Ray Angular Distributions Research Articles

Investigation of secondary γ -ray angular distributions using the N15(p,α1γ)C*12 reaction

The observation of secondary $\ensuremath{\gamma}$-rays provides an alternative method of measuring cross sections that populate excited final states in nuclear reactions. The angular distributions of these $\ensuremath{\gamma}$-rays also provide information on the underlying reaction mechanism. Despite the large number of data of this type in the literature, publicly available $R$-matrix codes do not have the ability to calculate these types of angular distributions. In this paper, the mathematical formalism derived by C. R. Brune and R. J. deBoer [Phys. Rev. C 102, 024628 (2020)] is implemented in the $R$-matrix code azure2 and calculations are compared with previous data from the literature for the $^{15}\mathrm{N}(p,{\ensuremath{\alpha}}_{1}\ensuremath{\gamma})^{12}\mathrm{C}^{*}$ reaction. In addition, new measurements, made at the University of Notre Dame Nuclear Science Laboratory using the Hybrid Array of Gamma Ray Detectors (HAGRiD), are reported that span the energy range from ${E}_{p}=0.88$ MeV to ${E}_{p}=4.0\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. Excellent agreement between the data and the phenomenological fit is obtained up to the limit of the previous fit at ${E}_{p}=2.0\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and the $R$-matrix fit is extended from ${E}_{x}\ensuremath{\approx}13.5$ MeV up to ${E}_{x}\ensuremath{\approx}15.3$ MeV, where $^{15}\mathrm{N}+p$ and $^{12}\mathrm{C}+\ensuremath{\alpha}$ reactions are fit simultaneously for the first time. An excellent reproduction of the $^{15}\mathrm{N}(p,{\ensuremath{\alpha}}_{1}\ensuremath{\gamma})^{12}\mathrm{C}^{*}$ and $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\alpha})^{12}\mathrm{C}$ data is achieved, but inconsistencies and difficulty in fitting other data are encountered and discussed.

Investigation of the cosmic ray angular distribution and the East–West effect near the top of Etna volcano with the MEV telescope

An experimental investigation of cosmic muons has been carried out with the Muography of Etna Volcano (MEV) tracking telescope, installed at an altitude of about 3100 m a.s.l. in front of the North-East Etna crater. The analysis of a statistically significant data sample ($$\sim 10^7$$ events), taken during a period of approximately 2 months, has been carried out to investigate the angular distribution of cosmic muons originating both from the open sky side and from a large solid rock thickness (Etna side). Due to the geographical orientation of the MEV telescope, anisotropies caused by the East–West effect could also be observed, extracting the asymmetry factor in small steps of the zenithal angle.

Astrophysical S-factor for the 2H(ρ,γ)3He reaction at big-bang nucleosynthesis energies

We report on our latest experimental study of the 2H(ρ,γ)3He reaction in the energy range of interest for big-bang nucleosynthesis. The differential cross section at 135° and γ)-ray angular distributions were measured and compared with the results deduced from the latest ab-initio calculation. The astrophysical S-factor for the 2H(ρ,γ)3He reaction was obtained in the center-of-mass energy range E = 97-210 keV, and it is found to be in reasonable agreement with that predicted by the ab-initio calculation.

Investigation of mechanisms of formation of the second spherical harmonics of the galactic cosmic ray angular distribution

Mechanisms of formation of a second spherical harmonic of an angular distribution of galactic cosmic rays in the heliosphere are investigated. On the basis of data of Nagoya multidirectional muon telescope using a method of tensor anisotropy of cosmic rays time courses of symmetric diurnal, antisymmetric diurnal and semidiurnal variations of cosmic rays were obtained for the period 1971-2017. An abrupt offset of a phase of the semidiurnal variation to the earlier time during a positive polarity of the general magnetic field of the Sun, which closely correlates with the temporal change of a phase of the symmetric diurnal variations. It was shown the existence of annual variations of the tensor anisotropy components, which can be satisfactorely described by a single modulation factor - a screening of cosmic rays by the sector-structured interplanetary magnetic field. Moreover, the theory indicates on the existense of a stable north-south asymmetry of the interplanetary magnetic field - shift of the neutral current sheet to the south of solar equator.

Inelastic neutron scattering studies of Se76

The low-lying, low-spin levels of $^{76}\mathrm{Se}$ were studied with the $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction. Gamma-ray excitation function measurements were performed at incident neutron energies from 2.0 to 3.5 MeV, and $\ensuremath{\gamma}$-ray angular distributions were measured at neutron energies of 2.4, 3.0, and 3.7 MeV. From these measurements, level spins, level lifetimes, branching ratios, and multipole mixing ratios were determined. We established the ${0}_{2}^{+}$ band, which supports the shape coexistence in $^{76}\mathrm{Se}$ predicted by large-scale shell model calculations and the interacting boson model.

Consistent Empirical Physical Formula Construction for Gamma Ray Angular Distribution Coefficients by Layered Feedforward Neural Network

Multipolarities of gamma rays and spins-parities of nuclear states are usually investigated by the angular distribution of gamma rays emitted from aligned states formed by nuclear reactions. For different multipolarities of the transitions, the distribution shows different characteristics. The distribution is obtained by using angular distribution formula which has literature tabulated coefficients for different spins and multipolarities. However, these coefficients involve -fold tensor products and they are highly nonlinear in nature. Furthermore, as the calculation of these coefficients implicitly involves highly complicated integral quantities, they are very difficult to handle explicitly for larger values. In this respect, as we theoretically proved in a previous paper, universal nonlinear function approximator layered feedforward neural network (LFNN) can be applied to construct consistent empirical physical formulas (EPFs) for nonlinear physical phenomena. In this paper, by concentrating on the integer spins of nuclear states and dipole and quadrupole type multipolarities of the transitions, we consistently estimated the coefficients by constructing suitable LFNNs. The LFNN-EPFs fitted the literature coefficient data very well. Moreover, magnificent LFNN test set forecastings over previously unseen data confirmed the consistent LFNN-EPFs for the determination of coefficients. In this sense, we can conclude that the LFNN consistently infers nonlinear physical laws governing the angular distribution of gamma rays, which are otherwise difficult to obtain by conventional coefficient calculation methods.

The $\gamma$ γ -ray angular distribution in fast neutron inelastic scattering from iron

The angular distribution of $ \gamma$ -rays emitted after inelastic scattering of fast neutrons from iron was determined at the n ELBE neutron time-of-flight facility. An iron sample of natural isotopic composition was irradiated by a continuous photo-neutron spectrum in the energy range from about 0.1 up to 10 MeV. The de-excitation $\gamma$ -rays of the four lowest excited states of 56Fe and the first excited state of 54Fe were detected using a setup of five high-purity germanium (HPGe) detectors and five LaBr3 scintillation detectors positioned around the sample at $ 30^\circ$ , $55^{\circ}$ , $90^{\circ}$ , $ 125^{\circ}$ and $150^{\circ}$ with respect to the incoming neutron beam. The resulting angular distributions were fitted by Legendre polynomials up to 4th order and the angular distribution coefficients $a_{2}$ and $ a_{4}$ were extracted. The angular distribution coefficients of three transitions in 56Fe are reported here for the first time. The results are applied to a previous measurement of the inelastic scattering cross section determined using a single HPGe detector positioned at $125^{\circ}$ . Using the updated $\gamma$ -ray angular distribution, the previous cross section results are in good agreement with reference data.

Stretched configuration of states as inferred from $ \gamma$ γ -ray angular distributions in 40Ar + 208Pb neutron transfer reactions

Angular distributions of $ \gamma$ -rays for selected transitions in 40, 41, 42Ar isotopes have been studied with the PRISMA magnetic spectrometer coupled to the CLARA $ \gamma$ array. These transitions were populated in Ar isotopes reached via neutron transfer in the 40Ar + 208Pb reaction. By comparison with the shape of the experimental angular distribution of the known E2 transitions we established more firmly the spin and parity of excited states. In particular, in 41Ar for the $ (11/2^-)$ state through the $ (11/2^-) \rightarrow 7/2^-$ transition whose structure was discussed in terms of a phonon-fermion coupled state. The comparison with the expected fully aligned spin indicated that a high level of spin alignment has been reached.

Lifetimes in Te124 : Examining critical-point symmetry in the Te nuclei

The Doppler-shift attenuation method following inelastic neutron scattering was used to determine the lifetimes of nuclear levels to 3.3-MeV excitation in $\phantom{\rule{0.16em}{0ex}}^{124}\mathrm{Te}$. Level energies and spins, $\ensuremath{\gamma}$-ray energies and branching ratios, and multipole-mixing ratios were deduced from measured $\ensuremath{\gamma}$-ray angular distributions at incident neutron energies of 2.40 and 3.30 MeV, $\ensuremath{\gamma}$-ray excitation functions, and $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence measurements. The newly obtained reduced transition probabilities and level energies for $\phantom{\rule{0.16em}{0ex}}^{124}\mathrm{Te}$ were compared to critical-point symmetry model predictions. The $E(5)$ and ${\ensuremath{\beta}}^{4}$ potential critical-point symmetries were also investigated in $\phantom{\rule{0.16em}{0ex}}^{122}\mathrm{Te}$ and $\phantom{\rule{0.16em}{0ex}}^{126}\mathrm{Te}$.

Nuclear structure of Ge76 from inelastic neutron scattering measurements and shell model calculations

The low-lying, low-spin levels of $^{76}\mathrm{Ge}$ were studied with the $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction. Gamma-ray excitation function measurements were performed at incident neutron energies from 1.6 to 3.7 MeV, and $\ensuremath{\gamma}$-ray angular distributions were measured at neutron energies of 3.0 and 3.5 MeV. From these measurements, level spins, level lifetimes, $\ensuremath{\gamma}$-ray intensities, and multipole mixing ratios were determined. No evidence for a number of previously placed levels was found. Below 3.3 MeV, many new levels were identified, and the level scheme was re-evaluated. The $B(E2)$ values support low-lying band structure. The ${2}^{+}$ mixed-symmetry state has been identified for the first time. A comparison of the level characteristics with large-scale shell model calculations yielded excellent agreement.

Inspection of56Feγ-Ray angular distributions as a function of incident neutron energy using optical model approaches

Neutron inelastic scattering cross sections measured directly through (n,n) or deduced from γ-ray production cross sections following inelastic neutron scattering (n,n′ γ) are a focus of basic and applied research at the University of Kentucky Accelerator Laboratory (www.pa.uky.edu/accelerator). For nuclear data applications, angle-integrated cross sections are desired over a wide range of fast neutron energies. Several days of experimental beam time are required for a data set at each incident neutron energy, which limits the number of angular distributions that can be measured in a reasonable amount of time. Approximations can be employed to generate cross sections with a higher energy resolution, since at 125o , the a 2 P 2 term of the Legendre expansion is identically zero and the a 4 P 4 is assumed to be very small. Provided this assumption is true, a single measurement at 125o would produce the γ-ray production cross section. This project tests these assumptions and energy dependences using the codes CINDY/SCAT and TALYS/ECIS06/SCAT. It is found that care must be taken when interpreting γ-ray excitation functions as cross sections when the incident neutron energy is < 1000 keV above threshold or before the onset of feeding.

Dynamical Dipole mode in heavy-ion fusion reactions

The excitation of the Dynamical Dipole mode along the fusion path was investigated for the first time in the formation of a heavy compound nucleus in the A~190 mass region. The compound nucleus was formed at identical conditions of excitation energy and spin from two entrance channels having different charge asymmetry: the charge asymmetric 40 Ca + 152 Sm and the nearly charge symmetric 48 Ca + 144 Sm at Elab =11 and 10.1 MeV/nucleon, respectively. Both fusion–evaporation and fission events were studied simultaneously for the first time. The Dynamical Dipole mode excitation in the charge asymmetric channel was evidenced, in a model-independent way, by comparing the γ -ray multiplicity spectra and angular distributions of the two entrance channels with each other.

One-neutron pickup intoCa49: Bound neutrong9/2spectroscopic strength atN=29

The highly selective, intermediate-energy heavy-ion-induced neutron-pickup reaction, in combination with $\ensuremath{\gamma}$-ray spectroscopy using the $\ensuremath{\gamma}$-ray energy-tracking in-beam nuclear array (GRETINA), is shown to provide reliable relative spectroscopic strengths for high-$\ensuremath{\ell}$ orbitals in nuclei more neutron rich than the projectile. The reaction mechanism gives a significant final-state-spin alignment that is validated through $\ensuremath{\gamma}$-ray angular-distribution measurements enabled by the position sensitivity of GRETINA. This is the first time that $\ensuremath{\gamma}$-ray angular distributions could be extracted from a high-luminosity, fast-beam reaction other than inelastic scattering. This holds great promise for the restriction and assignment of ${J}^{\ensuremath{\pi}}$ quantum numbers in exotic nuclei. We advance this approach to study the crucial $N=28$ shell closure and extract the ratio ${g}_{9/2}:{f}_{5/2}$ of bound neutron single-particle strengths in $^{49}\mathrm{Ca}$, a benchmark for emerging multi-shell ab initio and configuration-interaction theories that are applicable along the Ca isotopic chain.

Using CHIMERA detector at LNS for gamma-particle coincidences

We have recently evaluated the quality of γ -ray angular distributions that can be extracted in particle-gamma coincidence measurements using the CHIMERA detector at LNS. γ -rays have been detected using the CsI(Tl) detectors of the spherical part of the CHIMERA array. Very clean γ -rays angular distributions were extracted in reactions induced by different stable beams impinging on 12 C thin targets. The results evidenced an effect of projectile spin flip on the γ -rays angular distributions. γ -particle coincidence measurements were also performed in reactions induced by neutron rich exotic beams produced through in-flight fragmentation at LNS. In recent experiments also the Farcos array was used to improve energy and angular resolution measurements of the detected charged particles. Results obtained with both stable and radioactive beams are reported.

Structure ofLa130at low and medium spins

Low- and medium-spin states of the odd-odd nucleus $^{130}\mathrm{La}$ were studied by in-beam and pulsed-beam $\ensuremath{\gamma}$-ray spectroscopy using the $^{121}\mathrm{Sb}(^{12}\mathrm{C},3n)$ and $^{116}\mathrm{Sn}(^{16}\mathrm{O},pn)$ fusion-evaporation reactions. The decay out of the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ and $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{7/2}$ rotational structures to the ground state has been elucidated. Spin and parity values have been assigned to most of the newly observed states, as well as to the bandheads of the rotational bands. Two isomeric states were identified and placed in the level scheme, with the characteristics ${J}^{\ensuremath{\pi}}={5}^{+},{E}_{x}=214.0$ keV, ${T}_{1/2}=0.76(9)$ $\ensuremath{\mu}$s and ${J}^{\ensuremath{\pi}}={6}^{+},{E}_{x}=319.1$ keV, ${T}_{1/2}=33(1)$ ns. The magnetic and quadrupole interactions of the ${6}^{+}$ isomeric state have been investigated by the time-differential perturbed $\ensuremath{\gamma}$-ray angular distribution method. The $g$ factor value, $g({6}^{+})=+0.48(3)$, and the quadrupole coupling constant in polycrystalline metallic Sn lattice, ${\ensuremath{\nu}}_{Q}({6}^{+})=37(4)$ MHz, have been derived. The experimental data are compared with the predictions of two-quasiparticles plus rotor model calculations.

AstrophysicalSfactor of3He(α,γ)7Be

Background: The ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\gamma})}^{7}$Be reaction is important for the neutrino production in the sun's core and the production of ${}^{7}$Li during big bang nucleosynthesis. The reaction mechanism is characterized by a strong direct capture component and nearby broad unbound resonance levels.Purpose: Recent experiments have opened up a new energy window into the reaction mechanism and it becomes more and more evident that, in order to understand the shape of the $S$ factor, theoretical calculations need to take into account possible resonance contributions from higher energies as well.Method: In the present work, a relatively wide energy window was investigated, ${E}_{c.m.}=300$--1460 keV, by detecting the prompt $\ensuremath{\gamma}$ rays from the reaction. An extensive $R$-matrix analysis was performed, utilizing all modern literature capture data, as well as elastic scattering data, which are important in constraining some $R$-matrix parameters.Results: The new experimental data agree very well with the modern literature data. The final result from the $R$-matrix fit gives a zero-energy $S$ factor of $S(0)=0.554(20)$ keV b. A table with the newly calculated reaction rate is given.Conclusions: The simultaneous $R$-matrix analysis of the ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\gamma})}^{7}$Be and ${}^{3}$He${(\ensuremath{\alpha},\ensuremath{\alpha})}^{3}$He channels yielded a reliable fit, consistent with all the included experimental data sets. In order to further constrain the reaction rate within the $R$-matrix framework, additional high-energy capture data, $\ensuremath{\gamma}$-ray angular distributions, and the inclusion of other relevant reaction channels are necessary.

γ-ray linear polarization measurements and(g9/2)−3neutron alignment in91Ru

Linear polarization measurements have been performed for $\gamma$-rays in $^{91}$Ru produced with the $^{58}$Ni($^{36}$Ar, $2p1n$$\gamma$)$^{91}$Ru reaction at a beam energy of 111 MeV. The EXOGAM Ge clover array has been used to measure the $\gamma$-$\gamma$ coincidences, $\gamma$-ray linear polarization and $\gamma$-ray angular distributions. The polarization sensitivity of the EXOGAM clover detectors acting as Compton polarimeters has been determined in the energy range 0.3$-$1.3 MeV. Several transitions have been observed for the first time. Measurements of linear polarization and angular distribution have led to the firm assignments of spin differences and parity of high-spin states in $^{91}$Ru. More specifically, calculations using a semi-empirical shell model were performed to understand the structures of the first and second (21/2$^{+}$) and (17/2$^{+}$) levels. The results are in good agreement with the experimental data, supporting the interpretation of the non yrast (21/2$^{+}$) and (17/2$^{+}$) states in terms of the $J_{\rm max}$ and $J_{\rm max}-2$ members of the seniority-three $\nu(g_{9/2})^{-3}$ multiplet.

Time-dependent Monte Carlo calculations of recoil-in-vacuumg-factor data for122,126,130,132Te

A method for extracting nuclear $g$ factors from the attenuation coefficients ${G}_{k}$ ($k=2$,4) of $\ensuremath{\gamma}$-ray angular distributions or particle-$\ensuremath{\gamma}$ angular correlations measured with the recoil-in-vacuum (RIV) technique is presented. The method uses time-dependent Monte Carlo simulations for ${G}_{k}$ as a function of the $g$ factor for a given nuclear lifetime. It is based on atomic-structure calculations from first principles using the grasp2k code by J\"onsson et al. [Comput. Phys. Commun. 177, 597 (2007)]. The simulations are compared with results of RIV measurements for the first excited states (${2}_{1}^{+}$) in ${}^{122,126,130,132}$Te. The choice of the electronic configurations and the effect of the charge-state distributions on ${G}_{k}$ are discussed. New ${2}_{1}^{+}$ $g$-factor values are obtained. These are compared with nuclear-model calculations.

Cosmic ray angular distribution employing plastic scintillation detectors and flash-ADC/FPGA-based readout systems

Abstract It is known that secondary cosmic rays are high energetic particles which are products of shower particles, when primary cosmic rays from outer space hit the atmosphere molecules. Many studies of cosmic rays show that cosmic flux depends on the depth of atmosphere. At ground level, most secondary cosmic rays are muons, a type of charged particle, and have angular dependence. The purpose of this article was to develop the telescope with two plastic scintillation detectors to investigate the angular distribution of cosmic rays at ground level. Directions of investigation were carried out vertical, 45-degree oblique and horizontal directions with respect to earth surface, approximately from North to South. Electronic readout system was developed from Flash Analog Digital Converter (Flash-ADC) of 8 bits-250Ms/sec, and Embedded Field Programmable Gate Array (FPGA)-based trigger. LabVIEWTM interface was written for controlling trigger system and taking data. For each direction measurement, the deposited energy spectra in the scintillators were obtained. The interest of cosmic-ray events was analyzed for counting. Angular distribution was obtained quantitatively. The experiment has been done at University of Science-HCMC.

Multi-intruder structures in34P

The available experimental information on ${}^{34}$P has been greatly increased through the analysis of $\ensuremath{\gamma}$ decays in coincidence with protons from the interaction of an ${}^{18}$O beam at 24 MeV with an ${}^{18}$O target. Light charged particles from the reaction were detected with Microball, and multiple $\ensuremath{\gamma}$-ray coincidences with Gammasphere. Many observed $\ensuremath{\gamma}$ transitions have been identified and placed in the level scheme. Additionally, for most states, spins have been assigned based on measured $\ensuremath{\gamma}$-ray angular distributions while parities were inferred from lifetimes determined through Doppler-broadened line-shape analysis. Most of the states observed have been interpreted in terms of shell-model calculations using the WBP-a and SDPF-NR interactions having one particle in the $0{f}_{7/2}$ or $1{p}_{3/2}$ orbital. The two calculations agree almost equally well with the data resulting in root-mean-square differences of about 200 keV. However, a few high-lying states observed with long lifetimes challenge current calculations. Two of these may be associated with stretched $\ensuremath{\pi}{f}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{f}_{7/2}$ states, but the calculations overpredict their energies by 2--3 MeV. Furthermore, a long-lived 7919-keV state is established for which no explanation is available at present.