Study of the 13N(p, γ)14O reaction at stellar energies in a microscopic coupled-channel approach

We have studied the ¹³N(p, γ)¹⁴O reaction at stellar energies within a microscopic coupled channel approach based on the generator coordinate method. Our calculation improves previous investigations as we explicitly take into account the internal excitation of the ¹³N fragment nucleus. We find that the cross section at stellar energies is mainly dominated by the J^π = 1⁻ resonance at E = 0.547 MeV in ¹⁴O for which we calculate a γ-width of Γ_γ = 1.6 eV. For temperatures T = 10⁸ to 10⁹ K the thermally averaged ¹³N(p, γ)¹⁴O reaction rate is also sensitive to a direct capture contribution which we derive consistently within our microscopic study. Finally we discuss the astrophysical implications of the ¹³N(p, γ)¹⁴O rate for which we adopt a mean value of the various theoretical estimates of the γ-width of the 1⁻ resonance (Γ_γ = 1.8 eV).     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

Spectroscopy of 13Be

Six quasi-stationary states of ¹³Be populated in the ¹⁴C(¹¹B,¹²N) ¹³Be reaction at E_lab = 190 MeV are reported. A Q-value = −39.60(9) MeV and a mass excess, M.E.= 33.95(9) MeV, have been found for the lowest observed spectral line. The ground state is unstable with respect to one-neutron emission by 0.80(9) MeV. Excitation energies of 1.22(10), 2.10(16), 4.14(12), 5.09(14) and 7.0(2) MeV have been obtained for the observed spectral lines.     

Investigation of one-nucleon transfer reactions between complex nuclei at incident energies between 3 and 8

Angular distributions of the ground state transitions in the reactions ¹¹B(¹⁴N, ¹⁵O)¹⁰Be, ¹¹B(¹⁴N, ¹³C)¹²C, ¹²C(¹¹B, ¹²C)¹¹B and ¹³C(¹²C, ¹³C)¹²C have been measured with a magnetic spectrometer as an identification system. The first two reactions (angular momentum transfer l = 2) measured at 41, 77 and 113 MeV show a clear damping of the oscillatory structures in the angular distributions. This effect was qualitatively reproduced by DWBA calculations which take into account a recoil phase, thus showing that the damping of the structures is due to the recoil of the transferred particle on the system. The reaction ¹¹B(¹²C, ¹¹B)¹²C (l = 2) at 87 MeV with Q = 0 is well reproduced by the calculations, whereas the ¹³C(¹²C, ¹³C)¹²C reaction as the only l = 0 transition is in complete disagreement with theoretical expectations.     

Cross sections of the reactions16O(γ,x)13 N and16O (γ,x)11 C,and Yield of12C (γ, t) up to 55 MeV

Yield curves of the reactions¹⁶O (γ, x)¹¹C,¹⁶O (γ, x)¹³N and¹²C(γ, t) have been measured relative to¹²C(γ, n)¹¹C with bremsstrahlung. The cross section σ[¹⁶O(γ, x)¹¹C] has a shape similar to σ[¹⁶O(γ, t)] and shows a broad maximum near 38 MeV. Differences between σ[¹⁶O(γ, x)¹³ N] and σ[¹⁶O(γ, t)] point to a reaction mechanism via quadrupole absorption in¹⁶O. The yield of¹²C(γ, t) exceeds the¹⁶O(γ,t) yield by a factor of two.     

Spin dipole excitations in radiative pion capture on 1p shell nuclei

Shell-model calculations for spin-dipole transitions in the (π^?,γ) reaction on ^6,7Li, ⁹Be, ¹¹B, ¹³C and ¹⁴N are compared with experimental data. The gross structure of resonance is discussed in terms of configurational splitting and symmetry considerations. Quantum numbers of resonances, total and partial yields are considered. Selected (π^?, γn) and (gp^?, γnγ′) coincidence experiments are proposed. The role of quadrupole and quasielastic excitation is also briefly discussed.     

KeV astrophysics with GeV beams; blazing a new trail on the summit of Nuclear Astrophysics

GeV beams of light ions and electrons are used for creating a high flux of real and virtual photons, with which some problems in Nuclear Astrophysics are studied. GeV ⁸B beams are used to study the Coulomb dissociation of ⁸B and thus the ⁷Be(p,γ)⁸B reaction. This reaction is one of the major source of uncertainties in estimating the ⁸B solar neutrino flux and a critical input for calculating the ⁸B solar neutrino flux. The Coulomb dissociation of ⁸B appears to provide a viable method for measuring the ⁷Be(p,γ)⁸B reaction rate, with a weighted average of the RIKEN1, RIKEN2, GSI1 and MSU published results of S ₁₇(0)=18.9±1.0 eV-b. This result, however, does not include a theoretical error estimated to be ±10%. GeV electron beams on the other hand, are used to create a high flux of real and virtual photons at TUNL-HIGS and MIT-Bates, respectively, and we discuss two new proposals to study the ¹²C(α,γ)¹⁶O reaction with real and virtual photons. The ¹²C(α,γ)¹⁶O reaction is essential for understanding Type II and Type Ia supernova. It is concluded that virtual and real photons produced by GeV light ions and electron beams are useful for studying some problems in Nuclear Astrophysics.     

Asymptotic normalization coefficients and astrophysical direct capture rates

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The ¹⁰B(⁷Be, ⁸B)⁹Be and ¹⁴N(⁷Be, ⁸B)¹³C reactions have been used to measure the ANC appropriate for determining the ⁷Be(p,γ)⁸B rate, and the ¹⁴N(¹¹C, ¹²N)¹³C reaction has been used to measure the ANC required to calculate the ¹¹C(p,γ)¹²N rate. Received: 1 May 2001 / Accepted: 4 December 2001     

The 14C(p, γ0)15N cross section below Ep = 12 MeV

The cross section for the ¹⁴C(p.γ₀)¹⁵N reaction has been measured up to E_p = 12 MeV. These measurements cover the region of the main component of the giant dipole resonance in ¹⁵N previously observed in the inverse ¹⁵N(γ, p₀)¹⁴C reaction. The structures seen are compared to recent measurements of the ¹⁴N(p, γ₀)¹⁵O cross section at corresponding energies in ¹⁵O, allowing clear identification of $\text{T =}\text{1}\text{2}\text{and}\text{3}\text{2}$ states. A comparison of the present experimental results is also made to recent bound and continuum shell model calculations for this region of ¹⁵N.     

Spectroscopy of 13B, 14B, 15B and 16B using multi-nucleon transfer reactions

New information has been obtained on excited states of the neutron-rich boron isotopes ¹⁴B, ¹⁵B and ¹⁶B, using the reactions ¹²C(¹⁴C,¹²N)¹⁴B, ¹³C(¹⁴C,¹²N)¹⁵B and ¹⁴C(¹⁴C,¹²N)¹⁶B at about 24 MeV/A. The mass excess of ¹⁶B has been measured for the first time, it is 37.08(6) MeV. This means that ¹⁶B is unbound by only 0.04(6) MeV. Furthermore, the nucleus ¹³B has been investigated with the four reactions ¹⁶O(¹⁴C,¹⁷F), ¹²C(¹⁴C,¹³N), ¹²C(¹³C,¹²N) and ¹²C(¹⁵N,¹⁴O). Choosing different target-projectile combinations, it was possible to populate states with different selectivity. New states are observed in ¹³B at excitation energies above the threshold for two-neutron decay. Received: 27 December 1999 / Revised version: 11 February 2000     

Interfering transfer processes in heavy-ion reactions

Heavy-ion reactions in which two different transfer processes may interfere are analyzed. Angular distributions of the reactions ¹⁴C(¹⁶O, ¹⁷O)¹³C and ¹⁴C(¹⁶O, ¹⁸O)¹²C were measured at incident energies of 20, 25 and 30 MeV. The strong oscillations observed at the Coulomb barrier together with a backward rise at higher energies are taken as evidence for the superposition of two competing transfer reactions. DWBA calculations for the two single transfer processes were performed using the fixed-range approximation, and the two transition amplitudes were summed coherently. The experimental angular distributions are well reproduced. The DWBA also explains the disappearance of the interference structures for higher transferred angular momenta l. Data on the reaction ¹¹B(¹⁶O, ¹⁵N)¹²C measured earlier are included in the analysis in order to show the systematic dependence on l-values.     

Compound transfer and direct transfer reactions induced by 17O on 13C

The elastic scattering, inelastic scattering, single-neutron transfer reactions ¹³C(¹⁷O, ¹⁶O) ¹⁴C, ¹³C(¹⁷O, ¹⁸O)¹²C and ¹³C(¹⁷O, ¹⁸O_{2+, 1.98})¹²C, and seven other exit channels which involve ⁷Li, ⁹Be, ¹¹B and ¹⁵N have been measured for the system ¹⁷O+¹³C at 12.9 and 14 MeV c.m. It is shown that all reactions mentioned above have significant contributions from compound nuclear decay, following fusion of projectile and target.     

Transfer and fragmentation reactions of14N at 60 MeV/u

Inclusive energy spectra and cross sections of reaction products close to the¹⁴N projectile (¹¹C,¹²C,¹³C,¹⁵N and¹⁵O) have been measured in the angular rangeθ _L =1.2°–4.2° at an incident energy of 60 MeV/u for five different target nuclei (¹²C,²⁷Al,⁵⁸Ni,⁹⁰Zr and²⁰⁸Pb). Two components are found to be systematically present in the energy spectra of the carbon isotopes, the first similar to that observed at relativistic energies and the second shifted down in energy characteristic for a very dissipative process. The dependence of the differential and integrated cross sections on the target mass indicates that the two-body final channels (¹⁴N,¹³C), (¹⁴N,¹⁵N) and (¹⁴N,¹⁵O) are strongly correlated to the fragmentation channels.     

天体演化过程中CNO核子辐射俘获反应

C和N核的质子辐射俘获反应对恒星平稳H燃烧阶段的能量产生和元素核合成起重要作用, C, N和O 核的中子辐射俘获是原初核合成和AGB星核合成的关键反应, 精确测定它们天体物理反应率有重要意义。 除13N(p, γ)14O和16N(n, γ)17N等不稳定核的核子辐射俘获反应外, 国际上已完成了其中若干反应的直接测量工作。 但12C(p, γ)13N, 13C(p, γ)14N和15N(p, γ)16O等CNO循环关键反应的实验测量还没有达到天体物理感兴趣的能区。 13C(n, γ)14C,15N(n, γ)16N和18O(n, γ)19O等中子辐射俘获反应测量的能量跨度较大, 截面仍存在较大的不确定性。 介绍了这些反应的研究进展, 并讨论了间接测量这些反应的方法和可行性。 The proton radiative capture reactions of C and N nuclei are important for the energy production and nucleosynthesis in the CNO cycle, and the neutron radiative capture reactions of C, N and O nuclei are key reactions for the inhomogeneous Big Bang nucleosynthesis as well as for the neutron induced CNO cycle in AGB stars. So far, most of these reactions have been measured except some reactions of the unstable nuclei, such as 13N(p, γ)14O and 16N(n, γ)17N. While the direct measured reactions, such as the  12C(p, γ)13N, 13C(p, γ)14N and 15N(p, γ)16O key reactions in CNO cycle, have not reached down to the stellar energies. In addition, the large uncertainties still exist in the measured neutron capture reactions such as 13C(n, γ)14C,15N(n, γ)16N and 18O(n, γ)19O. Thus it is significant to determine their astrophysical reaction rates via the indirect measurements. In this paper, the research status and feasibility of the indirect measurements for these reactions are discussed.     

A new determination of the partial widths of the 16.11 MeV state in 12C

The partial widths of the second T = 1 state of ¹²C, at 16.11 MeV excitation energy, have been determined by measuring the ¹¹B(p, γ) and ¹¹B(p, α) cross sections at the E_p = 163 keV resonance corresponding to this state. These measurements result in the new values of Γ_p = 21.7 ± 1.8 eV and Γ_γ = 21.6 ± 3.3 eV, for the partial widths of this state; approximately 3 times smaller and larger, respectively, than the present values in the literature. The new result for the proton width eliminates a serious discrepancy found in an earlier comparison of the partial widths of the T = 1 analogue states of the A = 12 system. Measurements were also made of the ¹¹B(d, n)¹²C¹ reaction to compare the proton widths of the 15.11 and 16.11 MeV T = 1 states; these measurements confirm the new, smaller proton width for the 16.11 MeV state. An attempt was also made to determine the γ-width of the 16.11 MeV state by measuring the γ-branching ratio in the ¹⁰B(³He, p)¹²C¹(γ)¹²C reaction.     

High-spin states in48Ti

The⁴⁵Sc(α, p γ) reaction has been investigated atE ^α=11, 12 and 13MeV. Theγ-decay of 198 levels in⁴⁸Ti up to 8,323 keV excitation energy has been observed. High-spin states were investigated by proton-γ ray angular correlation measurements atE=11 and 13MeV and by DSAM lifetime measurements atE=11 MeV. From the combined evidence spin (-parity) assignments were obtained for the levels atE _x =8,323 keV (J= 10,8,6), 8,091(12, 10, 8, 6), 7,668(10, 8), 7,427(9, 7), 7,374(11, 9, 7), 6,906(10, 8, 6), 6,172(8⁺,6⁺), 6,102(10⁺,8⁺), 6,039(6), 6,034(9⁺, 7⁺), 5,630(7), 5,197(8⁺), 5,169(7⁺), 5,155(5), 4,404(5), 4,398(6⁺) and 4,046keV (5). Most of the ambiguous spin assignments become unique if the 8,091 keV level hasJ=12, an assumption which is favoured by its excitation function. The level spectrum thus obtained is well reproduced by shell model calculations in the pure (f _7/2)⁸ configuration space. Discrepancies exist in the reproduction ofγ-decay modes. The reason is found in low-lying high-spin intruder states which include the 7,427 and 8,323 keV levels. The spectrum of negative-parity states is understood qualitatively by a comparison with⁴⁶Ti and⁴²Ca.     

π-π andK-¯K channel coupling and scalar mesons

Total nuclear reaction cross-sections are determined by means of a 4π-γ method. The results cover a wide span of targets for various stable beams. The validity of the method is shown in a combined systematics including also the results of transmission-type experiments. The data are very well described by the formula developed by Kox et al. The same method is applied to secondary fragment beams produced from a 44 MeV/u²²Ne beam on a 332mg/cm^{2 181}Ta target. Using the LISE spectrometer the fragments^{4, 6}He,^{6–9, 11}Li,^{7, 9–12, 14}Be,^{10–15, 17}B^11–19C,^13–19N,^15–21O,^{18– 21}F and^20,21 Ne are analyzed and transported to interact with a 199.4 mg/cm² Cu target surrounded by a 4π-γ counter. The measured total reaction cross-sectionsσ _R are discussed in terms of the reduced strong absorption radiusr ₀ and compared with other experimental results.     

The 11B(α, p)14C reaction below 1.7 MeV bombarding energy

For estimation of the production rate of the long-lived ¹⁴C isotope originating in the controlled thermonuclear synthesis ¹¹B + p the total cross section of the ¹¹B(α, p)¹⁴C reaction has been determined in the energy range of α-particles E_α = 0.9−1.7 MeV. Five resonances corresponding to states in ¹⁵N have been observed. The assignment of the resonance parameters is discussed.     

Effects of 8B size on the low-energy 7Be(p,γ)8B cross section

We calculate several “size-like” ⁸B observables within the microscopic three-cluster model and study their potential constraints on the zero-energy astrophysical S₁₇(0) factor of the ⁷Be(p,γ)⁸B reaction. We find within our three-cluster model that a simultaneous reproduction of the experimental data for the ⁸B radius and quadrupole moment and of the ⁸B⁸Li Coulomb displacement energy implies S₁₇(0) = (23–25) eV b.     

Properties of8Be and12C deduced from the folding-potential model

Theα-α differential cross sections are analyzed in the optical model using a double-folded potential. With the knowledge of this potential bound and resonance-state properties ofα-cluster states in⁸Be and¹²C as well as astrophysical S-factors of⁴He(α,γ)⁸Be and⁸Be(α,γ)¹²C are calculated. Γ_γ-widths and B(E2)-values are deduced.