Astrophysical S-factor of the d(p,γ)3He processby

We summarize the recent effective field theory (EFT) studies of low-energy electroweak reactions of astrophysical interest, relevant to big-bang nucleosynthesis. The zero energy astrophysical S(0) factor for the thermal proton radiative capture by deuteron is calculated with pionless EFT. The astrophysical S(0) factor is accurately determined to be S(0)=0.243 eV·b up to the leading order (LO). At zero energies, magnetic transition M₁ gives the dominant contribution. The M₁ amplitude is calculated up to the LO. A good, quantitative agreement between theoretical and experimental results is found for all observables. The demonstrations of cutoff independent calculation have also been presented.     

Astrophysical S-factor of the ~(12)C(α, γ)~(16)O reaction at solar energies

The astrophysical S-factor of the4He+12C radiative capture is calculated in the potential model at the energy range 0.1-2.0 MeV.Radiative capture12C(α,γ)16O is extremely relevant for the fate of massive stars and determines if the remnant of a supernova explosion becomes a black hole or a neutron star.Because this reaction occurs at low energies,the experimental measurements are very difficult and perhaps impossible.In this paper,radiative capture of the12C(α,γ)16O reaction at very low energies is taken as a case study.In comparison with other theoretical methods and available experimental data,good agreement is achieved for the astrophysical S-factor of this process.     

Fore-aft asymmetry of the 2H(n,γ)3H at very low energies

We have used the recent effective field theory (EFT) which is constructed from two-and three-nucleon interactions, using minimal substitution in the momentum dependence of these interactions. We present the calculations of the fore-aft asymmetry of γ-rays in the reaction ²H(n,γ)³H which are based on EFT up to next-to-next-to leading order (N²LO). The results are compared with the recently reported calculations and measurements of the fore-aft asymmetry of γ-rays from neutron-deuteron radiative capture. The calculated fore-aft asymmetry of the nd radiative capture process above deuteron breakup threshold is in good agreement with the available experimental data up to 20 MeV.     

Systematical law of (n, γ) reaction cross sections of even-even nuclei

We have derived a formula for the neutron radiative capture cross section in the framework of a statistical model approach to nuclear reactions. Based on this formula, new systematics are established between the (n, γ) reaction cross section and the energy level density of a compound nucleus or a relative neutron excess of an even-even target nucleus for neutron incident energy above the resonance region to MeV. Good agreement with experimental data suggests that this new systematical law is helpful to analyze the experimental data.     

Neutron-antineutron oscillations in the deuteron studied with NN and ■N interactions based on chiral effective field theory

Neutron-antineutron(n−n)oscillations in the deuteron are considered.Specifically,the deuteron lifetime is calculated in terms of the free-space n−n oscillation time τn−n based on NN and NN interactions derived within chiral effective field theory(EFT).This results in(2.6±0.1)×10^22τ2^n−n s,which is close to the value obtained by Dover and collaborators more than three decades ago,but disagrees with recent EFT calculations that were performed within the perturbative scheme proposed by Kaplan,Savage,and Wise.Possible reasons for the difference are discussed.     

Measurement of astrophysical S-factor for 9Be(d, α0)7Li and 9Be(d, α1)7Li* reactions at low energies

The thick-target yield of the ⁹Be(d,α0)7Li and ⁹Be(d,α1)7Li*reactions has been first directly measured over deuteron energies from 66 to 94 keV.The obtained S(Ei)ofα0 andα1 have similar trends calculated by the thin-target yield,consistent with Yan’s report within the errors.Furthermore,the parametric expression of S(E)was obtained to calculate the theoretical thick target yield,and it roughly agrees with the experimental thick target yield.     

Calculation of astrophysical reaction rate of 82Ge(n,γ)83Ge

The neutron capture reaction on a neutron-rich near closed-shell nucleus ⁸²Ge may play an important role in the r-process following the fallout from nuclear statistical equilibrium in core-collapse supernovae. By carrying out a DWBA analysis for the experimental angular distribution of ⁸²Ge(d, p)⁸³Ge reaction we obtain the single particle spectroscopic factors, S_2,5/2 and S_0,1/2 for the ground and first excited states of ⁸³Ge=⁸²Ge⊙n, respectively. And then these spectroscopic factors are used to calculate the direct capture cross sections for the ⁸²Ge(n, γ)⁸³Ge reaction at energies of astrophysical interest. The optical potential for neutron scattering on unstable nucleus ⁸²Ge is not known experimentally. We employed a real folding potential which was calculated by using the proper ⁸²Ge density distribution and an effective nucleon-nucleon force DDM3Y. The neutron capture reactions on neutron-rich closed-shell nuclei are expected to be dominated by the direct capture to bound states. We will show that the direct capture rates on these nuclei are sensitive to the structure of the low-lying states.     

Cross section of reaction 181Ta(p,nγ)181W and the influence of the spin cut-off parameter on the cross section

In this work, the program Cindy was modified to calculate the formation cross section of each energy level of residual nucleus ¹⁸¹W resulting from the reaction ¹⁸¹Ta(p,nγ)¹⁸¹W. The concerned cross sections calculated at proton energy E_p=4.5-8.5 MeV agreed well with experimental results. The influence of the spin cut-off parameter in the energy level density model on the cross section was studied. The obtained results show that the influence of spin cut-off is obvious for lower energy levels.     

Astrophysical S-factor of the d(p,γ)3He processby

We summarize the recent effective field theory (EFT) studies of low-energy electroweak reactions of astrophysical interest, relevant to big-bang nucleosynthesis. The zero energy astrophysical S(0) factor for the thermal proton radiative capture by deuteron is calculated with pionless EFT. The astrophysical S(0) factor is accurately determined to be S(0)=0.243 eV·b up to the leading order (LO). At zero energies, magnetic transition M₁ gives the dominant contribution. The M₁ amplitude is calculated up to the LO. A good, quantitative agreement between theoretical and experimental results is found for all observables. The demonstrations of cutoff independent calculation have also been presented.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.     

Determination of the ~(12)C(p, γ)~(13)N reaction rates fromthe ~(12)C(~7Li,~6He)~(13)N reaction

The angular distribution of the 12C(7Li,6He)13N reaction at E(7Li) = 44.0 MeV was measured at the HI-13 tandem accelerator of Beijing, China. The asymptotic normalization coefficient (ANC) of 13N → 12C + p was derived to be (1.64 ± 0.11) fm-1/2 through the distorted wave Born approximation (DWBA) analysis. The ANC was then used to deduce the astrophysical S (E) factors and reaction rates for the 12C(p,γ)13N direct capture reaction at energies of astrophysical relevance.     

Predictions of γ(4S)→h_b(1P,2P)π^+π^- transitions

We study the contributions of intermediate bottomonium-like Zb states and the bottom meson loops in the heavy quark spin flip transitionsγ(4 S)→hb(1 P,2 P)π+π-.Depending on the constructive or destructive interferences between the Zb-exchange and the bottom meson loops mechanisms,we predict two possible branching ratios for each process:BRγ(4 S)→hb(1 P)π+π-≈(1.20.40.8×10^-6)or(0.5-0.20.5×10^-6),and BRγ(4 S)→(2 P)π+π-≈(7.1-1.1+1.7×10^-10)or(2.4-0.10.2×10^-10)).The contribution of the bottom meson loops is found to be considerably larger than that of the Zbexchange in the T(4 S)→hb(1 P)ππtransitions,while its decay rates are not comparable to those of heavy quark spin conservedγ(4 S)→γ(1 S,2 S)ππprocesses.We also predict the contribution of the charm meson loops in the branch fractions ofΨ(3 S,4 S)→hc(1 P)ππ.     

Evaluation of the 1077 keV γ-ray emission probability from ~(68)Ga decay

68Ga decays to the excited states of68Zn through the electron capture decay mode. New recommended values for the emission probability of 1077 keV γ-ray given by the ENSDF and DDEP databases all use data from absolute measurements. In 2011, JIANG Li-Yang deduced a new value for 1077 keV γ-ray emission probability by measuring the69Ga(n,2n)68Ga reaction cross section. The new value is about 20% lower than values obtained from previous absolute measurements and evaluations. In this paper, the discrepancies among the measurements and evaluations are analyzed carefully and the new values are re-recommended. Our recommended value for the emission probability of 1077 keV γ-ray is(2.72±0.16)%.     

Tensor force manifestations in ab initio study of the 2H(d,γ)4He, 2H(d,p)3H, and 2H(d,n)3He reactions

The (2)H(d,p)(3)H, (2)H(d,n)(3)He, and (2)H(d,γ)(4)He reactions are studied at low energies in a multichannel ab initio model that takes into account the distortions of the nuclei. The internal wave functions of these nuclei are given by the stochastic variational method with the AV8' realistic interaction and a phenomenological three-body force included to reproduce the two-body thresholds. The obtained astrophysical S factors are all in very good agreement with the experiment. The most important channels for both transfer and radiative capture are identified by comparing to calculations with an effective central force. They are all found to dominate thanks to the tensor force.     

Determination of the reaction-matrix elements of the D(d,n)3He and D(d,p)3H reactions forE d ≤500 keV

All available data of the mirror fusion reactions D(d, n)³He and D(d, p)³H have been subjected to a new analysis in order to extract the matrix elements of all 16 transitions necessary for inclusion of alll2 waves. Their energy dependence was assumed to be governed solely by Coulomb penetrabilities. The Levenberg-Marquardt algorithm was used to fit all experimental data. The experimental data are reproduced satisfactorily. The results compare well with anR-matrix analysis and with refined resonating group calculations. No suppression of quintet entrance-state transitions and therefore no neutron suppression in polarized fusion can be derived from this analysis.This work was funded by the German Federal Ministers for Research and Technology (BMFT) under the contract numbers 06-OK-153 and 06-OK-272     

Determination of astrophysical ~7Be(p,γ)~8B reaction rates from the ~7Li(d,p)~8Li reaction

The7Be(p,γ)8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars.Study of this reaction requires the asymptotic normalization coefficient(ANC) for the virtual decay8 Bg.s.→7Be + p.By using the charge symmetry relation,we obtain this proton ANC with the single neutron ANC of8 Lig.s.→7Li + n,which is determined with the distorted wave Born approximation(DWBA) and adiabatic distorted wave approximation(ADWA) analysis of the7Li(d,p)8Li angular distribution.The astrophysical S-factors and reaction rates of the direct capture process in the7Be(p,γ)8B reaction are further deduced at energies of astrophysical relevance.The astrophysical S-factor at zero energy for direct capture,S17(0),is derived to be(19.9±3.5) e V b in good agreement with the most recent recommended value.The contributions of the1+and 3+resonances to the S-factor and reaction rate are also evaluated.The present result demonstrates that the direct capture dominates the7Be(p,γ)8B reaction in the whole temperature range.This work provides an independent examination to the current results of the7Be(p,γ)8B reaction.     

Nuclear structure studies of 125Te with (n,γ), (d,p) and (3He,α) reactions

Levels in ¹²⁵Te were investigated in the range up to 3.3 MeV excitation energy by the (n,γ), (d,p) and (³He,α) reactions. Over 160 levels and about 360 γ-transitions were established, most for the first time. The states below 2.3 MeV with the most complete spectroscopic information were interpreted in terms of the interacting boson-fermion model (IBFM). Unitary treatment of both positive- and negative-parity states is achieved with the same model parameter close to the intermediate case between O(6) and U(5) limits. Excitation energies, electromagnetic transition rates, γ-branchings and spectroscopic factors are discussed in connection with the possible structures. A family of low-spin negative-parity states has been identified and understood by the IBFM proving their antialigned origin.     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Study of the levels in 174Lu by (p, 3nγ) spectroscopy

The nuclear levels in ¹⁷⁴Lu were investigated by means of ¹⁷⁶Yb(p, 3nγ) reaction spectroscopy. Standard germanium detector techniques as well as an on-line curved crystal spectrometer were used. Six well-developed rotational bands are observed. These results confirm and extend the scheme previously obtained by direct reactions. The presented data document a study on the anomalous g-factors of the 142 d isomeric band.     

The nuclear structure of 126Te studied with (d,p), (d,3He) and (d,d′) reactions

At the Munich Tandem Accelerator the reactions ¹²⁵Te(d, p)¹²⁶Te, ¹²⁶Te(d, d′)¹²⁶Te and ¹²⁷I(d, ³He)¹²⁶Te were measured with deuteron energies between 24 and 28 MeV up to excitation energies of about 3.2 MeV. Using γ-lines from previous (n,γ), (n,n′γ) and (γ,γ′) experiments, a level scheme of ¹²⁶Te up to above 3 MeV was established. The results are compared with quasiparticle-phonon model calculations.