, and Antimony

High energy gamma-ray spectra from the radiative capture of 14-MeV neutrons in copper, zirconium, and antimony have been measured with a coincidence-anticoincidence telescope pair spectrometer. These spectra are compared with predictions from calculations using the semidirect (collective) capture model. The parameter values used were derived from other types of experiments and from nuclear models. Agreement is found both in shape and in magnitude without further adjustment of parameters. Partial radiative capture cross sections, obtained by integrating the gamma-ray spectra for gamma energies in excess of 14 MeV, are compared with values from other measurements.

Radiative capture of energetic neutrons by 208Pb

The radiative capture cross section of neutrons with energies covering the range 6.2–14.7 MeV has been measured for the 208Pb(n, γ) 209Pb reaction. Gamma-ray spectra were recorded with a NaI(Tl) anti-Compton spectrometer. A time-of-flight technique was used to reject undesirable background. Absolute cross sections were determined for γ-ray transitions to the g 9 2 ground state, the i 11 2 state at 0.78 MeV, the doublet of j 15 2 and d 5 2 states near 1.5 MeV, and the close pair of g 7 2 and d 3 2 states at about 2.5 MeV in 209Pb. All cross sections show a resonance behavior in accordance with the prediction of semi-direct capture theory as the neutron energy spans the giant-dipole resonance. The measured cross sections are a factor of 2–3 higher than the predicted values.

Doorway states and primary neutron capture gamma-rays

The Projection Operator formalism of nuclear reactions utilizing the doorway state assumption is applied to neutron capture reactions in the one-photon approximation. The transition matrix divides into three parts, a direct capture term, a semidirect term proceeding through doorway states and a compound nuclear part. The same doorway states contributing to semidirect capture are involved in the resonance term. The partial radiation width amplitude can be written, Γ yij 1 2 = C 1S jkΓ nio 1 2 +C 2jΓ io 1 2 + S jkΓ yiδDk 1 2 +Γ yiδDk 1 2 +Γ yij 1 2 ( random) . Γ nio , S jk 2 are the resonance and final state reduced neutron widths. C 1 and C 2 j are transition matrix elements from the initial single-particle state to the lowlying single-particle state k and the final state j, respectively. The two terms have possible enhancement factors. The third and fourth terms are doorway contributions. The giant dipole resonance is included in the theory. Expressions for the correlation coefficients C( Γ nio , Γ yij ), C( Γ yij , Γ yij′ ), C( S jk 2, Γ yij ) are given. An isolated doorway responsible for radiation to several final states and also connecting entrance channel and compound nucleus results in the first two coefficients being unity. The theory is extended to include the two-group model of the compound nucleus. Application of the theory is made specifically to neutron capture experiments in 93Nb, 165Ho, 166Er, 169Tm, and 183W. Capture ψ-ray results to-date can be understood in terms of the theory.