Statistical Model Code Research Articles

Impact of nuclear level density and γ-ray strength function in (n,γ) and Maxwellian-averaged cross-section of 69Zn nucleus

The present paper highlights the impact of nuclear level density (NLD) and γ-ray strength function (γ-SF) on (n,γ) and Maxwellian-averaged cross-section of 69Zn nucleus. At first, the existing NLD and γ-SF models (in TALYS statistical model code) have been utilized to understand the role of NLD and γ-SF in neutron capture reaction cross-section. It is seen that most of the combinations of existing NLDs and γ-SFs (phenomenological and/or microscopic) cannot explain the experimental data. Therefore, the microscopic exact pairing plus independent particle model (EP+IPM) and exact pairing plus phonon damping model (EP+PDM) have been carried out to calculate the NLD and γ-SF of 69Zn nucleus, respectively, by employing the exact treatment of thermal pairing. It is seen that microscopic EP+IPM NLD and EP+PDM γ-SF explain the experimental data better than all other combinations available in TALYS-1.95, indicating the impact of the exact treatment of thermal pairing correlation. In addition, the inclusion of an upbend (UB) structure in γ-SF further improves the comparison with the experimental data in the low energy region (∼0.01–0.15 MeV), indicating the possibility of having an UB structure in γ-SF of 69Zn. The 68Zn(n,γ)69Zn reaction cross-section obtained by utilizing the EP+IPM NLD and EP+PDM γ-SF including UB structure is then used to predict the Maxwellian-averaged cross-sections, and the obtained results show reasonable agreement with all the available experimental data taken from the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars. The present results reflect the impact of microscopic NLD and γ-SF on the precise description and/or prediction of the astrophysical reaction cross-section.

Investigating the influence of input angular momentum on independence hypothesis in heavy-ion induced fusion reactions

The experimental verification of compound nucleus theory has successfully been performed for light ion induced reactions using proton and α-particle beams on different targets. However, such studies using the heavy ion beams are scarce due to the complex nature of heavy ion interaction process. The present work is an attempt to validate the Bohr's independent hypothesis using heavy ion beam of 18O beam on 159Tb targets and 12C on 165Ho targets, forming the same compound nucleus 177Ta. A channel wise analysis of cross section data for evaporation residues produced in 18O+159Tb and 12C+165Ho systems has been performed within the framework of statistical model code PACE4 and found to reasonably agree with the experimental data. Further, a comparison of reaction cross section data for the same evaporation residues produced in the two different systems has been found to follow Bohr's compound nucleus hypothesis at relatively higher excitation energies. However, at relatively lower excitation energies, a significant deviation in the measured cross section data of the same residues in the above mentioned systems have been observed and is attributed to the discrepancies in angular momentum values. Such discrepancies are well explained on the basis of input angular momentum involved in the reactions.

Investigation of the fusion mechanism in the Li6 -induced reaction on Nb93

We attempt to put forth the competing reaction mechanisms through residual cross section measurement in $^{6}\mathrm{Li}$ fusion with $^{93}\mathrm{Nb}$. The measured residual cross sections in the 24--43 MeV energy range are analyzed with the theoretical estimations from pace4, empire3.2.2, and alice23 statistical model codes. The replication of major $xn$-channel cross sections by empire with enhanced generalized superfluid model (EGSM) level density confirms that the population of $xn$-channel residues is through the complete fusion (CF) mechanism. The preequilibrium (PEQ) emission signatures were witnessed in the case of $^{97}\mathrm{Ru}$ residue populated via the $2n$ channel. Amplification of major experimental $p$- and $\ensuremath{\alpha}$-channel cross sections relative to the optimal theory was interpreted by considering the possibility of an incomplete fusion (ICF) process in addition to CF, owing to the low breakup threshold of the $^{6}\mathrm{Li}$ projectile. Thus, the ICF strength fraction $({F}_{\mathrm{ICF}})$ was estimated. The ${F}_{\mathrm{ICF}}$ turned out to be $\ensuremath{\approx}8--20%$ with an increasing trend and is found to be thoroughly higher than the deduced ${F}_{\mathrm{ICF}}$ for $^{7}\mathrm{Li}$ reaction on $^{93}\mathrm{Nb}$ target. In the case of weakly bound $^{6,7}\mathrm{Li}$-induced reactions, the first attempt is made to understand the influence of entrance channel parameters such as bombarding energy, $\ensuremath{\alpha}$-separation energy, Coulomb factor, mass asymmetry, neutron skin thickness, angular momentum, etc., on ${F}_{\mathrm{ICF}}$. The observed trend of the isomeric cross section ratios from the relative population of isomeric and ground states of $^{96,94}\mathrm{Tc}$ radionuclides is also discussed.

Statistical (n,gamma ) cross section model comparison for short-lived nuclei

Neutron-capture cross sections of neutron-rich nuclei are calculated using a Hauser–Feshbach model when direct experimental cross sections cannot be obtained. A number of codes to perform these calculations exist, and each makes different assumptions about the underlying nuclear physics. We investigated the systematic uncertainty associated with the choice of Hauser-Feshbach code used to calculate the neutron-capture cross section of a short-lived nucleus. The neutron-capture cross section for ^{73}hbox {Zn}(n,gamma )^{74}hbox {Zn} was calculated using three Hauser-Feshbach statistical model codes: TALYS, CoH, and EMPIRE. The calculation was first performed without any changes to the default settings in each code. Then an experimentally obtained nuclear level density (NLD) and gamma -ray strength function (gamma hbox {SF}) were included. Finally, the nuclear structure information was made consistent across the codes. The neutron-capture cross sections obtained from the three codes are in good agreement after including the experimentally obtained NLD and gamma hbox {SF}, accounting for differences in the underlying nuclear reaction models, and enforcing consistent approximations for unknown nuclear data. It is possible to use consistent inputs and nuclear physics to reduce the differences in the calculated neutron-capture cross section from different Hauser-Feshbach codes. However, ensuring the treatment of the input of experimental data and other nuclear physics are similar across multiple codes requires a careful investigation. For this reason, more complete documentation of the inputs and physics chosen is important.

Farklı seviye yoğunluk modelleri kullanılarak reaksiyon eşik değerinden 20 MeV’e kadar Paladyum izotoplarının (n,2n), (n,p) ve (n,) tesir kesitlerinin hesaplanması

Bu çalışmada, Paladyum izotoplarının (102,104,106,108,110Pd) (n,2n), (n,p) ve (n,) reaksiyon tesir kesitleri Empire-3.2.3 (Malta) istatistiksel model kodu kullanılarak reaksiyon eşik değerinden 20 MeV’e kadar nötron enerjilerinde hesaplanmıştır. Hesaplamalar, dört farklı nükleer seviye yoğunluğu modeli (Genelleştirilmiş Süper Akışkan modeli, Gelişmiş Genelleştirilmiş Süper Akışkan modeli, Gilbert-Cameron modeli ve Hartree-Fock-Bogoliubov mikroskobik modeli) kullanılarak yapılmıştır. Hesaplardan elde edilen sonuçlar, EXFOR kütüphanesinde bulunan deneysel verilerle ve ENDF kütüphanesinden alınan ENDF/B-VIII.0 (USA,2018), TENDL-2019 (TALYS, 2019) ve JENDL-5 (Japan,2021) değerlendirilmiş verilerle karşılaştırılmıştır. 14.5 MeV civarında deneysel ve değerlendirilmiş verilerle karşılaştırıldığında, sonuçlar genel olarak tutarlı bir uyum göstermektedir.

Measurement of the integrated cross section of 110Pd(γ,n)109mPd, 110Pd(γ,n)109gPd, and 110Pd(γ,x)108mRh reactions with 70 MeV bremsstrahlung

We measured the integrated cross sections of 110Pd(γ,n)109mPd, 110Pd(γ,n)109gPd and 110Pd(γ,x)108mRh reactions in the energy range from the reaction threshold to 70 MeV bremsstrahlung end-point energy. Measurements were performed by means of the activation method in combination with off-line γ-ray spectrometry. The induced activity of radionuclides was measured with a high-purity germanium (HPGe) detector and necessary corrections for γ-ray interferences were made. The integrated cross section of the studied reactions was measured relative to that of the monitor reaction 27Al(γ,2pn)24Na. Current results are compared with theoretical predictions using the TALYS-1.9 statistical nuclear model code. Calculations were performed using six different level density models in combination with eight γ-strength functions to determine which combinations best fit the experimental results. The present results are measured for the first time.

A Study of Reaction Dynamics in the Interaction of 14N+59Co System at 32-56 MeV

The present work was done to investigate the reaction mechanisms involved in the interaction of 14 N projectile with 59 Co target at beam energies ∼32-56 MeV. The experimentally measured excitation functions available in the literature [2] were compared and analyzed with the statistical model code PACE4 calculation. For non-α emitting channels populated via complete fusion reaction, the measured excitation functions, after correcting them for possible contributions coming from higher charge isobaric precursor decays, were in general found to be in good agreement with theoretical predictions. However, for α-emitting channels, the experimentally measured excitation functions had more production cross-sections than what PACE4 predicted. The observed enhancement in the present case may be attributable to process of incomplete fusion from break-up of 14 N projectile. It may be pointed out that incomplete fusion reaction increases with increase in projectile energy. The observation of high incomplete fusion reaction is attributable to the prompt breakup of 14 N projectile into α-cluster. DOI: 10.7176/APTA/86-03 Publication date: October 31 st 2022

Determination of Co57(n,xp ) cross sections using the surrogate reaction ratio method

The compound nuclei $^{58}\mathrm{Co}^{*}$ and $^{61}\mathrm{Ni}^{*}$ have been populated at overlapping excitation energies by transfer reactions $^{56}\mathrm{Fe}(^{6}\mathrm{Li},\ensuremath{\alpha})^{58}\mathrm{Co}^{*}$ (surrogate of $n+^{57}\mathrm{Co}$) at ${E}_{\mathrm{lab}}$ = 35.9 MeV and $^{59}\mathrm{Co}(^{6}\mathrm{Li},\ensuremath{\alpha})^{61}\mathrm{Ni}^{*}$ (surrogate of $n+^{60}\mathrm{Ni}$) at ${E}_{\mathrm{lab}}$ = 40.5 MeV, respectively. The $^{57}\mathrm{Co}(n,xp$) cross sections in the equivalent neutron energy range of 8.6--18.8 MeV have been determined within the framework of surrogate reaction ratio method using $^{60}\mathrm{Ni}(n,xp$) cross section values from the literature as reference. The proton decay probabilities of the compound systems have been determined by measuring evaporated protons at backward angles in coincidence with projectile-like fragments detected around the grazing angle. The measured $^{57}\mathrm{Co}(n,xp$) cross sections are in good agreement with both the predictions of talys-1.8 statistical model code with default parameters using different microscopic level densities and data evaluation library jeff-3.3 up to equivalent neutron energy $\ensuremath{\approx}12.6$ MeV, while for higher energies the measured $^{57}\mathrm{Co}(n,xp$) cross sections are found to be consistently higher than the predictions. However, the talys-1.8 calculations with modified values of input potential parameters provide a reasonable reproduction of the measured $^{57}\mathrm{Co}(n,xp$) cross sections for the entire neutron energy range. The observed discrepancies at higher energies between the experimental data and the predictions of both the jeff-3.3 library and the talys-1.8 calculations with default parameters indicate the need of new evaluations for this reaction.

Multiparticle natSr(γ, ) reactions induced with bremsstrahlung end-point energies of 55, 60, and 65 MeV * *Supported by the National Research Foundation of Korea through a grant provided by the Ministry of Science and ICT (NRF-2017R1D1A1B03030484, NRF-2018R1A6A1A06024970)

This study measured the yields of the radionuclides 82Sr, 83(m+g)Sr, 85mSr, 85gSr, 87mSr, 81(g+0.976m)Rb,82mRb,83gRb,84(m+g)Rb, and 86(m+g)Rb produced in natSr(γ, xnyp) multiparticle reactions with bremsstrahlung end-point energies of 55, 60, and 65 MeV. The bremsstrahlung radiation was generated using the 100-MeV electron linear accelerator at the Pohang Accelerator Laboratory, Korea, and the reaction yields were derived from the induced activitiesmeasured using off-line γ-ray spectrometry. To obtain accurate experimental results, we performed the necessary γ-rayinterference corrections. The experimental results were compared with the theoretical predictions obtained usingthe TALYS-1.95 statistical nuclear model code. The calculations were performed using six different level-density models to ascertain which model best fitted the experimental results. The dependence of the reaction yield on the incident bremsstrahlung energy and on the number of nucleons emitted by the photonuclear reactions was also investigated.

Role of the entrance channel in the experimental study of incomplete fusion of 13 C with 93 Nb

We report measured cross-section data of the residues produced in the $^{13}\mathrm{C}$-induced reaction on $^{93}\mathrm{Nb}$ within the 63.7--87.1-MeV energy range. The off-line $\ensuremath{\gamma}$-ray spectroscopy method has been used to measure the cross sections of the radionuclides produced in this system. The analysis of present measured cross-section data has been carried out within the light of well-established statistical model code pace4. The excitation function of residues populated via $xn$ and/or $pxn$ channels are found to be in fair agreement with those estimated by the theoretical model code, which confirms the assembly of these residues via complete fusion process. A considerable enhancement in the measured cross-section data has been observed for the residues involving $\ensuremath{\alpha}$-emitting channels as compared to the theoretical predictions. The observed enhancement in the cross sections has been assigned to the incomplete fusion processes. Furthermore, in order to have a better insight into the onset and strength of incomplete fusion, termed as the incomplete fusion fraction has been deduced for the present paper and is compared with $^{16}\mathrm{O}$ and $^{18}\mathrm{O}$ beams on the same target $^{93}\mathrm{Nb}$. This suggests that the incomplete fusion fraction is strongly influenced by the entrance channel, which may be understood in terms of the projectile ${Q}_{\ensuremath{\alpha}}$ value. The comparison of this paper with literature data also shows that the incomplete fusion probability increases with various entrance channel parameters, such as projectile structure, projectile energy, and mass asymmetry of interacting partners.

A Study of excitation functions in the interaction of α + 59Co system at 4~9MeV/Nucleon

In this work, α-induced 59Co reactions in the energy range from 11- 41MeV were used in order to study the role of pre-equilibrium emission. The experimentally measured excitation functions for residues populated via (α, n),(α, 2n),(α,3n),(α,2p),(α, 3n 2p) and (α, 4n 2p) channels in the interaction of + 59Co system available in the literature [13] were compared with theoretical predictions obtained using the statistical model code COMPLET. It was observed that at higher energy points the pure compound nucleus predictions, in general, failed to reproduce the measured data at projectile energies ~11-41MeV, this shows significant contributions from pre-equilibrium emission. The study signified both equilibrium and pre-equilibrium emissions were required to reproduce the presently measured excitation functions. An attempt was made to deduce the contribution coming from pre-equilibrium emission. It was found that the pre-equilibrium contribution increases with increasing projectile energy. Furthermore, the present result revealed a strong correlation between pre-equilibrium contribution and particle multiplicity.

Effect of projectile structure on break-up fusion for 14N + 175Lu system at intermediate energies

In the present work, fusion in heavy-ion collisions at energies near the Coulomb barrier to ≈ 33% above it has been studied for 14N + 175Lu system. The excitation functions of several reaction channels expected to be populated via complete fusion and/or the incomplete fusion of the projectile have been measured. The experimental excitation functions have been critically compared with the predictions of the statistical model code PACE4. The observed enhancement in the measured cross-sections with respect to the theoretical model code PACE4 predictions of all the reactions having α-particle(s) in the exit channel is reminiscent of the fact that incomplete fusion (ICF) is at work in populating these channels besides the complete fusion process. The relative probability of incomplete fusion in fusion dynamics, obtained in terms of incomplete fusion strength function FICF has also been deduced. The observed behavior of FICF suggests the increasing probability of ICF contributions with projectile energy. A strong and a dictating dependence of FICF on projectile structure in terms of its Qα-value has been observed. The reduction procedures for the elimination of the geometric and the static effects suggest that the observed variation in the fusion data has a purely static origin i.e., a manifestation of different potential barriers and radii. The analysis done within the framework of universal fusion function indicates the fusion suppression of ≈ 5% for the 14N + 175Lu system.

Effect of non- α -cluster projectile on incomplete-fusion dynamics: Experimental study of the N14+Ta181 system

In order to study incomplete fusion (ICF) reaction dynamics, the present work manifests the role of a non-$\ensuremath{\alpha}$-cluster $^{14}\mathrm{N}$ projectile on $^{181}\mathrm{Ta}$ target at energies $\ensuremath{\approx}4--7$ MeV/nucleon using the offline $\ensuremath{\gamma}$-ray spectroscopy. The excitation functions for 15 reaction residues populated in $^{14}\mathrm{N}+^{181}\mathrm{Ta}$ system have been measured and analyzed within the framework of statistical model code PACE4. The experimentally measured excitation functions of evaporation residues populated via xn/pxn channels are found to be well reproduced by the predictions of code PACE4, which confirms their production solely via complete fusion process. However, an enhancement in the measured excitation function as compared to PACE4 calculations, particularly in tail portion of $^{192}\mathrm{Hg}$ residue ($3n$ channel) has been observed indicating the presence of precompound emission. A significant contribution from precursor decay in pxn channels has also been observed. An enhancement in the measured excitation functions for $\ensuremath{\alpha}$-emitting channels as compared to the PACE4 predictions has been observed and attributed to the incomplete fusion process. Further, the contribution from incomplete fusion process in the $^{14}\mathrm{N}+^{181}\mathrm{Ta}$ system has also been deduced in terms of strength function (${F}_{\mathrm{ICF}}$). The results have been discussed in terms of the parameters which influence the dynamics of ICF process. The ${F}_{\mathrm{ICF}}$ is found to depend strongly on projectile energies, the product of projectile and target charges, and $\ensuremath{\alpha}\ensuremath{-}Q$ value of the projectile.

Possibilities for synthesis of new transfermium isotopes in multinucleon transfer reactions

Multinucleon transfer mechanisms near barrier collisions between very heavy nuclei are investigated in the framework of the improved dinuclear system model by considering the influence of orientation effects combined with statistical model code gemini++. Several transfer reactions for different actinide targets ($^{238}\mathrm{U},^{248}\mathrm{Cm}$, and $^{249}\mathrm{Cf}$) are studied in detail. One notices that the isotopic distributions of the above-target products decrease drastically by a factor of 10 per proton, which is moved from projectile to target. However, the calculated and measured results show that the larger production cross sections above targetlike fragments can be produced by using the heaviest available target. The predicted cross sections and excitation functions of the new transfermium isotopes may be useful for future experiments.

Modeling photon-induced reactions on U233–238 actinide targets

Comprehensive calculations of cross sections of photon induced reactions on $^{233-238}$U targets for incident photon energies from 3 up to 30 MeV are undertaken with the statistical model code EMPIRE-3.2 Malta. Results are compared with the experimental data from EXFOR and with the current evaluations. The differences and the similarities between the models and parameters used in calculations of photon- and neutron-induced reactions on the same nuclei are discussed with focus on fission. The role of the extended optical model for fission in improving the description of the measured data and in determining consistent sets of barrier parameters is pointed out.

Effect of neutron excess in the entrance channel on the O18+Nb93 system: An experimental study relevant to incomplete-fusion dynamics

The incomplete fusion dynamics in the $^{18}\mathrm{O}+^{93}\mathrm{Nb}$ system at energies above the Coulomb barrier has been investigated. The experimentally measured cross sections have been compared with the theoretical predictions of the statistical model code pace4. To examine the effect of entrance channel parameters on the onset and strength of incomplete fusion, relative contributions of complete and incomplete fusion have been deduced from the analysis of measured excitation functions. The contribution of incomplete fusion deduced from the analysis of excitation functions has been studied in terms of various entrance channel parameters, namely, entrance channel mass asymmetry (${\ensuremath{\mu}}_{A}$) of interacting projectile and target combination, Coulomb factor (${Z}_{P}{Z}_{T}$), ground state $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value of the reaction, and neutron skin thickness of target nuclei. It has been found that the probability of incomplete fusion depends strongly on entrance channel parameters. Further, the incomplete fusion contribution for the $^{18}\mathrm{O}$ projectile with two excess neutrons is noticed to be relatively larger as compared to $^{16}\mathrm{O}$. This may be due to the larger probability of breakup for the $^{18}\mathrm{O}$ projectile resulting in rather weak binding forces as compared to $^{16}\mathrm{O}$. The existence of incomplete fusion below critical angular momentum (${\ensuremath{\ell}}_{\mathrm{crit}}$), i.e., $\ensuremath{\ell}\ensuremath{\leqslant}\phantom{\rule{4pt}{0ex}}{\ensuremath{\ell}}_{\mathrm{crit}}$, has also been observed for the studied system.

Projectile Break-up Effect on Fusion in 16O + 156Gd Reaction at Energy Range 4.3-6.3 MeV/A

We discuss our present understanding of the incomplete fusion (ICF) reaction dynamics, the excitation function of six evaporation residues (ERs) have been measured in 16O + 156Gd reaction at projectile energy range, E/A ~ 4.3-6.3 MeV/Nucleon. Some of the ERs are produced directly & indirectly (i.e. through pre-cursor), the pre-cursor contributions have been separated out from the measured cumulative cross-section with the help of Cavinato et al.1. After correcting the pre-cursor contribution, the independent yield has been compared with the statistical model code PACE-22, which describes the fusion reaction cross section. In order to optimize the parameter of the code PACE-2 that reproduces the cross section of all the complete fusion (CF) channels like xn and /or pxn-channels. Using the same set of input parameters, cross section of the ERs populated via incomplete fusion (ICF) channels have been measured. The enhancement in the measured cross section of the ERs populated via ICF channels over the PACE-2 prediction have been measured, which indicates the occurrence of the break-up of projectile 16O into (12C+α) and/or (8Be+2α) leading to ICF reaction dynamics.

Pion–kaon femtoscopy and the lifetime of the hadronic phase in Pb−Pb collisions at [formula omitted] TeV

In this paper, the first femtoscopic analysis of pion–kaon correlations at the LHC is reported. The analysis was performed on the Pb–Pb collision data at sNN=2.76 TeV recorded with the ALICE detector. The non-identical particle correlations probe the spatio-temporal separation between sources of different particle species as well as the average source size of the emitting system. The sizes of the pion and kaon sources increase with centrality, and pions are emitted closer to the centre of the system and/or later than kaons. This is naturally expected in a system with strong radial flow and is qualitatively reproduced by hydrodynamic models. ALICE data on pion–kaon emission asymmetry are consistent with (3+1)-dimensional viscous hydrodynamics coupled to a statistical hadronisation model, resonance propagation, and decay code THERMINATOR 2 calculation, with an additional time delay between 1 and 2 fm/c for kaons. The delay can be interpreted as evidence for a significant hadronic rescattering phase in heavy-ion collisions at the LHC.

Temperature and isospin dependence of the level-density parameter in the A≈110 mass region

$\ensuremath{\alpha}$-Particle evaporation spectra were measured at backward angles in $^{16}\mathrm{O}+\phantom{\rule{0.16em}{0ex}}^{94,100}\mathrm{Mo}$ reactions at multiple beam energies. Inverse level-density parameter, $K$, was determined for Cd nuclei of different isospins by simulating high-energy tail of the measured $\ensuremath{\alpha}$-particle evaporation spectra with statistical model code pace2. An overall increasing behavior of the $K$ value is observed with increasing temperature in the range of 1 to 2.5 MeV. It is observed that in the temperature region below 1.8 MeV, the parameter $K$ is higher for the neutron-rich nuclei by around 1 MeV. Semiclassical calculations were performed which treat single-particle level density of neutron and proton on different footing and this can account for the isospin effects. These calculations reproduce the $K$ values as determined from the statistical model analysis of $\ensuremath{\alpha}$-particle evaporation spectra. Present results clearly demonstrate the isospin dependence of the level-density parameter as conjectured by theoretical works.

The interplay between the nuclear level density and the separation energy of rotating superheavy nucleus Z = 119 at low temperature regime

The temperature dependence of the level density parameter and the neutron separation energy are determined under statistical assumptions with regard to the excitation energy using the statistical model code developed in FORTRAN language. The quadrupole deformation parameter and the inverse level density parameter are coinciding well with the experimental results concerning the available literatures. The interplay between the level density and the particle separation energy is displayed graphically to locate the possible neutron magicity and found N=176 suits well at low temperature regime. The excitation energy for the possible formation of 119295 is predicted as 33.3 MeV.