Compound Nucleus Process Research Articles

New experimental approach for developing a mass-energy systematics for precompound emission

A systematic analysis of the experimental cross-section data in odd mass number $(A)$ and odd atomic number $(Z)$ nuclei is reported to reveal a novel mass-energy systematics for the pre-compound emission of fast neutrons in $\ensuremath{\alpha}$-induced reactions at low energies. The experimental excitation functions have been analyzed within the framework of statistical model predictions to get information regarding pre-compound emission. The present analysis establishes for first time an interesting systematics, emphasizing that accessible excitation energy on peripheral nucleons of the systems is an exponential function of atomic mass number ($A$) of target nuclei. One of the most important features of this systematics is to provide a precise estimation of the pre-compound contribution for any nuclei, except closed-shell ones, over a wide range of mass number $63\ensuremath{\le}A\ensuremath{\le}109$ in the nuclear landscape. New results of the present analysis emphasize an additional subtle interconnection between the structure of nuclei and the nuclear reaction mechanism of the pre-compound emission process at low energies, where the compound nucleus process is more likely to be dominant.

Fission partition a reflection of shell closures: Decay of 220,224U⁎ at eight excitation energies

Decay modes of the compound systems formed in 86Kr + 134,138Ba → 220,224U⁎ reactions at eight excitation energies have been compared to explore the influence of shell closures and excitation energy. The mass distributions of the cross-sections have been calculated for the two compound systems by keeping their excitation energies the same. The production cross-section for the light particles, intermediate mass fragments, symmetric and asymmetric fission fragments, total fission fragments, percentage of the cross-section for symmetric and asymmetric fission fragments, the ratio of the cross-sections of the symmetric and asymmetric fission fragments and fission barrier as a function of the incident energy have been compared. The range of the incident energy which corresponds to the high probability of the compound nucleus process has been obtained. Three angular momentum windows have been realized from the variation of the production cross-section for the light particles, intermediate mass fragments, fission fragments and the total fragments as a function of the angular momentum which correspond to the dominance of a reaction mechanism in that window. The shell closures have been reflected in the fission partition and weaken with the increase of the incident energy along with the loss of odd-even effects. The mode of the reaction depends upon the excitation energy and angular momentum of the compound system.

Decay of Hot and Rotating $${}^{\boldsymbol{88}}$$Mo$${}^{\boldsymbol{*}}$$ at Incident Energies of 300, 450, and 600 MeV

The reaction mechanism for the decay of the hot and rotating compound system $${}^{88}$$ Mo $${}^{*}$$ formed in $${}^{48}\textrm{Ti}+^{40}$$ Ca reaction and the time for the emission of outgoing fragments have been analyzed within the quantum-mechanical fragmentation theory based dynamical cluster-decay model, at three incident energies. The incident energy effects have been analyzed by comparing the decay modes at three incident energies, i.e. we have calculated and compared the (i) mass, charge, and angular momentum distribution of the cross section for light particles and intermediate mass fragments, (ii) angular momentum distribution of the reaction cross section, (iii) probability of compound nucleus and evaporation processes in the reaction, (iv) mass variation of the kinetic energy, velocity, penetration path length and time for the penetration process, and (v) average time for the process of emission of light particles, intermediate mass fragments and fission fragments. The reaction mechanism has been analyzed from the study of the variation of the reaction cross section with angular momentum.

Angular momentum as a probe for the reaction mechanism: The [formula omitted] decay at three excitation energies

The angular momentum effects on the reaction mechanism in the decay of a hot system, formed in 48Ti + 40Ca → Mo⁎88 reaction at three excitation energies, have been studied using the dynamical cluster-decay model based on the quantum mechanical fragmentation theory. Angular momentum windows have been defined for the compound and non-compound nucleus processes (like deep inelastic collisions etc.) with respect to the angular momentum variation of the fission barriers of the incoming channel. First, the angular momentum distributions of the summed up preformation, penetration probabilities and the cross-sections for light particles, intermediate mass fragments and fission fragments have been calculated by considering the angular momentum up to the critical value. Then, the mass and charge distributions (with isotopic compositions) of the cross-sections have been calculated in accordance with the defined angular momentum windows. The cross-sections for fragments coming both from the compound nucleus decay and from other processes have been calculated and the total reaction cross-section is compared with the one presented in the work of Valdré and co-workers. The ratios of the observed fusion-evaporation and total fusion cross-sections to the total reaction cross-sections of (i) our calculation and (ii) presented in the work of Valdré and co-workers, are compared and found comparable. The change of the reaction mechanism has been analyzed as a function of the angular momentum variation of the cross-sections of the fission fragments. Finally, the effect of the incident energy on the compound nucleus formation and survival probabilities has been studied.

Cross section calculation of (n,p) and (n,2n) nuclear reactions on Zn, Mo and Pb isotopes with ~ 14 MeV neutrons

In this article, we are presenting the results of model calculations for (n,p) and (n,2n) reaction cross sections using the standard nuclear reaction codes TALYS-1.8 and EMPIRE-3.2 for 67,70Zn, 92,96,100Mo and 208Pb isotopes in neutron energy range 0–20 MeV. Different nuclear level density models and optical model potential available in the codes have been tested for the estimation of cross sections of desired nuclear reactions. Moreover, in this work, the contribution to the cross section from different reaction mechanisms such as compound nucleus process, pre-equilibrium emission and direct reaction is also discussed in detail. The calculated results are compared with the existing experimental data from the IAEA-EXFOR database.

Investigation of various decay mechanisms for Th*216 following the S32+W184 reaction in the range Ec.m.=118–196 MeV

Various decay possibilities of the $^{216}\mathrm{Th}^{*}$ nuclear system formed via interaction of a $^{32}\mathrm{S}$ projectile on a $^{184}\mathrm{W}$ target are investigated within the collective clusterization approach of the dynamical cluster-decay model (DCM). The study is carried out at center-of-mass energies spread across the Coulomb barrier ($118.8\ensuremath{\le}{E}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\le}195.9\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$) by including the quadrupole deformations (${\ensuremath{\beta}}_{2}$ static) and optimum orientations (${\ensuremath{\theta}}_{i}^{\mathrm{opt}.}$) of the decay fragments. According to experimental observation, the noncompound nucleus (nCN) component competes with the compound nucleus (CN) processes [evaporation residue (ER) and fusion-fission (ff)]. The anomalous behavior of calculated fission anisotropies ($A$) for the $^{216}\mathrm{Th}^{*}$ nucleus indicates the presence of nCN contributions, such as quasifission (QF) and fast fission (FF). With an aim to have comprehensive analysis of CN and nCN fission mechanisms (ff, QF, FF), the role of center-of-mass energy (${E}_{\mathrm{c}.\mathrm{m}.}$) and angular momentum ($\ensuremath{\ell}$) is explored in terms of various observables of DCM such as fragmentation potential, preformation probability, scattering potential, and penetrability. The fragmentation potential of the $^{216}\mathrm{Th}^{*}$ nucleus shows asymmetric fission mass distribution, independent of ${E}_{\mathrm{c}.\mathrm{m}.}$ and $\ensuremath{\ell}$ values. The capture excitation functions ${\ensuremath{\sigma}}_{\text{Cap.}}$ are obtained by adding the DCM-calculated CN (${\ensuremath{\sigma}}_{\mathrm{CN}}={\ensuremath{\sigma}}_{\mathrm{ER}}+{\ensuremath{\sigma}}_{\mathrm{ff}}$) and nCN (${\ensuremath{\sigma}}_{\mathrm{nCN}}={\ensuremath{\sigma}}_{\mathrm{QF}}+{\ensuremath{\sigma}}_{\mathrm{FF}}$) contributions. The calculated cross sections find nice agreement with the experimental data, and the evaporation residue contribution is predicted to be negligibly small. The compound nucleus fusion/formation probability ${P}_{\mathrm{CN}}$ is estimated as a function of ${E}_{\mathrm{c}.\mathrm{m}.}$, which in turn suggests that the maximum contribution from the CN channel is $\ensuremath{\approx}66%$. Finally, the effect of ${\ensuremath{\beta}}_{2}$-dynamic deformations on the various decay mechanisms of the $^{216}\mathrm{Th}^{*}$ nucleus is explored at highest center-of-mass energy (195.9 MeV), where nCN processes start competing with the CN decay mechanism.

Semiclassical and quantum mechanical analysis of α -particle-induced reactions on praseodymium: A study relevant to precompound emission

Background: The study of precompound emission has attracted considerable attention for testing nuclear models in light-ion-induced reactions at relatively higher energies above 10 MeV/nucleon.Purpose: Aiming to study the precompound emission and to develop systematics at low energies below 10 MeV/nucleon, where the compound emission process is likely to dominate, the excitation functions of the reaction residues produced in the interaction of $\ensuremath{\alpha}$ particles with $^{141}\mathrm{Pr}$ have been measured in the energy range $\ensuremath{\approx}14$--40 MeV. Further, the measured data have been analyzed within the framework of both the semiclassical and quantum mechanical models.Methods: The off-line $\ensuremath{\gamma}$-ray spectroscopy based stacked foil activation technique has been used to measure the excitation functions.Results: The experimentally measured excitation functions have been compared with the theoretical predictions based on both the semiclassical model codes, viz., pace4, talys-1.9, act, and alice91, and the quantum mechanical model code exifon. The analysis of the data shows that the experimental excitation functions could be reproduced only when the contribution of precompound emission, simulated theoretically, is taken into account. Further, the precompound fraction, which gives the relative importance of precompound emission over compound nucleus emission, has been deduced and is found to be energy dependent.Conclusions: Analysis of data indicates that in $\ensuremath{\alpha}$-induced reactions, the precompound emission plays an important role, even at the low incident energies, where the pure compound nucleus process is likely to dominate. The precompound fraction is found to strongly depend on the mass of the target nucleus and the excitation energy per surface nucleon of the composite system.

Analysis of experimental cross-section for ($\alpha$α, n) reactions in odd A and odd Z heavy nuclei: A systematics on pre-compound emission

Aiming to develop a systematics in the pre-compound emission process and to get its driving parameters, a sensitive analysis of the measured excitation functions for ($\alpha$, n) reaction channel on target nuclei viz., 139La, 159Tb, 181Ta, 197Au and 203Tl has been performed with codes PACE4 and ALICE at low projectile energies, where the compound nucleus process is dominant. The code PACE4 considers only compound nucleus emission, while the ALICE code takes into account both compound and pre-compound emissions. The observed enhancement in experimental excitation functions in the tail portion of energies as compared to calculations performed with code PACE4 may be attributed to the contribution from pre-compound emission. Further, the calculations performed with the ALICE code confirm the significant contribution of the pre-compound emission. The effect of various pre-compound parameters on measured excitation functions has also been studied. The energy dependent yield of the pre-compound contribution over the compound nucleus emission for neutron emission channels is deduced in terms of pre-compound fraction “FPCN” which gives a good systematics on such process. The developed systematics in $\alpha$-induced reactions on target nuclei reflects that the pre-compound process is governed by the excitation energy available with the nucleons at the surface of the composite systems. Furthermore, the mass number of the target nuclei may also play an important role in the pre-compound process at low projectile energies.

Dynamics of 47V* formed in 20Ne + 27Al reaction in view of fusion-fission and DIC mechanism

The decay mechanism of 47V* formed in direct kinematics (20Ne + 27Al is investigated within the collective clusterization approach of dynamical cluster decay model (DCM). All calculations are done for quadrupole (β 2i -deformed) choice of fragments by taking optimum orientations over a wide range of center of mass energies (E c. m. ∼ 83–125 MeV). According to the experimental evidence, there is a strong competition between fusion fission (FF) and deep inelastic collision (DIC) in the decay of 47V*, which are recognized as compound nucleus process and non-compound nucleus process, respectively. The decay cross sections of 47V* for both FF and DIC decay modes are addressed using DCM, and are found to be in agreement with the experimental data. It is important to mention that emitting fragments in both these decay channels maintain their homogeneity in terms of charge number, that lies in the region 3 ≤ Z ≤ 9. Hence, all possible isotopes contributing towards 3 ≤ Z ≤ 9 are taken into consideration here. Calculations of both FF and DIC are segregated on the basis of angular momentum windows, where 0 ≤ l ≤ l cr has been taken for FF and l cr < l ≤ l gr for DIC, as the later operates only due to the partial waves near grazing angular momentum. In DIC, preformation probability (P 0) is divided equally amongst the most favoured outgoing fragments. Moreover, the behavior of fragmentation potential, preformation probability, penetrability and emission time etc. is examined, in order to identify the most favorable isotopes contributing towards FF and DIC.

Pre-compound emission in low-energy heavy-ion interactions

Recent experimental studies have shown the presence of pre-compound emission component in heavy ion reactions at low projectile energy ranging from 4 to 7 MeV/nucleons. In earlier measurements strength of the pre-compound component has been estimated from the difference in forward-backward distributions of emitted particles. Present measurement is a part of an ongoing program on the study of reaction dynamics of heavy ion interactions at low energies aimed at investigating the effect of momentum transfer in compound, precompound, complete and incomplete fusion processes in heavy ion reactions. In the present work on the basis of momentum transfer the measurement of the recoil range distributions of heavy residues has been used to decipher the components of compound and pre-compound emission processes in the fusion of 16 O projectile with 159 Tb and 169 Tm targets. The analysis of recoil range distribution measurements show two distinct linear momentum transfer components corresponding to pre-compound and compound nucleus processes are involved. In order to obtain the mean input angular momentum associated with compound and pre-compound emission processes, an online measurement of the spin distributions of the residues has been performed. The analysis of spin distribution indicate that the mean input angular momentum associated with pre-compound products is found to be relatively lower than that associated with compound nucleus process. The pre-compound components obtained from the present analysis are consistent with those obtained from the analysis of excitation functions.

Precompound emission in low-energy heavy-ion interactions from recoil range and spin distributions of heavy residues: A new experimental method

Recent investigations of heavy-ion reactions at low incident energies have indicated the presence of precompound emission component in considerable strength. In most cases the strength of the precompound component is estimated from the difference in forward-backward distributions of emitted light fast particles and also from the analysis of the measured excitation functions. This paper reports a new method of deciphering the relative contributions of compound and precompound components associated with fusion of $^{16}\mathrm{O}$ with $^{159}\mathrm{Tb},^{169}\mathrm{Tm}$, and $^{181}\mathrm{Ta}$ targets by measuring the recoil ranges of heavy residues in an absorbing medium along with the online measurement of the spin distributions in reaction residues produced in the fusion $^{16}\mathrm{O}$ beam with $^{159}\mathrm{Tb}$ and $^{169}\mathrm{Tm}$ targets. Analysis of recoil range and spin distributions of the residues shows two distinct linear momentum-transfer components corresponding to precompound and compound nucleus processes. The input angular momentum associated with precompound products is found to be relatively lower than that associated with compound nucleus process. The precompound components obtained from the present analysis are consistent with those obtained from the analysis of excitation functions.

Competition between the compound and the pre-compound emission processes in α-induced reactions at near astrophysical energy to well above it

The study of pre-compound emission in α-induced reactions, particularly at the low incident energies, is of considerable interest as the pre-compound emission is more likely to occur at higher energies. With a view to study the competition between the compound and the pre-compound emission processes in α-induced reactions at different energies and with different targets, a systematics for neutron emission channels in targets 51V, 55Mn, 93Nb, 121, 123Sb and 141Pr at energy ranging from astrophysical interest to well above it, has been developed.The off-line γ-ray-spectrometry based activation technique has been adopted to measure the excitation functions. The experimental excitation functions have been analysed within the framework of the compound nucleus mechanism based on the Weisskopf-Ewing model and the pre-compound emission calculations based on the geometry dependent hybrid model. The analysis of the data shows that experimental excitation functions could be reproduced only when the pre-compound emission, simulated theoretically, is taken into account.The strength of pre-compound emission process for each system has been obtained by deducing the pre-compound fraction. Analysis of data indicates that in α-induced reactions, the pre-compound emission process plays an important role, particularly at the low incident energies, where the pure compound nucleus process is likely to dominate.

Dynamical cluster decay model applied to very light mass compound systems of mass A~30 formed in heavy ion reactions

The study of the decay of 32S* and 31P* compound systems formed in 20Ne+12C and 19F+12C reactions, respectively, is further extended on the basis of collective clusterization process within the dynamical cluster model (DCM) of Gupta and collaborators, with the effects of deformations and orientations included, at an excitation energy E*CN=60 MeV. In the present study, we have investigated the effects of deformations and orientations on the target, i.e., 12C like yield, denoted C-yield (σC), which contains fusion-fission (FF) decay cross-section, σFF, from compound nucleus process and deep inelastic orbiting (DIO) cross-section, σD1O, from non-compound nucleus process. As observed in one of our earlier study for 32S* system there is a competition between FF and DIO, while, for 31P* there is a contribution of FF cross-section only, in the total C-yield. The comparative analysis of C-Yield for the considerations of spherical and oriented nuclei, shows similar results with the only difference of the values of neck length parameter (ΔR), which are more for the later case. The calculated cross-sections ac show good agreement with experimental data for both the considerations.

The dynamical cluster-decay model of preformed clusters for a hot and rotating 116Ba* nucleus produced in the low-energy 58Ni + 58Ni reaction

The dynamical cluster-decay model (DCM) is extended to a positive Q-value (Qout), heavy compound system 116Ba*, with complete angular momentum and charge dispersion effects included in it. The contributions due to both the light particles (LPs) and intermediate mass fragments (IMFs) are considered to give the total cross section. Interestingly, instead of the complete IMF spectrum observed for lighter systems such as 48Cr* and 56Ni*, here two small ‘windows of IMFs’ are predicted, one for light masses (2 ⩽ Z ⩽ 9) and another for the heavy mass end of symmetric and nearly symmetric fragments (14 ⩽ Z ⩽ 28), in agreement with the available data for the light mass ‘IMF window’ and its indications of possible extension to the heavier mass fragments. Within a non-statistical model description, the definition of phase space is found to be contained in the DCM definition of the ‘IMF window’ for the compound nucleus process. As in experiments, the calculated excitation functions are shown to put a limit on the minimum incident centre-of-mass energy required for the production of IMFs, and it will be of further interest to observe in experiments the predicted structures in the excitation functions of both the individual fragments, like for 12C decay, and the summed-up cross sections. Also, further measurements of the total kinetic energies of the fragments are called for.

Unified formalism to study nonstatistical effects in radiative capture reactions.

Based upon a consistent description of the wave functions of the captured state and the final state, a unified formalism has been established to investigate the nonstatistical effects in radiative nucleon capture reactions at energies ranging from 0.1 to 20 MeV. This model includes the direct-semidirect capture and radiative capture in the compound elastic and inelastic channels. By applying this model theory and including also the statistical contributions of the compound-nucleus process, the radiative neutron capture cross sections in $^{27}\mathrm{Al}$, $^{55}\mathrm{Mn}$, $^{89}\mathrm{Y}$, and $^{208}\mathrm{Pb}$ have been calculated and the results are compared with the measured data. We have also investigated the relative importance of the operation for each nonstatistical mechanism in the total capture cross sections.

Higher moments of the fluctuatingS-matrix within the stochastic model for compound-nucleus scattering

We present expressions for the energy-averages of the most general products of fluctuatingS-matrix elements required to calculate the variance in the energy-averaged cross-section and related observables for compound-nucleus processes. The results, which areexact and hold from the regime of isolated resonances through to that of strongly-overlapping resonances (independently of the number of open channels), involve no more than straightforward three-dimensional integrals. In line with earlier general arguments, they are functions only of averageS-matrix elements. Explicit (asymptotic) expansions which approximate these results in the domain of strongly-overlapping resonances are also determined and the leading order corrections to Ericson's treatment of fluctuations deduced. Contrary to previous studies, we find that the fluctuatingS-matrix is not necessarily Gaussian distributed in this regime. In addition, we demonstrate how unitarity can be used to check our results both numerically and analytically. Other technical issues addressed include the casting of the generating function used into an “optimal” form, the treatment of complications due to its non-trivial dependence on the source matrix, and identities for the extraction of the maximal order term. These lay a foundation for other applications of the stochastic model for compound-nucleus processes.

The categorical space of fission

The dualistic view of fission and evaporation as two distinct compound nucleus processes is substituted with a unified view in which fission, complex fragment emission and light particle evaporation are seen as part of a single process. The underlying connection between these decay modes is the mass asymmetry coordinate and the ridge line as the locus of the associated conditional barriers. The theoretical generalization is carried out explicitly. Complex fragment production at all mass asymmetries, throughout the periodic table, from low to intermediate bombarding energies is discussed in the light of compound nucleus decay.

Some remarks on the neutron elastic—And inelastic—Scattering cross sections of palladium

The cross sections for the elastic-scattering of 5.9, 7.1 and 8 MeV neutrons from elemental Pd were measured at 40 scattering angles distributed between ≈15 and 160°. The inelastic-scattering cross sections for the excitation of Pd levels at energies of 260–560 keV were measured with high resolution at the same energies, and at a scattering angle of 80°. The experimental results were combined with lower-energy values previously obtained by this group to provide a comprehensive data base extending from near the inelastic-scattering threshold to 8 MeV. That data base was interpreted in terms of a coupled-channels model, including the inelastic excitation of one- and two-phonon vibrational levels of the even isotopes of Pd. It was concluded that the Pd inelastic-scattering cross sections, at the low energies of interest in assessment of fast-fission-reactor performance are large (≈50% greater than given in widely-used evaluated fission-product data files). They primarily involve compound-nucleus processes, with only a small direct-reaction component attributable to the excitation of the one-phonon 2 + vibrational levels of the even isotopes of Pd.

Multistep processes in nuclear reactions

Abstract The theories of nuclear reactions are reviewed with particular attention to the recent work on multistep processes. The evidence for compound nucleus and direct interaction reactions is described together with the results of comparisons between theories and experimental data. These theories have now proved inadequate, and there is evidence for multistep processes that take place after the initial direct stage but long before the attainment of the statistical equilibrium characteristic of compound nucleus processes. The theories of these reactions are described and it is shown how they can account for the experimental data and thus give a comprehensive understanding of nuclear reactions.

E1-E2interference in(γ159,n) and(γ209,n) reactions

Angular distributions of fast neutrons from the (\ensuremath{\gamma},n) reactions on $^{159}\mathrm{Tb}$ and $^{209}\mathrm{Bi}$ were measured. Gamma sources in the 7--11.4 MeV range were obtained from (n,\ensuremath{\gamma}) reactions using thermal neu- trons. Pronounced asymmetries around 90\ifmmode^\circ\else\textdegree\fi{} were observed for the angular distributions of photoneu- trons leading to the ground and a few excited states, in both the spherical $^{209}\mathrm{Bi}$ and the deformed $^{159}\mathrm{Tb}$ nuclei. These asymmetries indicate strong and similar E1-E2 interference effects in the two nuclei. The direct-semidirect model was modified to be used for target nuclei with one proton outside an even-even core. From a detailed comparison of the data with calculations using the modified direct-semidirect model, the contributions of different partial waves are estimated. Contributions of the compound nucleus process are included, and are shown to affect to some extent the calculated angular distribution's energy dependence.