Radiative capture of low-energy neutrons in the shell-model approach to nuclear reactions

The shell-model approach to photonuclear reactions is applied to the radiative capture of low-energy neutrons. The direct, compound and channel resonant contributions to the collision matrix appear in a natural way. We show that the experimental data in the vicinity of the 3s giant resonance can be quantitatively interpreted in terms of the channel resonant capture. The relationship with the R-matrix approach of Lane and Lynn is discussed.     

Analysis of E1 radiative neutron capture based on the optical model

The optical model formula of Lane and Mughabghab for E1 radiative neutron capture has been applied to resonance capture in ⁵⁶Fe and ⁹⁰Zr. It is shown that in general the optical model predicts the contributions to the radiative widths which are correlated with the neutron widths, except for a depletion factor representing the proportion of E1 single-particle strength remaining near the neutron threshold. The degree of correlation between measured and calculated radiative widths is related to the ratio of the variances of these widths. This enables an estimate of the factor . It is shown that the theoretical value for the ratio of the radiative to neutron widths is to a good approximation independent of the imaginary part of the optical potential. The calculated radiative width is thus well defined. The results are compared with those from the valence model and from experiment. The direct background contribution is found to be negligible compared to the average compound cross section. The contribution of d-waves to the radiative capture cross section is discussed.     

Average neutron resonance parameters and radiative capture cross sectins for the isotopes of molybdenum

The neutron capture cross sections of the stable molybdenum isotopes have been measured with high energy resolution (ΔE/E ? 0.2 %), between 3 and 90 keV neutron energy, at the 40 m station of ORELA. Average resonance parameters are extracted for s- and p-wave resonances. The s-wave neutron strength function is close to 0.5 × 10^?4 for all isotopes, but the p-wave strength function exhibits a well defined peak near At~ 95.Both s- and p-wave radiative widths decrease markedly as further neutrons are added to the closed shell. The p-wave radiative widths are generally greater than the s-wave widths showing the presence of non-statistical γ-decay mechanisms.Valence neutron theory fails to explain the magnitude of the p- to s-wave radiative width disparity and doorway state processes are invoked. In particular, the data for ⁹⁸Mo appear to violate the usual valence theory, since the correlations between radiative and neutron strengths are small. Further, the radiative widths are smaller than can be explained on the valence model. An explanation for the loss of valence strength is advanced.Interpolated resonance parameters allow an estimate for the unknown cross section for ⁹⁹Mo(n, γ).     

Resonance and background interference in 54Fe neutron capture

Asymmetric s-wave resonances observed in the neutron capture cross section of ⁵⁴Fe can be explained by interference between resonance valence components. An upper limit is obtained for the background capture cross section which is much smaller than that expected from the large correlation observed between s-wave reduced neutron widths and radiative widths.     

Valence-doorway model for radiative capture

A model of radiative capture is presented in which the T-matrix for valence capture is expressed as the sum of three terms, viz., a direct capture term, a term that describes the coupling between a single-particle resonance and the many possible continuum channels, and a pure single-particle resonance term. Expressions for the target excitations are not explicitly included, and projection operators are used to break up the single-particle space into resonant and nonresonant parts. The spreading of single-particle resonances is described through the coupling to particle-vibration doorways. The model is applied to the cases of ⁹⁸Mo(n, γ) ⁹⁹Mo and ⁹²Mo(n, γ) ⁹³Mo for an energy range of 0–3 MeV. In these cases the single-particle resonance amplitude is overwhelmingly dominant, and doorway effects are found to be relatively unimportant. Radiative widths obtained from our calculated average cross sections are compared to the corresponding widths obtained by averaging over the detailed fine structure measurements of Chrien et al. for ⁹⁹Mo. Good agreement is obtained. The valence capture cross section in ⁹³Mo is considerably smaller than in ⁹⁹Mo. This is consistent with the measurements of Chrien et al. and in good agreement with a recent analysis by Soloviev and Voronov.     

Relation between the background cross section and the correlation between partial widths

A relation is derived between the background cross section and the correlation coefficient between partial width amplitudes, in the frame of the shell-model approach to nuclear reactions. It involves explicitly the resonance parameters, and in contrast to an otherwise equivalent relation recently derived by Lane, a direct contribution. We apply our result to the reactions ²⁹Si(γ, n), ¹⁶⁹Tm(n, γ) and ²⁰⁸Pb(γ, n). We show that the relationship between the observation of an asymmetric resonance peak and the existence of a sizable background cross section is not straightforward.     

A generalized r-matrix interpretation of the 89Y + n total cross section at low incident energies

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross-section measurements in the range of 0.9 to 1.2 MeV neutron energy is investigated using a comprehensive theory of nuclear reactions. A shell-model calculation which formed the initial stage of this study predicts satisfactorily the energies of the negative-parity states that contribute to the observed anomalies. The neutron decay widths for these resonances are evaluated using the model wave functions. The general trends in the energy dependence of the total cross section are satisfactorily reproduced by the theory. The factors that could contribute to the discrepancies between theory and experiment are discussed. The theoretical estimates of the damping widths for the two 1^? anomalies that occur in this region were within 20 to 25% of the experimental values and support the view that these are intermediate-type resonances. Their configurational structure as predicted by the model calculation suggests that they are the parent states of the T_> components of the giant dipole resonance near 21.0 MeV in ⁹⁰Zr. The distribution of E1 widths calculated for a proposed 1^? → 2⁺ (at 0.78 MeV) transition in ⁹⁰Y indicates that an anomaly corresponding to these 1^? states can also be expected in the (n, γ) reaction.     

Neutron capture gamma-rays from the low-lying resonances of 54Fe

Neutron capture γ-rays have been observed from the low-lying resonances of ⁵⁴Fe using the Harwell electron linear accelerator HELIOS as a neutron source. Relative values for the partial radiative widths of resolved lines were obtained by area analysis of the γ-rays peaks over neutron resonance regions, and absolute values were obtained by a shape analysis fit to the yield deduced by comparison with a ¹⁰B(n, αγ)⁷Li measurement. For the 7.8 keV s-wave resonance, a comparison of the partial widths with the predictions of the valence model has been made. In both relative and absolute senses, there is good agreement.     

Fast neutron radiative capture in silicon

Using the²⁸Si(n, γ)²⁹Si reaction, transitions to the ground state and first excited state in²⁹Si have been studied in the neutron energy range 3–14 MeV with improved neutron energy resolution (of about 100 keV). The 90° cross sections show considerable structure in the entire neutron energy range. Comparison with theoretical calculations shows that compound-nucleus and direct-semidirect processes account for the non-resonant part (smoothly varying part) of the cross section. A microscopic model is, however, required to describe the resonance structure. Continuum shell-model calculations have proven to be a very promising means towards a better understanding of the capture process in, and below, the giant resonance region in light nuclei. The angular distributions of gamma rays in the neutron energy range 8–14 MeV indicate that the capture reaction is mainly of direct character and that the effect of interference between the electric dipole and isoscalar quadrupole resonance is weak.     

Resonance neutron capture in 56Fe

The neutron capture cross section of ⁵⁶Fe has been measured with 0.2–0.3% energy resolution from 2.5 keV up to the inelastic neutron scattering threshold. Results are compared with recent total cross-section data and average parameters are derived for s-, p- and d-wave resonances. The low correlation coefficient observed between the s-wave reduced neutron and radiative widths is consistent with the minor contribution of the valence capture mechanism as calculated in the framework of the optical model. Broad E1 and M1 doorway states for s-, p- and d-wave resonances are postulated to explain the cross-section data and γ-ray spectra up to 1 MeV.     

On the relativistic field theory model of the deuteron II

The relativistic field theory model of the deuteron suggested previously is revised and applied to the calculation of the cross sections of the low-energ radiative neutron-proton capture n + p → D + γ and the low-energy two-proton fusion p + p → D + e⁺ + ν_e. For the low-energy data and the potential model prediction. In the case of the two-proton fusion the cross section obtained is 2.9 times as much as that given by the potential approach. The obtained result is discussed in connection with the solar neutrino problem.     

Properties of nuclear levels excited by neutron capture γ-rays from cobalt

Neutron capture γ-rays from cobalt have been used to photoexcite nuclear levels in the 5–8 MeV region. The decay properties of the 7491 keV level in ⁵⁵Mn and the 6877 keV level in ¹⁴²Nd were studied in detail. Total and partial radiative widths of nuclear levels in several isotopes were determined using nuclear self-absorption, temperature variation, and absolute scattering cross section measurements. The total radiative widths were found to be of the same magnitude as those of unbound levels populated in neutron resonances. The spins and parities of some resonance levels were determined by carrying out angular distribution and polarization measurements, respectively.     

The19F(n, γ)20F reaction

The gamma-ray spectrum emitted following thermal neutron capture in¹⁹F has been studied with curved crystal and Ge(Li) spectrometers. From the 109 transitions assigned to²⁰F, 85 have been placed in a level scheme containing 26 levels. An average gammaray multiplicity of 2.8 gammas per neutron capture was observed. The neutron binding energy was found to be 6601.33(14) keV. The experimental level scheme is compared to rotational model predictions. In addition it is shown that the decay of the capture state is non-statistical and that there is a strong correlation between the strengths of excitation of levels by the (n, γ) and (d, p) reactions. Calculations of the partial cross-sections using the direct capture theory of Lane and Lynn give order of magnitude agreement with experiment.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Reaction efficiencies in nucleon channels for 7Li and 9Be nuclei

Reaction cross sections of the radiative capture of nucleons ⁶Li(n, γ)⁷Li, ⁶He(p, γ)⁷Li, and ⁸Li(p, γ)⁹Be in the region of low astrophysical energies are calculated using the dynamic potential cluster model. The results are compared to the available experimental and theoretical data. The yields of these reactions are also calculated, based on the established theoretical results.     

Properties of the quasiparticle excitations in 207Pb and 209Pb from an extrapolation of the optical-model potential

A previously developed dispersion relation approach is used to calculate the shell-model potential in the case of neutrons in ²⁰⁸Pb, in the energy domain (-50 MeV, 0). This potential contains a dispersive contribution besides a Hartree-Fock type component, and thereby includes correlation and polarization effects. The shell-model and the Hartree-Fock type potentials are assumed to have Woods-Saxon shapes with diffuseness a_v = 0.70 fm; the energy dependence of their depths and radii is calculated. The energy dependence of the shell-model potential is characterized by the effective mass, whose dependence upon radial distance and neutron energy is determined. The effective mass is a sensitive function of energy, in contrast to its Hartree-Fock type component which is nearly independent of energy. Attention is drawn to the fact that the effective mass in nuclear matter cannot be straightforwardly identified with the effective mass at the nuclear centre. The effective mass presents a sharp peak at the nuclear surface near the Fermi energy and a dip at the surface for energies 10 to 20 MeV away from the Fermi energy. The spectroscopic factors of single-particle excitations in ²⁰⁷Pb and ²⁰⁹Pb are calculated from the difference between the effective mass and its Hartree-Fock type component. The predicted values of the valence single-particle wave functions at large radial distances are in fair agreement with experimental values deduced from analyses of sub-Coulomb pickup reactions. It is shown that the dispersive contribution increases the level density parameter by about 25%, in agreement with previous microscopic or semi-phenomenological models; the calculated level density parameter is in good agreement with the empirical value.     

Radiative capture reactions with the participation of weakly bound light nuclei

Reactions of radiative capture of weakly bound light nuclei are investigated in the scope of the potential model. The applicability of the approach is demonstrated with an analysis of the cross section for the ⁶Li(p, ??)⁷Be reaction. Good agreement with the available experimental data is shown. The radiative capture cross section for the ⁶He(p, ??)⁷Li reaction in the region of low sub-barrier energies is evaluated. It is concluded that reactions involving ⁶He could also play a noteworthy part in stellar nucleosynthesis processes.     

An interference effect in the channel radiative neutron capture process

This study shows that the small thermal neutron radiative capture cross sections in ¹²C and neighbouring nuclides are the result of destructive interference between the potential scattering wave and the resonance scattering wave near the nuclear surface, resulting in a drastic cancellation in the radial integral. The behaviour of the scattering wave function is examined, and the general condition for the occurrence of such cancellation is discussed. The expression for the channel radiative capture cross section which has been derived has the same structure as the Lane-Lynn formula but is expressed in terms of different parameters. In addition, this investigation shows that if the optical model well depth is adjusted so that the binding energy of the $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbit in ¹²C is kept at the experimental value, then the calculated results for the potential and channel radiative neutron capture cross sections are insensitive to the value of the nuclear radius.