Direct Capture Model Research Articles

Direct capture cross section of Be9(n,γ)Be10

The cross section of the $^{9}$Be(n,$\gamma$)$^{10}$Be reaction was calculated in the direct capture model. All parameters of the calculations were adjusted to properties of the $^{9}$Be + n system at thermal energies. The calculated cross section at thermonuclear energies shows the expected $1/v$ behavior of $s$-wave capture at low energies, but increases towards higher energies as typical $p$-wave capture. Excellent agreement between new experimental data in the astrophysically relevant energy region and the present calculation is found.

Comment on “Structure effects in theN15(n,γ)N16radiative capture reaction from the Coulomb dissociation ofN16”

In their recent study Neelam, Shubhchintak, and Chatterjee have claimed that ``it would certainly be useful to perform a Coulomb dissociation experiment to find the low-energy capture cross section for the reaction'' $^{15}\mathrm{N}$($n,\ensuremath{\gamma}$)$^{16}\mathrm{N}$. However, it is obvious that a Coulomb dissociation experiment cannot constrain this capture cross section because the dominating branchings of the capture reaction lead to excited states in $^{16}\mathrm{N}$, which do not contribute in a Coulomb dissociation experiment. An estimate of the total $^{15}\mathrm{N}$($n,\ensuremath{\gamma}$)$^{16}\mathrm{N}$ cross section from Coulomb dissociation of $^{16}\mathrm{N}$ requires a precise knowledge of the $\ensuremath{\gamma}$-ray branchings in the capture reaction. Surprisingly, the calculation of Neelam, Shubhchintak, and Chatterjee predicts a strongly energy-dependent ground-state branching of the order of 0.05% to 0.6% at energies between 100 and 500 keV, which is almost 2 orders of magnitude below calculations in the direct capture model. Additionally, this calculation of Neelam, Shubhchintak, and Chatterjee deviates significantly from the expected energy dependence for $p$-wave capture.

Direct capture in the130Sn(n,γ)131Sn and132Sn(n,γ)133Sn reactions underr-process conditions

The cross sections of the ${}^{130}$Sn($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$)${}^{131}$Sn and ${}^{132}$Sn($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$)${}^{133}$Sn reactions are calculated in the direct capture model at low energies below 1.5 MeV. Using recent data from ($d\phantom{\rule{-0.16em}{0ex}},\phantom{\rule{-0.16em}{0ex}}p$) transfer experiments on ${}^{130}$Sn and ${}^{132}$Sn, it is possible to avoid global input parameters with their inherent uncertainties and to determine all inputs to the direct capture model by local adjustments. The calculated direct capture cross sections of ${}^{130}$Sn and ${}^{132}$Sn are almost identical and have uncertainties of less than a factor of 2. The stellar reaction rates ${N}_{A}\ensuremath{\langle}\ensuremath{\sigma}v\ensuremath{\rangle}$ show a slight increase with temperature. Finally, an estimate for the influence of low-lying resonances to the stellar reaction rates is given.

Revised result for theCl32(p,γ)Ar33reaction rate for astrophysicalrp-process calculations

The $^{32}\mathrm{Cl}$(p,\ensuremath{\gamma})$^{33}\mathrm{Ar}$ reaction rate is of potential importance in the rp process powering type I x-ray bursts. Recently, Clement et al. [Phys. Rev. Lett. 92, 172502 (2004)] [1] presented new data on excitation energies for low-lying proton unbound states in $^{33}\mathrm{Ar}$ obtained with a new method developed at the National Superconducting Cyclotron Laboratory. We use their data, together with a direct capture model and a shell model calculation, to derive a new reaction rate for use in astrophysical model calculations. In particular, we take into account capture on the first excited state in $^{32}\mathrm{Cl}$, and we also present a realistic estimate of the remaining uncertainties. We find that the $^{32}\mathrm{Cl}$($p,\ensuremath{\gamma}$)$^{33}\mathrm{Ar}$ reaction rate is dominated entirely by capture on the first excited state in $^{32}\mathrm{Cl}$ over the whole temperature range relevant in x-ray bursts. In the temperature range from 0.2 to 1 GK the rate is up to a factor of 70 larger than the previously recommended rate based on shell model calculations only. The uncertainty is now reduced from up to a factor of 1000 to a factor of 3 at 0.3--0.7 GK and a factor of 6 at 1.5 GK.

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.

TheB10(p⃗,γ)C11reaction at astrophysically relevant energies

The $^{10}\mathrm{B}(\stackrel{P\vec}{p},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction was studied by detecting the $\ensuremath{\gamma}$-rays produced when 100-, 130-, and $160\text{\ensuremath{-}}\text{keV}$ polarized protons were stopped in a thick $^{10}\mathrm{B}$ target. Polarized and unpolarized incident beams were used to measure the cross section and vector analyzing power as a function of angle and energy for capture to the ground $({J}^{\ensuremath{\pi}}=3∕{2}^{\ensuremath{-}})$, the second $(E=4319\phantom{\rule{0.3em}{0ex}}\mathrm{keV},{J}^{\ensuremath{\pi}}=5∕{2}^{\ensuremath{-}})$, and the fifth $(E=6478\phantom{\rule{0.3em}{0ex}}\text{keV},{J}^{\ensuremath{\pi}}=7∕{2}^{\ensuremath{-}})$ excited states of $^{11}\mathrm{C}$. The data were analyzed to obtain the amplitudes and phases of the contributing transition-matrix elements at each measured energy for all three transitions. Values of the astrophysical $S$ factors were obtained from the cross section data and are compared to previous results. A direct capture plus resonance model calculation was performed in an attempt to account for all measured quantities. It was found that the large $(\ensuremath{\sim}32%)$ value of ${A}_{y}(90\ifmmode^\circ\else\textdegree\fi{})$ observed in the case of capture to the ground state could be accounted for by including the sub-threshold resonance at $8420\phantom{\rule{0.3em}{0ex}}\text{keV}$.

Low-energy direct capture in the8Li(n,γ)9Liand8B(p,γ)9Creactions

The cross sections of the ${}^{8}\mathrm{Li}(n,\ensuremath{\gamma}{)}^{9}\mathrm{Li}$ and ${}^{8}\mathrm{B}(p,\ensuremath{\gamma}{)}^{9}\mathrm{C}$ capture reactions have been analyzed using the direct capture model. At low energies, which are the astrophysically relevant regions, the capture process is dominated by $E1$ transitions from incoming s waves to bound p states. The cross sections of both mirror reactions can be described simultaneously with consistent potential parameters, whereas previous calculations have overestimated the capture cross sections significantly. However, the parameters of the potential have to be chosen very carefully because the calculated cross section of the ${}^{8}\mathrm{Li}(n,\ensuremath{\gamma}{)}^{9}\mathrm{Li}$ reaction depends sensitively on the potential strength.

Cross Section for the Astrophysical14C(n, γ)15C Reaction via the Inverse Reaction

The 14C(n, γ)15C reaction is important in neutron-induced CNO cycles of stellar evolution phases beyond the main sequence. The chain of reactions in primordial nucleosynthesis in the neutron-rich environment of an inhomogeneous big bang also involves the 14C(n, γ)15C reaction. We have used a beam of 15C ions at E/A = 35 MeV to measure cross sections for 15C breakup on targets of C, Al, Zn, Sn, and Pb. The Coulomb part of the breakup cross section was determined as a function of decay energy. By the principle of detailed balance, the neutron capture cross section was then determined as a function of neutron energy. This excitation function rises with energy to 7 μbarns at 300 keV and falls to 2 μbarns at 1.2 MeV. In the stellar-burning region, our cross section exceeds a previous measurement by a factor of 3. Neither the shape nor the magnitude of the excitation function agrees with those of theoretical calculations based on the direct capture model. The reaction rate is calculated reliably up to ~T9 = 5. In the temperature range of inhomogeneous big bang models, our rate exceeds the rate of the 14C(p, γ)15N reaction for T9 < 1.2.

Reaction rates for neutron capture reactions to C, N, and O isotopes to the neutron rich side of stability

The reaction rates of neutron capture reactions on light nuclei are important for reliably simulating nucleosynthesis in a variety of stellar scenarios. Neutron capture reaction rates on neutron-rich C-, N-, and O-isotopes are calculated in the framework of a hybrid compound and direct capture model. The results are tabulated and compared with the results of previous calculations as well as with experimental results.

AstrophysicalSfactors for the9Be(p→,γ)10Breaction

Analyzing powers for the ${}^{9}\mathrm{Be}(\stackrel{\ensuremath{\rightarrow}}{p},\ensuremath{\gamma}{)}^{10}\mathrm{B}$ reaction were measured by stopping a 100 keV polarized proton beam in a ${}^{9}\mathrm{Be}$ target. The measured vector analyzing power is ${A}_{y}(90\ifmmode^\circ\else\textdegree\fi{})=0.18\ifmmode\pm\else\textpm\fi{}0.03$ for capture to the ground state, with smaller values at $90\ifmmode^\circ\else\textdegree\fi{}$ for the first three excited states. Astrophysical $S$ factors were calculated for each of the final states using a direct capture plus resonance model which fit both the present analyzing power data and the previously reported cross section data. The calculated $S$ factors at ${E}_{p}=0 \mathrm{keV}$ for capture to the ground state and first three excited states were 0.25, 0.34, 0.27, and 0.10 keV b, respectively, which are considerably smaller than previously reported. The observed analyzing powers are explained, within experimental uncertainty, as arising from the interference of the $E1$ direct capture amplitude with the tails of nearby $p$-wave and $s$-wave resonances.

Low-energy neutron direct capture by12Cin a dispersive optical potential

A dispersive optical potential for the interaction between low-energy neutrons and ${}^{12}\mathrm{C}$ nuclei is derived from a dispersion relation based on the Feshbach generalized optical model. The potential reproduces completely neutron total cross sections below 1.0 MeV and substantially reproduces the energy of the $3090\mathrm{keV}{(1/2}^{+})$ level in ${}^{13}\mathrm{C}$ which is of nearly pure ${2s}_{1/2}$ single-particle character. It is found that direct-capture model calculations with this potential explain quite successfully the observed off-resonance capture transitions to the ground ${(1/2}^{\ensuremath{-}}),$ $3090\mathrm{keV}{(1/2}^{+}),$ $3685\mathrm{keV}{(3/2}^{\ensuremath{-}}),$ and $3854\mathrm{keV}{(5/2}^{+})$ levels in ${}^{13}\mathrm{C}$ at neutron energies of 20--600 keV. Special emphasis is laid on the fact that in these model analyses, account should be taken of the spatial nonlocality of the neutron-nucleus interaction potential, in particular for negative energies.

Halo Properties of the First1/2+State inF17from theO16(p,γ)F17Reaction

The capture cross section of the reaction ${}^{16}\mathrm{O}(p,\ensuremath{\gamma}{)}^{17}\mathrm{F}$ was measured in the energy range from ${E}_{\mathrm{c}.\mathrm{m}.}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}200--3750\mathrm{keV}$ using the windowless gas target facility Rhinoceros. The low-energy $S$ factor that is dominated by the transition to the $1/{2}^{+}$ first excited state in ${}^{17}\mathrm{F}$ increases strikingly with decreasing energy. This behavior is explained by the halo properties of this $1/{2}^{+}$ state within the framework of the direct capture model.

7Li(p→,γ)8Bereaction atEp=80–0 keV

The ${}^{7}\mathrm{Li}(p\ensuremath{\rightarrow},\ensuremath{\gamma}{)}^{8}\mathrm{Be}$ reaction has been studied in the laboratory energy range ${E}_{p}=80$--0 keV. The vector analyzing powers ${A}_{y}(\ensuremath{\theta})$ and the angular distributions of the cross section $d\ensuremath{\sigma}/d\ensuremath{\Omega}(\ensuremath{\theta})$ for capture to the ground, first-, and third-excited states are reported. Additionally, the absolute cross section ${\ensuremath{\sigma}}_{T}(E)$ and (equivalently) the astrophysical $S$ factor $S(E)$ have been measured for capture to the third-excited state. Calculations have been performed for all three transitions using the direct capture model to which the known nearby $M$1 resonances were added. While they predict the angular distribution observed for the cross section and analyzing power in the case of both the first and third-excited states of ${}^{8}$Be, they do not reproduce those for the ground state. These calculations predict negligible $M$1 strength below 80 keV for capture to the third-excited state ${(2}^{+}$, $T=0+1$, 16.6 MeV), and we therefore conclude that the extrapolation of the astrophysical $S$ factor for the ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$ reaction, which has been performed previously by assuming pure $E$1 capture, is valid with regard to the neglect of any significant $p$-wave capture strength.

Direct neutron capture of48Ca atkT=52 keV

The neutron capture cross section of ${}^{48}$Ca was measured relative to the known gold cross section at $\mathrm{kT}$=52 keV using the fast cyclic activation technique. The experiment was performed at the Van de Graaff accelerator, Universit\"at T\"ubingen. The new experimental result is in good agreement with a calculation using the direct capture model. The $1/v$ behavior of the capture cross section at thermonuclear energies is confirmed, and the adopted reaction rate which is based on several previous experimental investigations remains unchanged.

Measurement of neutron capture on 48Ca at thermal and thermonuclear energies.

At the Karlsruhe pulsed 3.75 MV Van de Graaff accelerator the thermonuclear $^{48}\mathrm{Ca}$(n,\ensuremath{\gamma}${)}^{49}$Ca(8.72 min) cross section was measured by the fast cyclic activation technique via the 3084.4 keV \ensuremath{\gamma}-ray line of the $^{49}\mathrm{Ca}$ decay. Samples of ${\mathrm{CaCO}}_{3}$ enriched in $^{48}\mathrm{Ca}$ by 77.87% were irradiated between two gold foils which served as capture standards. The capture cross section was measured at the neutron energies 25, 151, 176, and 218 keV, respectively. Additionally, the thermal capture cross section was measured at the reactor BR1 in Mol, Belgium, via the prompt and decay \ensuremath{\gamma}-ray lines using the same target material. The $^{48}\mathrm{Ca}$(n,\ensuremath{\gamma}${)}^{49}$Ca cross section in the thermonuclear and thermal energy range has been calculated using the direct-capture model combined with folding potentials. The potential strengths are adjusted to the scattering length and the binding energies of the final states in $^{49}\mathrm{Ca}$. The small coherent elastic cross section of $^{48}\mathrm{Ca}$+n is explained through the nuclear Ramsauer effect. Spectroscopic factors of $^{49}\mathrm{Ca}$ have been extracted from the thermal capture cross section with better accuracy than from a recent (d,p) experiment. Within the uncertainties both results are in agreement. The nonresonant thermal and thermonuclear experimental data for this reaction can be reproduced using the direct-capture model. A possible interference with a resonant contribution is discussed. The neutron spectroscopic factors of $^{49}\mathrm{Ca}$ determined from shell-model calculations are compared with the values extracted from the experimental cross sections for $^{48}\mathrm{Ca}$(d,p${)}^{49}$Ca and $^{48}\mathrm{Ca}$(n,\ensuremath{\gamma}${)}^{49}$Ca. \textcopyright{} 1996 The American Physical Society.

Neutron capture cross section of 15N at stellar energies.

The neutron capture rate on $^{15}\mathrm{N}$ may be of considerable importance for s-process nucleosynthesis in red giants as well as for the nucleosynthesis in inhomogeneous big bang scenarios. We measured the reaction cross section of $^{15}\mathrm{N}$(n,\ensuremath{\gamma}${)}^{16}$N at the Forschungszentrum Karlsruhe with a fast cyclic neutron activation technique at laboratory neutron energies of 25, 152, and 370 keV. Direct capture and shell model calculations were performed to interpret the results. The presented reaction rate is 30--50 % smaller than the previously used theoretical rates. \textcopyright{} 1996 The American Physical Society.

Direct neutron capture for magic-shell nuclei.

In neutron capture for magic-shell nuclei the direct reaction mechanism can be important and may even dominate. As an example we investigated the reaction {sup 48}Ca({ital n},{gamma}){sup 49}Ca for projectile energies below 250 keV in a direct capture model using the folding procedure for optical and bound state potentials. The obtained theoretical cross sections are in agreement with the experimental data showing the dominance of the direct reaction mechanism in this case. The above method was also used to calculate the cross section for {sup 50}Ca({ital n},{gamma}){sup 51}Ca. {copyright} {ital 1996 The American Physical Society.}

Neutron capture cross section of 18O and its astrophysical implications.

The neutron capture rate on $^{18}\mathrm{O}$ is of considerable interest in the interpretation of nucleosynthesis in inhomogeneous big bang scenarios and for stellar helium burning in massive red giant stars as well as AGB stars. We measured the reaction cross section of $^{18}\mathrm{O}$(n,\ensuremath{\gamma}${)}^{19}$O at the Forschungszentrum Karlsruhe with a fast cyclic neutron activation technique at laboratory neutron energies of 25, 129, 152, 250, and 370 keV. Direct capture and shell model calculations were performed to interpret the results as well as previous unpublished data. Contributions to the reaction cross section and to the new stellar reaction rate will be discussed. \textcopyright{} 1996 The American Physical Society.

Cross section ofS36(n,γ)37S

At the Karlsruhe pulsed 3.75 MV Van de Graaff accelerator the {sup 36}S({ital n},{gamma}){sup 37}S(5.05 min) cross section was measured by the fast cyclic activation technique via the 3.103 MeV {gamma}-ray line of the {sup 37}S decay. Samples of elemental sulfur enriched in {sup 36}S by 5.933% were irradiated between two gold foils which served as capture standards. The capture cross section was measured at neutron energies 25, 151, 176, and 218 keV, respectively. The {sup 36}S({ital n},{gamma}){sup 37}S cross section in the thermonuclear and thermal energy range has been calculated using the direct-capture (DC) model combined with the folding procedure used for the determination of the potentials. The nonresonant experimental data for this reaction can be reproduced excellently using this method. The input parameters of the DC calculation (masses, {ital Q} values, nuclear density distributions, spectroscopic factors, spin-parity assignments, and excitation energies of the low-lying states of the residual nucleus) have been taken from the available experimental data.

The S(E) factor of7Li(p, ?)8Be and consequences for S(E) extrapolation in7Be(p, ?0)8B

Excitation functions and forward-backward anisotropies have been measured for the7Li(p, γ)8Be capture reaction over the proton energy rangeE p =100 to 1500 keV, using a 4π summing crystal and Ge(Li) detectors, respectively. The data show at all energies the presence of El and M1 capture amplitudes arising from the direct capture (DC) process and theE R =441 and 1030 keV resonances, respectively. Due to the observed DC process, the present data increase significantly the reaction rates (up to a factor of 110) compared to values given in the compilation. The data and their analyses remove the recent criticism on DC model calculations, which had implied a significant reduction in the extrapolated S(E) factor for7Be(p,γ)B and thus in the predicted flux of high-energy solar neutrinos; thus, the solar neutrino problem is still with us.