Direct Radiative Capture Research Articles

Examination of direct radiative capture formalism

Within the direct reaction framework the formalism and approximations used to describe particle radiative capture processes at low to medium energies are reviewed. Survey calculations documenting sizeable cross-section sensitivity to different forms of the electromagnetic interaction (Siegert's theorem versus J · A ) that preserve overall gauge invariance are reported. The source of this large difference is the inconsistent use of different initial and final state model hamiltonians. This defect, common to most reaction theories using optical-model wave functions, generates wave function nonorthogonality effects which are found to be significant for M1 transitions. The importance of the spin-flip contribution to both electric and magnetic transitions is also investigated.

Direct capture cross sections at low energy

We derive simple expressions for the low-energy behavior of direct radiative capture cross sections, particularly those important in solar nucleosynthesis, such as (^3)He(α,γ)(^7)Be, (^3)H(α,γ)(^7)Li, and (^7)Be(p,y)(^8)B. Our results for the (^3)He(α,γ)(^7)Be reaction are inconsistent with a measurement by Rolfs et al. [NUCLEAR REACTIONS (^3)He(α,γ)(^7)Be, (^3)H(α,γ)(^7)Li, E<300 keV, (^7)Be(p,y)(^8)B, l E<lOO keV, extrapolated S.]

Direct radiative capture of high-energy electrons by atomic ions

Cross sections for the direct radiative capture of electrons in the keV range by highly stripped ionic targets are estimated using the effective-charge approximation and the scaling property.

On the direct capture to unbound states

Recently a discrepancy between the theory of direct radiative capture to unbound states and experimental results for the reaction 12C(p, γ 1) 13N (2366 keV, unbound) has arisen at low γ-energies (150 keV < E γ < 500 keV). It is shown that this discrepancy can be removed by a careful evaluation of the theoretical expression for the usual theory of direct capture to unbound states.

Radiative capture of electrons by Mo ions

We present results for direct radiative capture of 1-100-keV electrons by Ar-like, Ne-like, and completely ionized Mo ions. The dependence on incident electron energy and degree of ionization is discussed.

Radiative capture and recombination in electron-atom collisions

A comprehensive theory of electron scattering from atoms and ions at high energies is formulated, incorporating the coupling of the scattering system to the radiation field. In particular, the photocapture process is discussed in detail, which can proceed either by a direct radiative capture or by dielectronic recombination following a radiationless capture into excited states. The latter process involves a collisional excitation of the inner-shell electrons of the target, followed by radiative decay of that excited state. The required sum over excitation probabilities to all the allowed bound states is estimated using the semiclassical projection operators and the single-particle model for the target system. A preliminary estimate of the cross sections for these modes of capture is obtained for the case of a hot-electron plasma interacting with highly ionized impurity ions.

The 16O(p, γ)17F Direct Capture Cross Section with an Extrapolation to Astrophysical Energies

The cross section for the direct radiative capture of protons by 16O has been measured relative to the proton elastic scattering cross section for energies from 800 to 2400 keV (CM). The elastic scattering cross section was normalized to the Rutherford scattering cross section at 385.5 keV. The capture cross section for the reaction 16O(p,γ)17F, which plays a role in hydrogen burning stars, has been extrapolated to stellar energies using a theoretical model which gives a good fit to the measured cross sections. The model involves calculation of electromagnetic matrix elements between initial and final state wave functions evaluated for Saxon–Woods potentials with parameters adjusted to fit both elastic scattering data and binding energies for the ground and first excited states of 17F. Cross sections for capture to the 5/2+ ground and 1/2+ first excited states of 17F in terms of astrophysical S factors valid for energies ≤ 100 keV have been found to be: S5/2+ = (0.317 + 0.0002E) keV b (± 8%); S1/2+ = (8.552 − 0.353E + 0.00013E2) keV b (± 5%).

Proton capture by 15N at stellar energies

Excitation functions of the 15N(p, γ) 16O proton capture reaction have been obtained at θ γ = 45° and E p = 150–2500 keV. Below E p = 400 keV, the reaction is dominated by capture into the ground state of 16O. The observed excitation function for the latter process can be explained if, in addition to the two well-known J π = 1 − resonances at E p = 338 and 1028 keV, a direct radiative capture process (DC → 0) is included in the analysis. The direct capture component in the capture reaction is enhanced through interference effects on the tails of the two resonances. From the observed direct capture cross section, a single-particle spectroscopic factor of C 2 S(1p) = 1.8 ± 0.4 has been deduced for the ground state in 16O. The extrapolated astrophysical S-factor of S(0) = 64 ± 6 keV · b for the 15N(p, γ 0) 16O reaction is a factor of 2.5 larger than previously reported. This result amplifies the role of the oxygen side cycle in the CNO hydrogen burning process. The observed excitation function of the 15N(p, α 1 γ 1) 12C reaction at E p = 150 – 2500 keV shows that this reaction makes a negligible contribution to hydrogen burning at stellar energies [ S(0) ≈ 0.1 keV · b] compared to 15 N( p, γ 0) 16 O and 15 N( p, α o ) 12 C .

Interference effects in 12C(p, γ) 13N and direct capture to unbound states

Excitation functions of the capture reaction 12C(p, γ 0) 13N have been obtained at θ γ = 0° and 90° and E p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in 13N is included in the analysis in addition to the two well-known resonances in this beam energy range [E p = 457( 1 2 +) and 1699 ( 3 2 −) keV] . The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C 2 S( l = 1) = 0.49 ± 0.15 has been deduced for the 1 2 − ground state in 13N. Excitation functions for the reaction 12C(p,γ 1p ∗) 12C have been obtained at θ γ = 0° and 90° and E p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the 2366 ( 1 2 +) keV unbound state. Above E p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E p = 1 MeV, i.e., E p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at E p ⪆ 1 MeV , a spectroscopic factor of C 2 S( l = 0) = 1.02 ± 0.15 has been found for the 2366 ( 1 2 +) keV unbound state. A search for direct capture transitions to the 3512 ( 3 2 −) and 3547 ( 5 2 +) keV unbound states resulted in upper limits of C 2 S( l = 1) ≦ 0.5 and C 2 S( l = 2) ⪅ 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the 12C(p, γ 0) 13N reaction also is discussed.

Direct and semi-direct radiative capture of nucleons in deformed nuclei

The theory of the direct and semi-direct (collective) radiative capture of nucleons is extended to the case of deformed nuclei. Particular attention is paid to the giant dipole resonance, excited by the coupling of the incident particle to collective vibrations of the target nucleus. Captured single-particle bound states in the deformed potential are calculated using the method which solves the coupled differential equations derived on the Kapur-Peierls basis. The cross sections are found to be quite sensitive to the choice of parameters used in the numerical calculation, such as the giant resonance widths, γ-absorption cross section and strength of the isospin-dependent potential. Applications are made to the radiative capture of 14 MeV neutrons on 160Gd and 238U. Radiative capture of neutrons on 208Pb and 159Tb is also included to discuss some ambiguities in the choice of parameters and in the calculation of bound states.

THE RATE OF THE ^{14}N(α,γ)^{18} F REACTION.

view Abstract Citations (25) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS THE RATE OF THE ^{14}N(α,γ)^{18} F REACTION. Couch, R. G. ; Spinka, H. ; Tombrello, T. A. ; Weaver, T. A. Abstract New experimental and theoretical results are presented on the 14N(a, )18 reaction. A new resonance has been found at F = 0.56 MeV with (2J + 1) /F = 2.8 + 0.5 X 10- eV (lab). From a theoretical calculation of the cross-section for direct radiative capture, and an extrapolation of the tails of the measured resonances to Ea = 0.0, a value S 0.7 MeV-barns is estimated for the nonresonant S-factor. The reaction rate is calculated, and the significance of this rate is discussed. It is found that in most stars a-capture by `4N takes place after the initiation of helium burning by the 3a `2C reaction. Publication: The Astrophysical Journal Pub Date: March 1972 DOI: 10.1086/151359 Bibcode: 1972ApJ...172..395C full text sources ADS |

Total cross-section measurements for [formula omitted

Total cross section measurements have been made for the 14N(α,γ) 18F reaction for 0.5 ≦ E α ≦ 1.2 MeV. A new resonance has been found at E α (lab) = 0.56 MeV, corresponding to the 4.849 MeV state in 18F. The quantity (2 J + 1) Γ α Γ γ / Γ was determined to be (2.79±0.5) × 10 −4 eV and 0.108±0.015 eV for states at E α = 0.56 and 1.14 MeV, respectively. From a theoretical calculation of the cross section for direct radiative capture and an extrapolation of the tails of the measured resonances to E α = 0.0, a value S ≈ 0.7 MeV · b has been estimated for the non-resonant S-factor. The astrophysical significance of the 14N(α,γ) 18F reaction is discussed and the reaction rate, N A〈 σν 〉, is calculated for temperatures 0.01 ≦ T 9 ≦ 1.0. The rate is accurately determined by the experimental measurements for T 9 > 0.09.

Radiative capture cross sections in medium-weight and heavy nuclei

Induced radioactivity methods have been used to measure radiative capture cross sections of alpha particles in 139La (bombarding energy 10–36 MeV), tritons in 138Ba (6–13 MeV), deuterons in 139La and 30Si (6–18 MeV) and protons in 82Se and 100Mo (5–50 and 5–20 MeV, respectively). The results are diffucult to reconcile with statistical theory. The direct radiative capture cross section calculated for the two proton capture reactions when enhanced by the particle-hole interaction approximates the experimental data over the entire energy range.

Interference between collective and direct nucleon radiative capture

The interference term between direct and collective dipole radiative capture of nucleons by nuclei is obtained. The cross-section is written in a Breit-Wigner form as a sum of three terms: direct capture, collective or « resonant » capture and interference term. The expression of the latter term is investigated and the conditions for constructive, destructive and zero interference are given. The nucleon capture cross-sections for130Te,142Ce and208Pb are calculated. Taking into account the interference between direct and collective processes, a better agreement between theory and experiment is achieved.

The spin-orbit interaction in the collective and direct nucleon radiative capture

The expression for the nucleon radiative capture cross-section by nuclei via a collective mechanism is completed in order to take into account the spin-orbit interaction. The direct and collective cross-sections for208Pb(n, γ) and208Pb(p, γ) reactions are calculated. A good agreement between calculated and measured cross-sections is obtained using optical parameters which describe quite accurately experimental differential elastic scattering, reaction cross-sections and polarization data.

The photodisintegration of 3He from a direct capture model of the [formula omitted] reaction

Differential and total cross sections have been obtained for the reaction 3He(γ, p)d by applying the reciprocity theorem to results calculated for the reaction d(p, γ) 3He on the basis of a simplified two-body direct radiative capture model. The proton-deuteron interaction is described by a square well plus Coulomb potential in both continuum and bound states. An attempt is made to relate the continuum wave functions used in the model to the p-d scattering data. Contributions from M1, E1 and E2 radiations are considered and good agreement is found with recent experimental data from threshold to 40 MeV. The E1-E2 interference is found to be of importance even at low energies.

(d, n) thresholds and direct proton capture

An examination is made of the correlation between the occurence of intense neutron thresholds in (d, n) reactions and the observation of direct radiative capture to the corresponding levels in (p, γ) reactions on the same target nuclei. It is concluded that all experimental evidence favours a one-to-one correspondence between these effects, indicating large proton reduced widths for all levels observed as intense (d, n) thresholds. It is argued that direct radiative capture should be observable in the B 10(p, γ)C 11 reaction and to a lesser extent in certain other reactions.

Direct radiative capture into a resonant state

A theory of the direct radiative capture into a resonant final state is given. The part which results from the interaction with the Coulomb potential can be neglected compared with that from the nuclear potential. The radial matrix element is essentially only a product of the depth of the nuclear potential and the Coulomb functions at the nuclear radius. A formula for the total cross section is derived. The theory is compared with experiment for the two reactions C 12(p, γp′)C 12 and C 13(p, γp′C 13. The aggreement between theory and experiment is satisfact

The structure of the giant dipole resonance: (III). Fluctuations and direct interaction in light nuclei

Data on the structure and angular distribution of the radiative capture of protons by seven light nuclei are summarized and analysed in terms of the theory of statistical fluctuations and compared with direct radiative capture calculations. It is concluded that 1. (1) Much of the structure observed in (p, γ) measurements has no great significance for the giant dipole resonance, being in fact due to weak compound nucleus effects interfering with a dominant direct interaction. 2. (2) A giant quadrupole resonance probably exists which may be due to simple radiative capture of the proton into a potential well. 3. (3) The giant dipole resonance, although probably a direct (i.e. short lifetime) phenomenon, is not due to simple capture into a potential well but must involve a few scatterings of the ingoing proton by nucleons of the target which serve to concentrate the resonance strength at higher excitation.

Direct radiative proton capture reactions in cerium and bismuth

The direct radiative capture cross-section is evaluated using the formalism of Lane and Lynn with a diffuse optical potential and an improved method of evaluating the integrals. These refinements are found to worsen the agreement with experiment. Calculations are also made for the proton capture reactions on cerium and bismuth studied by Daly and Shaw and the theory is found able to account for the data above 20 MeV, but not at lower energies.