Values Of Reaction Cross Section Research Articles

Comprehensive analysis of uncertainty quantification for the 58Ni(n, p)58Co reaction cross section* *Project supported by the Scientific and Industrial Research (CSIR), Government of India (File No 09/013(882)/2019-EMR-1) for providing senior research fellowships, the IUAC-UGC, Government of India (Sanction No. IUAC/XIII.7/UFR- 71353), and Institutions of Eminence (IoE) BHU (Grant No. 6031).

In this study, we measured the 58Ni(n, p)58Co reaction cross section with neutron energies of 1.06, 1.86, and 2.85 MeV. The cross section was measured using neutron activation techniques and γ-ray spectroscopy, and it was compared with cross section data available in the EXFOR. Furthermore, we calculated the covariance matrix of the measured cross section for the aforementioned nuclear reaction. The uncertainties of the theoretical calculation for 58Ni(n, p)58Co reaction cross section were calculated via Monte Carlo method. In this study, we used uncertainties in the optical model and level density parameters to calculate uncertainties in the theoretical cross sections. The theoretical calculations were performed by using TALYS-1.96. In this study, we aim to analyze the effect of uncertainties of the nuclear model input as well as different experimental variables used to obtain the values of reaction cross section.

Excitation function of neutron induced reaction on isotopes of cadmium (106Cd, 108Cd &110Cd) in the energy range of 13–15 MeV

This study focuses on the theoretical calculations of neutron-induced reaction cross-sections on several stable isotopes of cadmium within the energy range of 13–15 MeV. The nuclei produced in this process include 105Cd, 106Ag, 107Cd, 109Cd, and 110Ag. To calculate the reaction cross-sections for specific reactions such as 106Cd (n, 2n) 105Cd, 106Cd (n, p) 106Ag, 108Cd (n, 2n) 107Cd, 110Cd (n, 2n) 109Cd, and 110Cd (n, p) 110Ag, we employed the Alice 91-based computer code. The calculated results were then compared and tabulated alongside experimental data obtained from the International Atomic Energy Agency (IAEA) data source, EXFOR library. Additionally, we plotted the reaction cross-sections against neutron energy (excitation function) for each reaction channel. Our findings demonstrate a strong agreement between the calculated and experimental data within the specified neutron energy range. Furthermore, we introduced several statistical parameters to assess the fitting quality between the theoretically calculated and experimentally measured reaction cross-section values.

Astrophysical $$\boldsymbol{S}$$-Factor Calculations under the Effects of Gamma-Ray Strength Functions for Some Alpha Capture Reactions

The reaction cross section and the energy, at which this value is obtained, are extremely important parameters in the calculation of astrophysical $$S$$ -factor. Astrophysical $$S$$ -factor values can be shown as one of the most notable values not only for nuclear reactions occurring at low energies but also for deeper understanding of astrophysical processes too. Considering the importance of this variable, it has been made possible to calculate it with theoretical methods when it cannot be measured experimentally. Theoretical calculations require the energy and the reaction cross section values. While the reaction cross section value, which can be explained as the probability of occurrence of a reaction, is obtained by theoretical calculations, the result can be affected by many parameters. In this study, it is aimed to investigate the effects of gamma-ray strength functions on the calculations of the astrophysical $$S$$ -factor values of $${}^{96}$$ Ru( $$\alpha$$ , $$\gamma$$ ) $${}^{100}$$ Pd, $${}^{106}$$ Cd( $$\alpha$$ , $$\gamma$$ ) $${}^{110}$$ Sn, $${}^{112}$$ Sn( $$\alpha$$ , $$\gamma$$ ) $${}^{116}$$ Te, $${}^{113}$$ In( $$\alpha$$ , $$\gamma$$ ) $${}^{117}$$ Sb, and $${}^{144}$$ Sm( $$\alpha$$ , $$\gamma$$ ) $${}^{148}$$ Gd reactions by using the cross section values obtained via utilizing different gamma-ray strength functions, which is one of the parameters known to have an effect on the cross section calculations. All calculation results were obtained using a well-known computation code TALYS, and the data obtained were analysed both graphically and statistically against available experimental data from the Experimental Nuclear Reaction Data (EXFOR) Library.

Quantification of trace amounts of transmuted nuclides in transmutation detectors using SIMS

Neutron detectors based on neutron induced transmutation of nuclides of high-purity materials into other stable nuclides has been recently proposed to improve accuracy of long-term measurement of neutron fluence in fission nuclear reactors. The inductively coupled plasma mass spectrometry (ICP-MS) and the prompt gamma neutron activation analysis (PGNAA) have been used for the measurement of concentration of transmuted nuclides, which was then converted into neutron fluence using known neutron-reaction cross sections.In this work, the concentrations of transmuted elements were measured with a magnetic-sector secondary ion mass spectrometer (SIMS) instead of ICP-MS or PGNAA. Single crystals of Si, Ge and a polycrystalline metal foil of Ni were used as detector materials. The concentrations were measured down to sub ppb range in Si and Ge crystals. 9 prospective nuclides for transmutation detectors — 25Mg, 26Mg, 27Al, 31P, 67Zn, 69Ga, 71Ga, 59Ni, 63Ni were measured and compared to a reference neutron activation detector (NAD) method with neutron reaction cross section values taken from two different databases. With exception of 26Mg, the values determined using SIMS were within 20 % compared to those obtained using NADs with a cross section value from one or both databases. In case of 26Mg the difference between the results of SIMS and NAD methods was higher than 45 % for data from both databases. This discrepancy for 26Mg measurement was assigned tentatively to uncertainties of the neutron reaction cross section values. Nevertheless, the experiments proved distinct advantages of SIMS over ICP-MS in sample preparation and throughput, and in consuming micro-volumes of material and identified at least one well performing transmutation detector for thermal neutrons (Ge - single crystal) with agreement within 3 % between SIMS-TMD and NADs.

Reaction Cross Section of Heavy Projectiles Using Coulomb Modified Glauber Model

We investigated reaction cross section and inelastic collisions of the wide number of projectile and target nuclei using the Coulomb Modified Glauber Model (CMGM). The total reaction cross sections were calculated with and without accounting for in-medium effect for various heavy projectiles such as 56Fe26, 84Kr36, 132Xe54, 197Au79 and 238U92 that interact with Nuclear Emulsion Detector’s (NED) nuclei at incident energies at around 1 GeV/n. The calculated average values of reaction cross section are compared with the corresponding experimental data.

Analysis of Various Projectile Interactions with Nuclear Emulsion Detector Nuclei at ~1 GeV per Nucleon Using Coulomb Modified Glauber Model

The total nuclear reaction cross section is calculated considering the cases with and without medium effect by employing Coulomb modified Glauber model (CMGM) for interactions of projectiles 56Fe26, 84Kr36, 132Xe54, 197Au79, and 238U92 with nuclear emulsion detector (NED) nuclei at around 1 GeV per nucleon incident kinetic energy. These calculated nuclear reaction cross sections are correlated with the different target groups of the NED nuclei. The average value of various parameters is also calculated and compared with the corresponding experimental results. The number of shower particles emitted in an interaction is also calculated and showed good agreement with the experimental result. We observed that the total nuclear reaction cross section increases with increasing the target mass number in case of all the considered projectiles. In addition, it is shown that the average value of reaction cross section with nuclear medium effect is in good agreement with the experimental results for projectiles 56Fe, 84Kr, and 132Xe, although results of projectiles 197Au and 238U are not in agreement with the experimental observations. This study sheds some light on the energy dependence of the nuclear reaction cross section.

Search for halo structure inMg37using the Glauber model and microscopic relativistic mean-field densities

We have studied the ground state properties (binding energy and charge radius) using relativistic mean filed formalism (RMF) for Mg-isotopes in the valley of stability to drip line region. The RMF densities have been analyzed in context of reaction dynamics. The calculated results of $^{24-40}$Mg+$^{12}$C reactions at projectile energy 240 AMeV using Glauber model with the conjunction of densities from relativistic mean field formalism are compared with experimental data. We found remarkable agreement of estimated values of reaction cross sections with experimental data except for $^{37}$Mg isotope. In view of this, the halo status of $^{37}$Mg is examined through higher magnitude of rms radius and small value of longitudinal momentum distribution. Finally, an effort is made to explore the structure of $^{37}$Mg halo candidate using Glauber few body formalism.

89Y(γ,xn) reaction cross-section measurements with bremsstrahlung end-point energies of 50–65 MeV

The cross-sections for 89Y(γ, n)88Y, 89Y(γ, 2n)87Y, 89Y(γ, 3n)86Y, and 89Y(γ, 4n)85Y reactions for the end-point bremsstrahlung energies of 50 and 65 MeV were determined by using an activation and an off-line γ-ray spectrometric techniques with the electron linear accelerator at the Pohang Accelerator laboratory (PAL), Korea. The photon-induced reaction cross-sections of 89Y as functions of the photon energy were taken from the TENDL-2013 nuclear data library based on the TALYS 1.6 program. For comparison with our experimental results, the flux-weighted average cross-sections for the existing experimental data with mono-energetic photons and the theoretical values from TENDL-2013 were obtained. The reaction cross-section values measured at different end-point bremsstrahlung energies from the present work and from literature are found to be in good agreement with the theoretical values. The 89Y(γ, xn, x = 1 - 4) reaction cross-sections were observed to increase sharply from their threshold values to certain energies, until the next reaction channel opens, after which it remained constant for a while until the next reaction channel opened. Then, it decrease slowly with increasing of end-point bremsstrahlung energy due to the opening of different reaction channels.

Coulomb-nuclear potential resonances for oscillatory structure in second energy derivative of fusion cross section times energy

In a nucleus-nucleus collision, resonances depicted by larger values of reaction cross section (σ R) at specific energies are generated by the combined Coulomb-nuclear potential by virtue of well-developed pocket in it. The generation of such resonance is ascertained by the peak value of phase-shift time or dwell time at the resonance energy. We extract the results of fusion cross section (σ F) from σ R in the presence of such resonances and present them in the form of a quantity D F(E) = (d2(Eσ F)/dE 2): the second energy derivative of the product of σ F and energy E. In principle the variation of the quantity D F(E) as a function of energy shows two peaks and a negative dip between them around each resonance energy stated above. There can be several resonances in a given angular momentum trajectory denoted by partial wave l. Hence each l would carry a number of peaks and dips for the result of D F(E) over a range of energy. These results of D F(E) from a large number of ls involved in a heavy-ion collision shall be added together and, after some mutual cancellation and/or addition, the final result of D F(E) will show an oscillatory structure with a large number of residual peaks and dips present over the range of energy of variation. These calculated results of D F(E) give successful explanation of the corresponding results extracted from the experimental results of σ F at different energies in the cases of heavy-ion system of reactions, namely 16O + 208Pb, 36S + 110Pd, 58Ni + 60Ni and thereby it is confirmed that peaks and dips found in the variation of D F(E) extracted from the measured results of σ F as a function of the energy are critically influenced by the potential pocket resonances generated in the reactions.

Cross-section measurement of theBa130(p,γ)La131reaction forγ-process nucleosynthesis

Background: Deviations between experimental data of charged-particle-induced reactions and calculations within the statistical model are frequently found. An extended data base is needed to address the uncertainties regarding the nuclear-physics input parameters in order to understand the nucleosynthesis of the neutron-deficient $p$ nuclei.Purpose: A measurement of total cross-section values of the $^{130}\mathrm{Ba}(p,\ensuremath{\gamma})^{131}\mathrm{La}$ reaction at low proton energies allows a stringent test of statistical model predictions with different proton+nucleus optical model potentials. Since no experimental data are available for proton-capture reactions in this mass region around $A \ensuremath{\approx}130$, this measurement can be an important input to test the global applicability of proton+nucleus optical model potentials.Method: The total reaction cross-section values were measured by means of the activation method. After the irradiation with protons, the reaction yield was determined by use of $\ensuremath{\gamma}$-ray spectroscopy using two clover-type high-purity germanium detectors. In total, cross-section values for eight different proton energies could be determined in the energy range between 3.6 MeV $\ensuremath{\le}{E}_{p}\ensuremath{\le}$ 5.0 MeV, thus, inside the astrophysically relevant energy region.Results: The measured cross-section values were compared to Hauser-Feshbach calculations using the statistical model codes TALYS and SMARAGD with different proton+nucleus optical model potentials. With the semimicroscopic JLM proton+nucleus optical model potential used in the SMARAGD code, the absolute cross-section values are reproduced well, but the energy dependence is too steep at the lowest energies. The best description is given by a TALYS calculation using the semimicroscopic Bauge proton+nucleus optical model potential using a constant renormalization factor.Conclusions: The statistical model calculation using the Bauge semimicroscopic proton+nucleus optical model potential deviates by a constant factor of 2.1 from the experimental data. Using this model, an experimentally supported stellar reaction rate for proton capture on the $p$ nucleus $^{130}\mathrm{Ba}$ was calculated. At astrophysical temperatures, an increase in the stellar reaction rate of 68% compared to rates obtained from the widely used NON-SMOKER code is found. This measurement extends the scarce experimental data base for charged-particle-induced reactions, which can be helpful to derive a more globally applicable proton+nucleus optical model potential.

Quantum dynamics on S(1D) + H2 reaction: effect of orientation and rotation

Time-dependent quantum mechanical wave packet calculations have been carried out to study the effect of orientation and rotation of the hydrogen molecule on the reaction S (1D) + H2(X1 Σ + )(v = 0, j = 0–3) → SH(X2 Π) + H(2S) using the double many-body expansion (DMBE)/complete basis set (CBS) potential energy surface (PES) by Song and Varandas [J. Chem. Phys. 130, 134317 (2009)]. Reaction probability and integral cross section values were calculated over a range of collision energy values. The cross section values are compared with the experimental values as well as with the other quantum mechanical results. Our calculation shows that reaction probability values strongly depend on the orientation and rotation of the hydrogen molecule. It was also found that rotational excitation of H2 molecule significantly enhances integral reaction cross section values contrary to earlier reported quasi-classical trajectory calculation results.

Comparison of level density models in (γ, n) reactions of some lanthanide nuclei

Level densities are required at excitation energies where discrete level information is not available or incomplete to get a reliable theoretical analysis of cross sections, spectra, and angular distributions. The total reaction cross sections of some lanthanides (141Pr, 142Nd, 144Sm, 153Eu, 160Gd, 159Tb, 165Ho, 175Lu) were calculated using TALYS 1.2 code for gamma-induced reactions through the five level density models in the incident gamma energy range from 5 to 30 MeV. All calculations from the present study were compared with each other and with the experimental data obtained from EXFOR library. The total photo-neutron reaction cross-section values obtained from the model calculations and experimental measurements taken from EXFOR confirm the presence of systematical disagreements reported in the literature, except 165Ho case where one can see a satisfactory agreement.

Importance of Coriolis Coupling in Isotopic Branching in (He, HD+) Collisions

A three-dimensional time-dependent quantum mechanical wave packet approach is used to calculate the reaction probability (P(R)) and integral reaction cross section values for both channels of the reaction He + HD(+)(v = 1; j = 0) --> HeH (D)(+) + D (H) over a range of translational energy (E(trans)) on the McLaughlin-Thompson-Joseph-Sathyamurthy potential energy surface including the Coriolis coupling (CC) term in the Hamiltonian. The reaction probability plots as a function of translational energy for different J values exhibit several oscillations, which are characteristic of the system. The sigma(R) values obtained by including CC and not including it are nearly the same over the range of E(trans) investigated for the HeD(+) channel. For the HeH(+) channel, on the other hand, sigma(R) values obtained from CC calculations are significantly smaller than those obtained from coupled state calculations. These results are compared with the available experimental results. The computed branching ratios (Gamma(sigma) = sigma(R) (HeH(+))/sigma(R) (HeD(+))) are also compared with the available experimental results.

Quantum dynamics of (H −, HD) collisions at low energies

Time-independent quantum mechanical results are reported for H − + HD ( v = 1, j = 0) rearrangement reaction at low energies, for a range of total angular momentum values. Initial state selected reaction probability and integral reaction cross section values, when plotted as a function of relative translational energy reveal a number of prominent resonances arising from the quasibound states of the H −⋯HD van der Waals complex. It is shown that the nonreactive vibrational quenching dominates over both the exchange reactions and that H 2 formation is more favourable than HD.

Influence of Reagent Rotation on (H-, D2) and (D-, H2) Collisions: A Quantum Mechanical Study

Time-independent quantum mechanical (TIQM) approach (helicity basis truncated at k = 2) has been used for computing differential and integral cross sections for the exchange reaction H- + D2 (v = 0, j = 0-4) --> HD + D- and D- + H2 (v = 0, j = 0-3) --> HD + H- in three dimensions on an accurate ab initio potential energy surface. It is shown that the j-weighted differential reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder at four different relative translational energies (Etrans = 0.55, 0.93, 1.16 and 1.48 eV) for (H-, D2) and at one relative translational energy (Etrans = 0.6 eV) by Haufler et al. for both (H-, D2) and (D-, H2) collisions. The j-weighted integral reaction cross section values are in good agreement with the crossed beam measurements by Zimmer and Linder in the Etrans range 0.5-1.5 eV and close to the guided ion beam results by Haufler et al. for (H-, D2) in the range 0.8-1.2 eV. Time-dependent quantum mechanical (TDQM) results obtained using centrifugal sudden approximation are reported in the form of integral reaction cross section values as a function of Etrans in the range 0.3-3.0 eV for both reactions in three dimensions on the same potential energy surface. The TDQM reaction cross section values decline more sharply than the TIQM results with increase in the initial rotational quantum number (j) for the D2 molecules in their ground vibrational state (v = 0) for (H-, D2) collisions. The computed j-weighted reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder for (H-, D2) collisions and guided ion beam results by Haufler et al. for both (H-, D2) and (D-, H2) collisions for energies below the threshold for electron detachment channel.

Laser Spectroscopic Excitation Function and Reaction Threshold Studies of the H + DCl → HCl + D Gas-Phase Isotope Exchange Reaction

The dynamics of the gas-phase hydrogen atom exchange reaction H + DCl --> HCl + D were studied using the pulsed laser photolysis/laser induced fluorescence "pump-and-probe" method. Laser photolysis of H2S at 222 nm was used to generate nonequilibrium distributions of translationally excited hydrogen atoms at high dilution in a flowing moderator gas (Ar)/reagent (DCl) mixture. H and D atoms were detected with sub-Doppler resolution via Lyman-alpha laser induced fluorescence spectroscopy, which allowed the measurement of the line shapes of the moderated H atom Doppler profiles as well as the concentration of the D atoms produced in the H + DCl --> HCl + D reaction. From the measured H atom Doppler profiles, the time evolution of the initially generated nascent nonequilibrium H atom speed distribution toward its room-temperature thermal equilibrium form was determined. In this way, the excitation function and the reaction threshold (E0 = 0.65 +/- 0.13 eV) for the H + DCl --> HCl + D reaction could be determined from the measured nonequilibrium D atom formation rates and single collision absolute reaction cross-section values of 0.12 +/- 0.04 A2 and 0.45 +/- 0.11 A2 measured at reagent collision energies of 1.0 and 1.4 eV, respectively.

Isotopic Branching in (He, HD+) Collisions

A three-dimensional time-dependent quantum mechanical approach is used to calculate the reaction probability (P(R)) and the integral reaction cross section (sigma(R)) for both channels of the reaction He + HD+(v = 0, 1, 2, 3; j = 0) --> HeH(D)+ + D(H), over a range of translational energy (E(trans)) on two different ab initio potential energy surfaces (McLaughlin-Thompson-Joseph-Sathyamurthy and Palmieri et al.). The reaction probability plots as a function of translational energy exhibit several oscillations, which are characteristic of the system. The vibrational enhancement of the reaction probability and the integral reaction cross section values are reproduced qualitatively by our calculations, in accordance with the experimental results. The isotopic branching ratio for the reaction decreases in going from v = 0 to v = 1 and then becomes nearly v-independent in going from v = 1 to v =3 on both the surfaces.

A method for measuring light ion reaction cross-sections

An experimental procedure for measuring reaction cross-sections of light ions in the energy range 20–50 MeV/nucleon, using a modified attenuation technique, is described. The detection method incorporates a forward detector that simultaneously measures the reaction cross-sections for five different sizes of the solid angle in steps from 99.1% to 99.8% of the total solid angle. The final reaction cross-section values are obtained by extrapolation to the full solid angle.

Reaction probabilities and reaction cross sections for three-dimensional He+H2+(v) collisions: A time-dependent quantum mechanical study

Vibrational (v) state-selected reaction probabilities (PvjJ) have been calculated for the reaction He+H2+(v=0,1,2,3)→HeH++H, for H2+ in its ground rotational state (j=0) for a range of total angular momentum (J) values, for total energy (E) in the range 0.94–1.4 eV, using time-dependent quantum mechanical (TDQM) approach and centrifugal sudden approximation. The number of oscillations in Pv0J(E) decreases with increase in J. In addition, there is a noticeable increase in the threshold energy (Eth) with increase in J. The magnitude of Pv0J decreases with increase in J resulting in converged cross section values by the time J becomes 35–45, depending upon v and E under investigation. The resulting (converged) reaction cross section values are in excellent agreement with the experimental results at E=1.14 eV, both in terms of the magnitude and in terms of the observed vibrational enhancement. Interestingly, there is a noticeable discrepancy between our TDQM results and earlier time-independent quantum mechanical studies at higher energies, for v=1 and 2. For v=3, the difference between the two theoretical studies is the largest near the threshold. Our results for v=2 and 3 suggest that the oscillations in the vibrational state-selected reaction cross section values are amenable to experimental observation.

Heavy ion interactions of ( [formula omitted]) Pb with U

The interactions of 208 Pb projectiles with nat U target have been studied at 14.0 MeV/u beam energy using two different threshold detectors; mica and lexan. The elastic scattering data have been separated from the binary events and used for the determination of quarter-point angle θ 1/4 (≡ grazing angle θ gr). The values of maximum angular momentum l max , radius of interaction R int and reaction cross-section σ R exp(el.) were then deduced by making use of the value of θ 1/4. The data of inelastic events of different multiplicities have been used to determine partial reaction cross-sections. The sum of the partial cross-sections, therefore, yielded another independent value of reaction cross-section σ R exp(inel.) that in turn was used to derive the alternative values of l max , θ gr, and R int independently. The average of these quantities provided the experimental values of the reaction parameters that are comparable to the theoretical predictions.