Direct Capture Cross Section Research Articles

Spectroscopic factors from direct proton capture

Spectroscopic factors derived from direct capture studies are systematically compared to those obtained from transfer reaction experiments and from shell model calculations for the $\mathrm{A}=16--32$ target mass region. The direct proton capture and proton transfer spectroscopic factors are obtained in the present work from a reanalysis of literature data by using the same bound state potential parameters. Our direct capture spectroscopic factors differ significantly from the values originally reported in the literature. The sensitivity of the direct capture cross section to different choices for the scattering potential is explored. We find evidence that spectroscopic factors obtained from direct capture studies are as reliable as those extracted from transfer measurements if the (direct capture) radial scattering wave function is calculated with a zero nuclear scattering potential instead of the common choice of a hard-sphere potential.

Nonresonant capture cross sections ofB11(n,γ)andC12(n,γ)at stellar energies

The nonresonant direct radiative capture (DRC) cross sections of $^{11}\mathrm{B}(n,\ensuremath{\gamma})$ and $^{12}\mathrm{C}(n,\ensuremath{\gamma})$ at stellar energies are deduced by means of the asymptotic normalization coefficient (ANC) method. The ANC factors were extracted from the peripheral transfer reactions of $^{11}\mathrm{B}(d,p)$ and $^{12}\mathrm{C}(d,p)$. The deduced DRC cross sections of $^{12}\mathrm{C}(n,\ensuremath{\gamma})$ are in good agreement with experimental results of direct measurement. The DRC cross sections of $^{11}\mathrm{B}(n,\ensuremath{\gamma})$ at low energies are obtained for the first time.

The 17F( p,γ) 18Ne direct capture cross section

The 17F( p,γ) 18Ne direct capture cross section is important for understanding nucleosynthesis in novae. We have measured cross sections for the proton-transfer reaction 14N( 17F, 18Ne) 13C in order to determine asymptotic normalization coefficients for the 17F+ p system and hence the 17F( p,γ) 18Ne direct capture cross section. The technique and preliminary results are presented.

Radiative cascade transitions and the12C(α,γ)16OE2cross section to the ground state of16O

The $\ensuremath{\alpha}$-particle width of the 6.917 MeV, ${J}^{\ensuremath{\pi}}{=2}^{+}$ state in ${}^{16}\mathrm{O}$ is the most uncertain value in the determination of the $E2$ radiative ground state transition of the astrophysically important ${}^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{16}\mathrm{O}$ reaction at energies relevant to stellar helium burning. As discussed previously in literature it is possible in principle to derive a precise value of the $\ensuremath{\alpha}$ width of the 6.917 MeV state by measuring the $E2$ direct capture into this state. Here the theory based on the R-matrix formalism connecting the cascade direct capture and the $E2$ ground state transition is described in more complete form than hitherto and resulting direct capture cross sections are estimated. In addition, conditional fits are made to existing data and the resulting value of the $\ensuremath{\alpha}$-particle width is discussed. From these considerations the cascade cross sections are found to be of the order of 10 nb in an extended energy range proposed to be measured. Angular distributions for the primary $\ensuremath{\gamma}$ transition are also given. Conclusions for future experiments are then drawn. The branching ratio of the $7.\stackrel{\ensuremath{\rightarrow}}{1}6.9\mathrm{MeV}\ensuremath{\gamma}$ transition should also be measured.

Measurement of neutron capture on50Tiat thermonuclear energies

At the Karlsruhe and T\"ubingen 3.75 MV Van de Graaff accelerators the thermonuclear ${}^{50}\mathrm{Ti}(n,\ensuremath{\gamma}{)}^{51}\mathrm{Ti}(5.8\mathrm{min})$ cross section was measured by the fast cyclic activation technique via the 320.852 and 928.65 keV $\ensuremath{\gamma}$-ray lines of the ${}^{51}\mathrm{Ti}$ decay. Metallic Ti samples of natural isotopic composition and samples of ${\mathrm{TiO}}_{2}$ enriched in ${}^{50}\mathrm{Ti}$ by 67.53% were irradiated between two gold foils which served as capture standards. The capture cross section was measured at the neutron energies of 25, 30, 52, and 145 keV, respectively. The direct capture cross section was determined to be $0.387\ifmmode\pm\else\textpm\fi{}0.011\mathrm{mb}$ at 30 keV. We found evidence for a bound state s-wave resonance with an estimated radiative width of 0.34 eV which destructively interferes with direct capture. The strength of a suggested s-wave resonance at 146.8 keV was determined. The present data served to calculate, in addition to the directly measured Maxwellian averaged capture cross sections at 25 and 52 keV, an improved stellar ${}^{50}\mathrm{Ti}(n,\ensuremath{\gamma}{)}^{51}\mathrm{Ti}$ rate in the thermonuclear energy region from 1 to 250 keV. The new stellar rate leads at low temperatures to much higher values than the previously recommended rate; e.g., at $kT=8\mathrm{keV}$ the increase amounts to about 50%. The new reaction rate therefore reduces the abundance of ${}^{50}\mathrm{Ti}$ due to s processing in asymptotic giant branch stars.

Measurement of direct neutron capture by neutron-rich sulfur isotopes

Thermal neutron capture cross sections for 34S(n,γ) 35S and 36S(n,γ) 37S have been measured and spectroscopic factors of the final states have been extracted. The calculated direct-capture cross sections reproduce the experimental data.

Neutron resonance parameters and thermal-neutron capture by 43Ca.

Neutron transmission measurements have been carried out on a small sample (205.9 mg) of ${\mathrm{CaCO}}_{3}$ with a $^{43}\mathrm{Ca}$ enrichment of 49.1%. The parameters (spins and neutron widths) of eight resonances below the neutron energy of 20 keV have been determined. This information was combined with a previously measured thermal-neutron coherent scattering length to deduce the separate scattering lengths for the two spin states present in s-wave scattering. These values were used to calculate the direct (potential + valence) capture cross sections of the primary electric-dipole gamma transitions in $^{44}\mathrm{Ca}$ using optical-model potentials with physically realistic parameters. For those states below 6.2 MeV for which the l=1 (d,p) spectroscopic factors are known, the experimental cross sections are consistent with our current understanding of the direct and compound-nuclear capture processes. The processes leading to states above 6.2 MeV require further experimental and theoretical studies.

Thermal-neutron scattering length and capture by 46Ca.

We have deduced the coherent scattering amplitude of $^{46}\mathrm{Ca}$ as 3.55\ifmmode\pm\else\textpm\fi{}0.21 fm by measuring the neutron-diffraction patterns of calcite enriched to 32% in $^{46}\mathrm{Ca}$. We have employed this value in calculating the direct-capture cross sections of the primary electric-dipole \ensuremath{\gamma} transitions in $^{47}\mathrm{Ca}$ using optical-model potentials with physically realistic parameters. The calculated cross sections agree reasonably well with measurements showing that thermal-neutron capture by $^{46}\mathrm{Ca}$ is controlled largely by a simple direct mechanism.

The 7Li( γ, n 0) 6Li cross section near threshold

A high-resolution measurement of the 7Li( γ, n 0) 6Li cross section near threshold is presented. Direct-capture cross section components for the inverse reaction 6Li(n, γ 0) were extracted and compared to values calculated using the assumption that properties of mirror direct-capture reactions can be explained by optical potentials having the same set of potential parameters and spectroscopic factors. The satisfactory agreement validates this assumption for the mirror reaction pair 6 Li( p, γ) and 6 Li( n, γ) . Implications for the “solar neutrino” problem are mentioned.

Direct thermal neutron capture

The authors discuss the direct capture theory pertaining to primary electric dipole (E1) transitions following slow neutron capture. For light nuclides that they have studied (including 9Be, 12C, 13C, 24Mg, 25Mg, 26Mg, 32S, 33S, 34S, 40Ca, and 44Ca), estimates of direct capture cross sections using optical model potentials with physically realistic parameters are in reasonable agreement with the data. Minor disagreements that exist are consistent with extrapolations to light nuclides of generally accepted formulations of compound nucleus capture. They also discuss the channel capture approximation which is, in general, a good representation of these cross sections in heavier nuclei, particularly if the scattering lengths are not different from the corresponding potential radii. They also draw attention to cases where the use of this formula leads to inaccurate predictions.

Analysis of primary electric dipole gamma rays from slow-neutron capture by Ca isotopes.

We have analyzed the available data on the primary $E1$ transitions in the thermal-neutron capture by even isotopes of calcium with the aim of determining the relative importance of direct and compound-nucleus mechanisms of capture in these nuclides. In some of these cases, the thermal-neutron scattering length, as well as the spectroscopic factors of the final states, is known, and an absolute estimate of the direct capture cross sections can be made. In these cases ($^{40}\mathrm{Ca}$, $^{44}\mathrm{Ca}$) the estimates made from a specialized optical model (which reproduces the scattering length precisely) and a global optical model with a valency contribution from a local level are in agreement and are also generally close in absolute value to the experimental cross sections. The detailed deviations can be accounted for as a compound-nucleus contribution to the transitions, which fluctuates, but has an overall magnitude in agreement with Cameron's semiempirical relationship for this mechanism. In both nuclides the compound-nucleus contribution to the capture can plausibly be attributed to a bound local level. For $^{48}\mathrm{Ca}$ there is some indirect evidence for the value of the thermal-neutron scattering length, and the use of this value in the calculations of direct capture leads to agreement with the data. There is no evidence for an important compound-nucleus contribution in this magic number nucleus. In $^{42}\mathrm{Ca}$ and $^{46}\mathrm{Ca}$ the thermal-neutron scattering length can be adjusted to "best fit" the calculation of direct capture from the optical model to the experimental data. After this adjustment the detailed agreement between theory and data is very good, indicating the major predominance of the direct mechanism in capture at thermal-neutron energies by these nuclides.

The16O(?, ?)20Ne direct capture reaction at low energies

The16O(α, γ)20Ne direct capture cross section has been calculated in a microscopically founded cluster model which reproduces simultaneously both the correct binding energies and the deformations of the20Ne bound states. Theα+16O scattering states are derived from a microscopically derived local potential. The astrophysicalS-factor is found to increase linearly with energy in the energy rangeE cm≈0.4–2 MeV and might therefore be determinable experimentally.

Proton direct capture on 40Ca

Excitation functions for the 40Ca(p, γ) 41Sc reaction have been measured at 0° and 90° in the proton energy range E p = 2.1–3.1 MeV. The experimental results have been interpreted in terms of the direct capture process to the first excited state of 41Sc. The direct capture transition to the ground state has been observed only at a few proton energies. The spectroscopic factor of the first excited state in 41Sc has been found to be 1.0 ± 0.3. The direct capture cross section to the ground state is consistent with the spectroscopic factor reported from stripping reactions.

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.]

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.

Cross sections for high-energy γ-transitions from MeV neutron capture in 206Pb

Gamma-ray spectra from neutron capture in 206Pb (radiogenic lead) in the energy range 1.5 to 8.5 MeV were recorded using time-of-flight techniques. The spectrometer was a NaI(Tl) crystal, 20.8 cm long and 22.6 cm in diameter. The spectra are dominated by γ-transitions to levels with large single-particle strength, in agreement with predictions of semi-direct capture theories. The theories predict enhancements of the direct capture cross section by a factor of 10–15 in the region of the giant dipole resonance. The observed enhancement is about 50.

Direct Neutron Capture inCo59(n, γ)Co60

The variation in intensity of 40 individual $\ensuremath{\gamma}$ rays produced by neutron capture in cobalt was observed for neutron energies less than 1500 eV. The observed variations were consistent with the existence of a direct component in the radiative capture reaction mechanism. A direct-capture cross section of 9.2\ifmmode\pm\else\textpm\fi{}2.4 mb at 1-eV neutron energy was deduced for the 7.492-MeV ground-state transition.

Direct neutron capture in lead

Data for neutron capture and photonuclear reactions in lead isotopes have been re-analysed and show consistent evidence for an asymmetry in the 43 keV resonance in 207Pb(n, γ). Interpretation of the asymmetry is complicated by the presence of small p-wave resonances but it can be explained by assuming a direct capture cross section of 0.04 b at 1 eV.

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.