Born Approximation Calculations Research Articles

The structure of low-lying 1− states in 90,94Zr from (α,α′γ) and (p,p′γ) reactions

The low-lying dipole strength was investigated in 90,94 Zr via the (p,p′γ) reaction at 80 MeV and via the (α,α′γ) reaction at 130 MeV. These experiments were performed at the Research Center for Nuclear Physics (Osaka University) and made combined use of the high-resolution magnetic spectrometer Grand Raiden and the CAGRA HPGe gamma array. The comparison of our results with existing (γ,γ′) reaction data shows differences in the excitation patterns. In the present experimental conditions, in fact, both α and p probes are exciting the investigated 1− states mainly through the short-range nuclear force, expected to favour the population of surface excitations. Distorted Wave Born Approximation (DWBA) calculations were made using form factors built assuming specific transition densities, characterized by a strong neutron component at the nuclear surface and based on Random Phase Approximation (RPA). A combined analysis of the (α,α′γ) and (p,p′γ) data was performed to investigate the isoscalar character of the 1− states in 90,94Zr. Although an overall general consistency was obtained in the studied energy intervals, not all (p,p′γ) cross sections were well reproduced using the isoscalar strength deduced from (α,α′γ) data. This might suggest that the mixing of isoscalar and isovector components and the degree of collectivity are not the same for all the 1− states studied.

Multichannel experimental and theoretical approach to the C12(O18,F18)B12 single-charge-exchange reaction at 275 MeV: Initial-state interaction and single-particle properties of nuclear wave functions

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay. Purpose: We intend to bring to light the main nuclear structure and reaction features involved in the O18+C12 collision at 275 MeV incident energy. In this paper, the main focus is on the role of the initial- and final-state interactions in the overall reaction dynamics and on the single-particle nuclear structure properties accessed via the study of single-nucleon transfer reactions. Forthcoming articles will be devoted to go into the details of the response to one- and two-particle/hole isospin probes. Methods: Cross-section energy spectra and angular distributions were measured in a unique experimental setup for the C12(O18,O18)C12 elastic and inelastic scattering, the C12(O18,O17)C13 one-neutron stripping, the C12(O18,F19)B11 one-proton pickup, and the C12(O18,F18)B12 single-charge-exchange nuclear reactions. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions using state-of-the-art nuclear structure and reaction theories, was performed, and it is presented for the first time in this article. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and worth of the work here presented. Results: The energy and angular resolutions achieved in each reaction channel allowed us to isolate specific transitions and to map the diffraction patterns in the angular distributions. The cross-section calculations describe well the experimental data, both in terms of the absolute values and diffraction patterns. Although the distorted wave Born approximation (DWBA) calculations prove to be accurate in describing all the studied channels, better results are achieved when the couplings to inelastic transitions in both the incoming and outgoing partitions are introduced, as done in the coupled channels Born approximation (CCBA) calculations. Otherwise, no real improvement is found when the coupling effects among different partitions are explicitly taken into account in the coupled reaction channels (CRC) calculations. Conclusions: The multichannel approach proposed in this paper is a promising method for accurate investigations of direct reactions originating in heavy-ion collisions. This is quite appealing for the precise spectroscopy of heavy nuclei proposed in many areas of nuclear physics. An example is the NUMEN project with its challenging commitment to provide valuable information on neutrinoless double beta decay nuclear matrix elements from single- and double-charge-exchange cross-section measurements.1 MoreReceived 18 July 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.024605©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCharge-exchange reactionsCollective modelsDirect reactionsNuclear many-body theoryOptical, coupled-channel & distorted wave modelsShell modelSpectroscopic factors & electromagnetic momentsTransfer reactionsProperties6 ≤ A ≤ 19TechniquesNuclear data analysis & compilationNuclear reactionsSpectrometers & spectroscopic techniquesNuclear Physics

Determination of the 3He(α, γ)7Be and 6Li(p, γ)7Be astrophysical factors down to zero energy using the asymptotic normalization coefficients

The p - p-chain reaction 3He(α, γ)7Be can sensitively influence the prediction of the 7Be and 8B neutrino fluxes. Despite its importance, the knowledge of its reaction cross section at energies of the core of the Sun (15 keV 30 keV) is limited and the accuracy far from the desired 3% level. In the present paper the indirect measurement of the external capture contribution using the asymptotic normalization coefficient (ANC) technique is reported. The angular distributions of deuterons emitted in the 6Li(3He,d)7Be α-transfer reactions were measured and the ANCs extracted from the scaling of distorted-wave Born approximation (DWBA) and coupled-channel (CC) calculations. Then, the astrophysical S-factor for the 3He(α, γ)7Be reaction was calculated assuming E1 direct capture and the zero energy value turned out to be 0.534 0.025 keVb. Both our experimental and theoretical approaches were benchmarked through the analysis of the 6Li(p,γ)7Be astrophysical factor, with interesting astrophysical applications to the understanding of the primordial lithium problem. In particular, the present work disfavors the occurrence of a claimed 200 keV resonance in the astrophysical factor.

Observation of a Near-Threshold Proton Resonance in ^{11}B.

A near-threshold proton resonance in ^{11}B at E_{ex}=11.44±0.04 MeV is observed via the reaction ^{10}Be(d,n)^{11}Be→^{10}Be+p in inverse kinematics, measured with a beam of the radioactive isotope ^{10}Be. The resonance energy at E_{res}=211(40) keV is consistent with a proton signal observed by Ayyad etal. in the β-delayed proton decay of ^{11}Be. By comparison to a distorted wave Born approximation calculation, a 0.27(6) spectroscopic factor is extracted and a tentative (ℓ=0) character is assigned for this resonance. The significant cross section in the proton-transfer (d,n) reaction, as well as the observation of its proton-decay signal, point to the threshold-resonance character of this state. The position of this state, its structure, and strong coupling to the s-wave continuum represent an ideal case to study quantum near-threshold many-body dynamics of unstable states. The presence of this state is an important step toward understanding the excessively large beta-delayed proton-decay branch of ^{11}Be.

Investigation of negative-parity states in 16C via deuteron inelastic scattering * *Supported by the National Key R & D Program of China (2018YFA0404403), the National Natural Science Foundation of China (11775004, U1867214, 11875074, 11961141003), the funding from the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2021ZZ01), and the funding from Heavy Ion Research Facility in Lanzhou (HIR2021PY002)

Two low-lying unbound states in 16C are investigated by deuteron inelastic scattering in inverse kinematics. Besides the 2 state at 5.45 MeV previously measured in a 1n knockout reaction, a new resonant state at 6.89 MeV is observed for the first time. The inelastic scattering angular distributions of these two states are well reproduced by the distorted-wave Born approximation (DWBA) calculation with an l = 1 excitation. In addition, the spin-parities of the unbound states are discussed and tentatively assigned based on shell model calculations using the modified YSOX interaction.

Fusion and proton transfer in the B10+Al27 system at sub-barrier energies

Background: Significant enhancement in sub-barrier fusion cross sections by several orders of magnitude, in the frame of one-dimensional barrier penetration models, is observed for a variety of nuclear systems. To understand this, one needs to find the fundamental degrees of freedom relevant in the sub-barrier fusion region by incorporating nonelastic channels such as coupling of the excited target and/or projectile nuclei, particle transfer channels, threshold variation of nuclear potential, etc.Purpose: We probe what degrees of freedoms are associated with the $^{10}\mathrm{B}+^{27}\mathrm{Al}$ reaction at energies $\ensuremath{\approx}18%$ below to $\ensuremath{\approx}12%$ above the Coulomb barrier.Method: An online $\ensuremath{\gamma}$-ray spectroscopy technique is used to determine the populated excitation functions in the $^{10}\mathrm{B}+^{27}\mathrm{Al}$ reaction. The reaction cross sections obtained from these $\ensuremath{\gamma}$ rays are compared with the statistical model to explore the mechanism of fusion reactions.Results: At energies near and below the Coulomb barrier, two isotopes of sulfur ($^{34}\mathrm{S}$ and $^{32}\mathrm{S}$) were found to reproduce cross section within the frame of the pace2 model based on Hauser-Feshbach calculations, whereas isotopes of chlorine ($^{35}\mathrm{Cl}$), sulfur ($^{35}\mathrm{S}$), and phosphorous ($^{32}\mathrm{P}$) agree well but at above-barrier energies. Isotopes of Ar, Cl, S, P, and Si show significant enhancement over an entire band of energies. This enhancement (suppression) in the experimental cross section at energies above (below) the barrier points towards the involvement of some nuclear reaction mechanism other than fusion-evaporation. Distorted-wave Born approximation calculations strongly support the population of $^{28}\mathrm{Si}$ residue via the one-proton transfer process. The total fusion cross section is found to follow the theory after the inclusion of coupling of low lying excited states of projectile and target. Calculations concerning the astrophysical $S$ factor and the logarithmic derivative factor support the idea of no fusion hindrance at the studied energies. The universal fusion function benchmark shows consistency with previous data for lithium (or Li isotopes) induced systems.Conclusions: The inclusion of inelastic couplings associated with both target and projectile is important to understand the behavior of total fusion cross section. The formation of $^{28}\mathrm{Si}$ via the one-proton transfer reaction supports the present experimental technique to make inclusive transfer measurements. The calculations with the universal fusion function present a slight suppression in the higher energy region, indicating possible breakup effects in this region. The present calculations show that till $18%$ below the barrier there is no fusion hindrance. On extrapolating the theoretical values we further observed that the present system has no fusion hindrance. No connection of $^{10}\mathrm{B}+^{27}\mathrm{Al}$ fusion with astrophysics has been made, which raises the question to think of cosmic ray reactions and perhaps reactions in the early solar system, but how the fusion reaction would fit into the picture is not clear at all.

Using spin alignment of inelastically excited nuclei in fast beams to assign spins: The spectroscopy of O13 as a test case

Excited states in 13O were investigated using inelastic scattering of an E/A=69.5-MeV 13O beam off of a 9Be target. The excited states were identified in the invariant-mass spectra of the decay products. Both single proton and sequential two-proton decays of the excited states were examined. For a number of the excited states, the protons were emitted with strong anisotropy where emissions transverse to the beam axis are favored. The measured proton-decay angular distributions were compared to predictions from distorted-wave born-approximation (DWBA) calculations of the spin alignment which was shown to be largely independent of the excitation mechanism. The deduced $^{13}$O level scheme is compared to ab initio no-core shell model with continuum (NCSMC) predictions. The lowest-energy excited states decay isotropically consistent with predictions of strong proton 1s1/2 structure. Above these states in the level scheme, we observed a number of higher-spin states not predicted within the model. Possibly these are associated with rotational bands built on deformed cluster configurations predicted by antisymmetrized molecular dynamics (AMD) calculations. The spin alignment mechanism is shown to be useful for making spin assignments and may have widespread use.

Search for $\alpha$ condensed states in $^{13}$C using $\alpha$ inelastic scattering

AbstractWe searched for the $\alpha$ condensed state in $^{13}$C by measuring the $\alpha$ inelastic scattering at $E_\alpha = 388$ MeV at forward angles including 0$^\circ$. We performed a distorted-wave Born approximation calculation with the single-folding potential and multipole decomposition analysis to determine the isoscalar transition strengths in $^{13}$C. We found a bump structure around $E_x = 12.5$ MeV due to the isoscalar monopole ($IS0$) transition. A peak-fit analysis suggested that this bump consisted of several $1/2^-$ states. We propose that this bump is due to the mirror state of the 13.5 MeV state in $^{13}$N, which dominantly decays to the $\alpha$ condensed state in $^{12}$C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $\alpha$ condensed state, but the $3\alpha + n$ orthogonality condition model suggests that the $\alpha$ condensed state is unlikely to emerge as the negative parity states. We also found two $1/2^+$ or $3/2^+$ states at $E_x = 14.5$ and 16.1 MeV excited with the isoscalar dipole ($IS1$) strengths. We suggest that the 16.1 MeV state is a possible candidate for the $\alpha$ condensed state predicted by the cluster model calculations on the basis of the good correspondence between the experimental and calculated level structures. However, the theoretical $IS1$ transition strength for this state is significantly smaller than the measured value. Further experimental information is strongly desired to establish the $\alpha$ condensed state in $^{13}$C.

Observation of He6+t cluster states in Li9

$^{6}$He+$t$ cluster states of exited $^{9}$Li have been measured by 32.7 MeV/nucleon $^{9}$Li beams bombarding on $^{208}$Pb target. Two resonant states are clearly observed with the excitation energies at 9.8 MeV and 12.6 MeV and spin-parity of 3/2$^{-}$ and 7/2$^{-}$ respectively. These two states are considered to be members of K$^{\pi}$=1/2$^{-}$ band. The spin-parity of them are identified by the method of angular correlation analysis and verified by the continuum discretized coupled channels (CDCC) calculation, which agrees with the prediction of the generator coordinate method (GCM). A monopole matrix element about 4 fm$^{2}$ for the 3/2$^{-}$ state is extracted from the distorted wave Born approximation (DWBA) calculation. These results strongly support the feature of clustering structure of two neutron-rich clusters in the neutron-rich nucleus $^{9}$Li for the first time.

Configuration mixing in Mg28 and the Mg26(t,p)Mg28 reaction

We have studied the $^{26}\mathrm{Mg}(t,p)^{28}\mathrm{Mg}$ reaction. The nucleus $^{28}\mathrm{Mg}$ lies between $^{24}\mathrm{Mg}$ and $^{32}\mathrm{Mg}$, the latter of which is central to the ``island of inversion'' characterized by low-lying neutron $fp$-shell configurations. The present results show that the second-excited ${0}^{+}$ state in $^{28}\mathrm{Mg}$ contains large $fp$-shell occupation for the neutrons. The experiment was performed in inverse kinematics using the HELIcal Orbit Spectrometer (HELIOS) at Argonne National Laboratory. Shell-model calculations using the SDPF-MU interaction yielded level energies and two-neutron transfer amplitudes that were used in one-step distorted-wave Born approximation calculations to provide theoretical predictions of the proton angular distributions. In many, but not all cases, the data were in good agreement with theoretical predictions.

Eikonal method for charge-exchange reactions at intermediate energies

A novel description of charge-exchange reactions at intermediate energies is developed, based on both phenomenological or microscopic eikonal phase-shift functions. The results obtained within this eikonal approach are in good agreement with the distorted-wave Born approximation calculations within the energy region where both approximations should be valid. They also compare well with the experimental data, even at relatively low energy domain. At higher energies, relativistic kinematics have also been added and shown to be relevant. Owing to the microscopic feature of the formulation, our theory also has the advantage that it can be applied to high energies where the phenomenological optical potentials are rarely available.

Level structure of S31 via S32(p,d)S31

Background: Properties of proton-unbound $^{31}\mathrm{S}$ states determine the $^{30}\mathrm{P}(p,\ensuremath{\gamma})^{31}\mathrm{S}$ reaction rate, which has a significant impact on explosive hydrogen burning in classical novae and type-I x-ray bursts. Despite several previous studies, uncertainties still remain with respect to the nuclear structure of $^{31}\mathrm{S}$ near the proton threshold.Purpose: The level structure of $^{31}\mathrm{S}$ has been presently investigated via a charged-particle spectroscopy experiment using the $^{32}\mathrm{S}(p,d)^{31}\mathrm{S}$ reaction.Method: Deuterons corresponding to $^{31}\mathrm{S}$ excited states with $3.285\ensuremath{\le}\phantom{\rule{4pt}{0ex}}{E}_{x}\phantom{\rule{4pt}{0ex}}\ensuremath{\le}10.8$ MeV were momentum analyzed via an Enge split-pole spectrograph at six laboratory angles between ${10}^{\ensuremath{\circ}}$ and ${62}^{\ensuremath{\circ}}$. Differential cross sections of the $^{32}\mathrm{S}(p,d)^{31}\mathrm{S}$ reaction were measured at ${E}_{p}\phantom{\rule{4pt}{0ex}}=34.5$ MeV. Distorted-wave Born approximation calculations were performed to constrain the spin-parity assignments of several of the observed levels.Results: We have detected 72 excited states of $^{31}\mathrm{S}$, out of which 17 are within the astrophysical region of interest corresponding to the temperature range of 0.1--1.5 GK. We have resolved the discrepancy in the spin and parity of an excited state with ${E}_{x}\phantom{\rule{4pt}{0ex}}=6542$ keV, showing that is it not ${J}^{\ensuremath{\pi}}\phantom{\rule{4pt}{0ex}}=3/{2}^{\ensuremath{-}}$, and therefore the contribution of this state to the $^{30}\mathrm{P}(p,\ensuremath{\gamma})$ reaction rate is likely much less significant than previously thought owing to the larger angular-momentum transfer required to populate this excited state. Moreover, our measurement results help consolidate the spin-parity assignments for the 6377 and 6636 keV states in $^{31}\mathrm{S}$.Conclusions: This work presents the most comprehensive spin-parity assignments to date from a single-neutron transfer reaction on $^{32}\mathrm{S}$ to $^{31}\mathrm{S}$ excited states in the region between 6 to 7 MeV excitation energy. This region is significant for the determination of the $^{30}\mathrm{P}(p,\ensuremath{\gamma})^{30}\mathrm{S}$ reaction rate over the temperatures characteristic of explosive hydrogen burning in novae.

Analysis of two-nucleon transfer reactions in the Ne20+Cd116 system at 306 MeV

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly relevant since the 116Cd nucleus is a candidate for the double-beta decay. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding S\~ao Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two- and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results: The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction mechanism. For the two-proton transfer case, the inclusion of the 1g7/2 and 2d5/2 orbitals in the model space is crucial.

Important Influence of Entrance Channel Reorientation Coupling on Proton Stripping

While it is well established that the ground state reorientation coupling can have a significant influence on the elastic scattering of deformed nuclei, the effect of such couplings on transfer channels has been much less well investigated. In this letter we demonstrate that the ^{208}hbox {Pb}(^7hbox {Li},^6hbox {He})^{209}hbox {Bi} proton stripping reaction at an incident energy of 52 MeV can be well described by the inclusion of the ^7hbox {Li} ground state reorientation coupling within the coupled channels Born approximation formalism. Full finite-range distorted wave Born approximation calculations were previously found to be unable to describe these data. Addition of coupling to the 0.478-MeV 1/2^- excited state of ^7hbox {Li}, together with the associated two-step transfer path, has little or no influence on the shape of the angular distributions (except that for stripping leading to the 1.61-MeV 13/2^+ level of ^{209}hbox {Bi} which is significantly improved) but does affect appreciably the values of the ^{209}mathrm {Bi} rightarrow {^{208}mathrm {Pb}} + p spectroscopic factors. Implications for experiments with weakly-bound light radioactive beams are discussed.

Multi-neutron transfer in He8 -induced reactions near the Coulomb barrier

The measured inclusive $^6$He and $^4$He production cross sections of G. Marqu{\'i}nez-Dur{\'a}n {\em et al.}, Phys.\ Rev.\ C {\bf 98}, 034615 (2018) are reexamined and the conclusions concerning the relative importance of 1n and 2n transfer to the production of $^6$He arising from the interaction of a 22 MeV $^8$He beam with a $^{208}$Pb target revised. A consideration of the kinematics of the 2n-stripping reaction when compared with the measured $^6$He total energy versus angle spectrum places strict limits on the allowed excitation energy of the $^{210}$Pb residual, so constraining distorted wave Born approximation calculations that the contribution of the 2n stripping process to the inclusive $^6$He production can only be relatively small. It is therefore concluded that the dominant $^6$He production mechanism must be 1n stripping followed by decay of the $^7$He ejectile. Based on this result we present strong arguments in favor of direct, one step four-neutron (4n) stripping as the main mechanism for $^4$He production.

Single-particle structure in neutron-rich Sr isotopes approaching the N=60 shape transition

Background: Neutron-rich nuclei around neutron number N=60 show a dramatic shape transition from spherical ground states to prolate deformation in Sr98 and heavier nuclei. Purpose: The purpose of this study is to investigate the single-particle structure approaching the shape transitional region. Method: The level structures of neutron-rich Sr93,94,95 were studied via the H2(Sr94,95,96,t) one-neutron stripping reactions at TRIUMF using a beam energy of 5.5 AMeV. γ-rays emitted from excited states and recoiling charged particles were detected by using the TIGRESS and SHARC arrays, respectively. States were identified by gating on the excitation energy and, if possible, the coincident γ radiation. Results: Triton angular distributions for the reactions populating states in ejectile nuclei Sr93,94,95 were compared with distorted wave Born approximation calculations to assign and revise spin and parity quantum numbers and extract spectroscopic factors. The results were compared with shell-model calculations and the reverse (d,p) reactions and good agreement was obtained. Conclusions: The results for the H2(Sr94,t)Sr93 and H2(Sr95,t)Sr94 reactions are in good agreement with shell-model calculations. A two-level mixing analysis for the 0+ states in Sr94 suggest strong mixing of two shapes. For the H2(Sr96,t)Sr95 reaction the agreement with the shell-model is less good. The configuration of the ground state of Sr96 is already more complex than predicted, and therefore indications for the shape transition can already be observed before N=60.9 MoreReceived 14 January 2020Accepted 17 August 2020DOI:https://doi.org/10.1103/PhysRevC.102.024335©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsSpectroscopic factors & electromagnetic momentsTransfer reactionsProperties90 ≤ A ≤ 149TechniquesRadioactive beamsNuclear Physics

Multistep processes in heavy-ion-induced single-nucleon transfer reactions

It was first noted during the 1970s that finite-range distorted wave Born approximation (FR-DWBA) calculations were unable satisfactorily to describe the shape of the angular distributions of many single-proton (and some single-neutron) transfer reactions induced by heavy ions, with calculations shifted to larger angles by up to ~ 4 degrees compared with the data. These reactions exhibited a significant mismatch, either of the reaction Q value or the grazing angular momentum of the entrance and exit channels, and it was speculated that the inclusion of multi-step transfer paths via excited state(s) of the projectile and/or ejectile could compensate for the effect of this mismatch and yield good descriptions of the data by shifting the calculated peaks to smaller angles. However, to date this has not been explicitly demonstrated for many reactions. In this work we show that inclusion of the two-step transfer path via the 4.44-MeV 2+ excited state of the 12C projectile in coupled channel Born approximation calculations enables a good description of the 208Pb(12C,11B)209Bi single-proton stripping data at four incident energies which could not be described by the FR-DWBA. We also show that inclusion of a similar reaction path for the 208Pb(12C,13C)207Pb single-neutron pickup reaction has a relatively minor influence, slightly improving the already good description obtained with the FR-DWBA.

Asymptotic normalization coefficients from transfer reactions and R -matrix analysis of direct capture in the Ne22(p,γ)Na23 reaction

The $^{22}$Ne(p,$\gamma$)$^{23}$Na reaction in NeNa cycle plays an important role in the production of only stable sodium isotope $^{23}$Na. This nucleus is processed by the NeNa cycle during hot bottom burning (HBB) in asymptotic giant branch (AGB) stage of low metallicity intermediate mass stats (4 M$_O$ $\leq$ M $\leq$ 6 M$_O$). Recent measurements have addressed the uncertainty in the thermonuclear reaction rate of this reaction at relevant astrophysical energies through the identification of low lying resonances at E$_p$ = 71,105, 156.2, 189.5 and 259.7 keV. In addition, precise measurements of low energy behaviour of the non-resonant capture has also been performed and the contribution of the sub-threshold resonance at 8664 keV excitation in $^{23}$Na has been established. Here, in this article, we have presented a systematic R-matrix analysis of direct capture to the bound states and the decay of the sub-threshold resonance at 8664 keV to the ground state of $^{23}$Na. A finite range distorted wave Born approximation (FRDWBA) calculation has been performed for $^{22}$Ne($^3$He,d)$^{23}$Na transfer reaction data to extract the asymptotic normalization coeeficients (ANC-s) required to estimate the non-resonant capture cross sections or astrophysical S-factor values in R-matrix analysis. Simultaneous R-matrix analysis constrained with ANC-s from transfer calculation reproduced the astrophysical S-factor data over a wide energy window. The S$_{tot}^{DC}$(0) = 48.8$\pm$9.5 keV.b compares well with the result of Ferraro, {\it et al.} and has a lower uncertainty. The resultant thermonuclear reaction is slightly larger in 0.1 GK $\le$ T $\le$ 0.2 GK temperature range but otherwise in agreeent with Ferraro, {\it et al.}.

Experimental study of the spectroscopic factors of Sn116–125

Enriched targets of $^{116,118,120,122,124}\mathrm{SnO}_{2}$ were bombarded with proton and deuteron beams, and the angular distributions of $(p,d)$ and $(d,p)$ on tin isotopes were accurately measured using the high-precision Q3D magnetic spectrograph at the Beijing HI-13 tandem accelerator of the China Institute of Atomic Energy. Distorted-wave Born approximation calculations were performed to extract the neutron spectroscopic factors (SFs) using two different sets of systematic optical potential parameters for these neutron transfer reactions. The SFs of $^{116--125}\mathrm{Sn}$ were obtained and compared to previous values. Our results are consistent with the average of the previous data within the error range. It is worth noting that the reaction products corresponding to $^{119}\mathrm{Sn}_{\text{G.S.}}$ and $^{119}\mathrm{Sn}_{\text{0.024}}^{*}$, to $^{123}\mathrm{Sn}_{\text{G.S.}}$ and $^{123}\mathrm{Sn}_{\text{0.025}}^{*}$, and to $^{125}\mathrm{Sn}_{\text{G.S.}}$ and $^{125}\mathrm{Sn}_{\text{0.028}}^{*}$ were first distinguished by the present experiment; therefore, our results of the low lying states of $^{119,123,125}\mathrm{Sn}$ are more reliable. However, the first excited state of $^{121}\mathrm{Sn}$ is only 0.006 MeV; we failed to identify the products that correspond to the ground state and the first excited state, and the extracted SFs of $^{120}\mathrm{Sn}_{\text{G.S.}}\ensuremath{\bigotimes}n\ensuremath{\rightarrow}^{121}\mathrm{Sn}_{\text{0.006.}}$ and $^{121}\mathrm{Sn}_{\text{0.006}}\ensuremath{\bigotimes}n\ensuremath{\rightarrow}^{122}\mathrm{Sn}_{\text{G.S}}$ are not reliable. A simple linear formula was used to analyze the relationship of SFs with neutron separation energy ${S}_{n}(N)$ and the even-$A$ Sn pairing gap $\mathrm{\ensuremath{\Delta}}(N)$, and SFs are found to be positively correlated to ${S}_{n}(N)$ and $\mathrm{\ensuremath{\Delta}}(N)$.

Characteristic X-ray yields and cross sections of thick targets of Al, Ti, Zr, W and Au induced by keV-electron impact

In this paper, pure thick Al (Z = 13), Ti (Z = 22), Zr (Z = 40), W (Z = 74) and Au (Z = 79) targets are bombarded by electrons in an energy range of 5–27 keV, and the experimental thick-target characteristic X-ray yields of K-shell and L-shell, the X-ray production cross sections and the ionization cross sections of inner shells are presented. The present experimental setup and data processing are improved, specifically, a deflection magnet is installed in front of the X-ray detector to prevent the backscattered electron from entering into the X-ray detector, and the bremsstrahlung background spectra calculated from PENELOPE Monte Carlo simulations are used to deduce the net peak areas. The X-ray detector used in this experiment is the XR-100SDD manufactured by Amptek Inc. with a 25 mm<sup>2</sup> C2 ultra-thin window which can detect the low-energy x-rays down to boron Kα line (0.183 keV). Standard sources (<sup>55</sup>Fe, <sup>57</sup>Co, <sup>137</sup>Cs and <sup>241</sup>Am) with an activity accuracy range of 1%–3% (<i>k</i> = 2), supplied by the Physikalisch-Technische Bundesanstalt, Germany (PTB), are used to perform the detector’s efficiency calibration, and in a low-energy range (< 3.3 keV) the efficiency calibration is accomplished by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thickness solid targets (i.e. by the characteristic peak method). The uncertainty of the detector’s efficiency calibration obtained in this paper is ~1.6%. The experimental thick-target characteristic X-ray yield data with an uncertainty of 1.7%–6.2% are compared with the PENELOPE Monte Carlo simulations, in which the inner-shell ionization cross sections are based on the distorted-wave Born approximation (DWBA) calculations, and they are in good agreement with a difference of less than or ~10%. According to the measured thick-target characteristic x-ray yields, the K-shell ionization cross sections for Al, Ti and Zr and the L-shell X-ray production cross sections for Zr, W and Au are also obtained with an uncertainty of 5%–8% (except for Al due to large K-shell fluorescence yield uncertainty), the difference between the experimental and theoretical data is also less than or ~10%. Moreover, by comparing the thick-target characteristic X-ray yields obtained from the analytical model and the PENELOPE Monte Carlo simulations at the electrons’ incident angles of 45° and 90°, it is found that the degree of agreement between the results from the analytical model and the Monte Carlo simulations at the incident angle of 90° is better than at the incident angle of 45°. Moreover, the contributions of the secondary electrons and bremsstrahlung photons to the characteristic X-ray yield are also given based on the PENELOPE Monte Carlo simulations. As for the elements studied in this paper, for the low ionization threshold energy, the contribution of the secondary electrons is ~2%, and however, for the high ionization threshold energy, the contribution is ~10%–20%. These contributions depend weakly on the energy of the incident electrons and show that these contributions are closely correlated with atomic number.