Projectile Nuclei Research Articles

Hurst Exponent and Event-by-Event Fluctuations in Relativistic Nucleus–Nucleus Collisions

A joint study of multi-particle pseudo-rapidity correlations and event-by-event fluctuations in the distributions of secondary particles and fragments of the target nucleus and the projectile nucleus was carried out in order to search for correlated clusters of secondary particles. An analysis of the collisions of the sulfur nucleus with photoemulsion nuclei at an energy of 200 A·GeV is presented based on experimental data obtained at the SPS at CERN. The analysis of multi-particle correlations was performed using the Hurst method. A detailed analysis of each individual event showed that in events of complete destruction of a projectile nucleus with a high multiplicity of secondary particles, long-distance multi-particle pseudo-rapidity correlations are observed. The distribution of average pseudo-rapidity in such events differs significantly from others, as it is much narrower, and its average value is noticeably shifted towards lower values <η>.

Theory of Majorana-Type Heavy Ion Double Charge Exchange Reactions by Pion–Nucleon Isotensor Interactions

The theory of heavy ion double charge exchange (DCE) reactions proceeding by effective rank-2 isotensor interactions is presented. Virtual pion–nucleon charge exchange interactions are investigated as the source for induced isotensor interactions, giving rise to the Majorana DCE (MDCE) reaction mechanism. MDCE is of a generic character, proceeding through pairs of complementary (π±,π∓) reactions in the projectile and target nucleus. The dynamics of the elementary processes is discussed, where the excitation of pion–nucleon resonances are of central importance. Investigations of initial and final state ion–ion interactions show that these effects are acting as vertex renormalizations. In closure approximation, well justified by the finite pion mass, the second-order transition matrix elements reduce to pion potentials and effective two-body isotensor DCE interactions, giving rise also to two-body correlations in either of the participating nuclei. Connections to neutrinoless Majorana double beta decay (MDBD) are elucidated at various levels of the dynamics, from the underlying fundamental electro-weak and QCD scales to the physical scales of nuclear MDBD and MDCE physics. It is pointed out that heavy ion MDCE reactions may also proceed by competing electro-weak charge exchange processes, leading to lepton MDCE by electrons, positrons, and neutrinos.

Exploring the role of softness on the fusion dynamics of 58,64Ni+92,100Mo reactions

The structure of target and projectile nuclei can significantly affect the reaction dynamics at low energies. In the present work, the fusion mechanism of 58,64Ni+92,100Mo reactions involving the Mo isotopes exhibiting peculiar soft nature is explored within the relativistic mean-field (RMF) formalism. The cross-section for the considered reactions is obtained using the ℓ-summed Wong model furnished with nuclear interaction potential calculated within the self-consistent RMF formalism. The calculations are done for the two sets of RMF parameters, namely, NL3∗ and NL1, which give different values for various characteristics of nuclear matter at the saturation. A lower fusion barrier and consequently, a higher cross-section is obtained for the parameter set with comparatively softer equation of state (EoS). On comparing the theoretical cross-section with the available experimental data, an underestimation of fusion cross-section with respect to the experimental data at the sub-barrier energies is noted for the NL3∗ parametrizations. The match improves for the NL1 set having soft EoS with slight underestimation of data noted for all the considered reactions. These observations infer that the incomprehensible softness of Mo-isotopes also persists in their fusion dynamics, and the nuclear potential obtained within the RMF formalism is observed to underestimate the fusion probability for the reactions involving Mo-isotopes. The compressible nature of Mo-isotopes is inferred to enhance the fusion cross-section, and nuclear potential obtained for parameter set with soft EoS is observed to be more suitable for the description of their fusion dynamics.

Theoretical estimation of synthesizing superheavy nuclei using neutron rich targets

The next double magic nucleus after the double magic nucleus lead (208Pb) proton number Z=82 and neutron number N=126 is predicted to be flerovium 298Fl, Z=114 and N=184, and “Island of Stability” around this nucleus is predicted in the nuclear chart. In the synthesis of new elements, it was assumed that the projectile and target nuclei used in the experiments would be stable nuclei. In particular, it was experimentally impossible to use unstable nuclei as target nuclei. Therefore, it was considered difficult to synthesize nuclei on Island of Stability because of the insufficient number of neutrons when it came to fusion between stable nuclei. To approaching Island of Stability, it is necessary to use unstable nuclei with an excess of neutrons. However, until now there has been no method to achieve this. Recently, a new method of colliding unstable nuclei has been planned. It has also been reported that neutron-rich nuclei in the superheavy mass region have lower neutron binding energy than stable nuclei and lower temperature due to neutron emission more quickly, resulting in a high survival probability even at medium and high excitation energies. The goal of this study is to create and analyze neutron emission and mass distribution of fission fragments in the superheavy mass region using the statistical and the dynamical model. In addition, we present the results of calculations using neutron-rich nuclei.

Quantum-mechanical four-body versus semi-classical three-body theories for double charge exchange in collisions of fast alpha particles with helium targets

AbstractWithin the two-channel distorted wave second-order perturbative theoretical formalism, we study capture of both electrons from helium-like targets by heavy nuclei as projectiles at intermediate and high impact energies. The emphasis is on the four-body single-double scattering (SDS-4B) method and the three-body continuum distorted wave impact parameter method (CDW-3B-IPM). The SDS-4B method deals with the full quantum-mechanical correlative dynamics of all the four interactively participating particles (two electrons, two nuclei). The CDW-3B-IPM is a semi-classical three-body independent particle model (one electron, two nuclei), using a combinatorial calculus to describe double capture by a product of two uncorrelated probabilities, integrated over impact parameters. Both theories share a common feature in having altogether two electronic full Coulomb continuum wave functions. One such function is centered on the projectile nucleus in the entrance channel, whereas the other is centered on the target nucleus in the exit channel. These two methods satisfy the correct initial and final Coulomb boundary conditions in the asymptotic region of scattering, at infinitely large inter-particle separations. Yet, it is presently demonstrated that most of the available experimental data on total cross sections for the double capture from helium by alpha particles distinctly favor the SDS-4B method. This is especially true at intermediate energies. Such energies are critically important in versatile applications under the general umbrella of ion transport in matter, including thermonuclear fusion (plasma physics) and ion therapy (medicine).

Evaporation residue cross-section measurements for 30Si+142Ce system

Evaporation residue (ER) cross-sections were measured for 30Si+142Ce reaction at laboratory energies in the range of 105 - 132 MeV using the HYbrid Recoil mass Analyzer (HYRA) at IUAC, New Delhi. The transmission efficiency of the HYRA was estimated using the calibration reaction 28Si+142Ce. Sub-barrier fusion enhancement was observed when compared with the one-dimensional barrier penetration model predictions for the present system. To explore the phenomena responsible for sub-barrier fusion enhancement, coupled-channels calculations were performed using the CCFULL code. The effect of couplings and the role of positive Q-value neutron transfer (PQNT) channels on sub-barrier fusion cross-sections were investigated. Coupled-channels calculations were able to reproduce the data by including the coupling in both projectile and target nucleus along with two neutron-transfer channels having positive Q-value. The measured ER cross-sections were compared with the nearby systems to explore the role of deformation of the colliding nuclei.

Signatures of elongated and compact configurations in the fusion barrier distribution of deformed nuclei

The fusion barrier distributions (BD) of 11 fusion reactions are investigated to understand the role of orientation as a degree of freedom in the fusion mechanism involving deformed nuclei, and seeking signatures of cold and hot fusion. We compared the experimentally extracted BD with those calculated using the coupled-channel method, starting from orientation-dependent folding potentials based on M3Y-Reid nucleon–nucleon interaction, with coupling to the anticipated vibrational and rotational excitations in projectile and target nuclei. We found that the signature of the hot fusion process within the compact configuration of the participating deformed nuclei is always evident in the extracted fusion barrier distribution. The different peaks appearing in the extracted BD can be individually assigned to the elongated-cold or compact-hot fusion process. The imprint of the compact-hot fusion may also manifest itself as a little increase in the value of the BD at certain related energy, compared with the preceding and succeeding values.

Isospin-dependence of the charge-changing cross-section shaped by the charged-particle evaporation process

We present the charge-changing cross sections (CCCS) of 11−15C, 13−17N, and 15,17−18O at around 300 MeV/nucleon on a carbon target, which extends to p-shell isotopes with N<Z for the first time. The Glauber model, which considers only the proton distribution of projectile nuclei, underestimates the cross sections by more than 10%. We show that this discrepancy can be resolved by considering the contribution from the charged-particle evaporation process (CPEP) following projectile neutron removal. Using nucleon densities from the deformed relativistic Hartree-Bogoliubov theory in continuum, we investigate the isospin-dependent CPEP contribution to the CCCS for a wide range of neutron-to-proton separation energy asymmetry. Our calculations, which include the CPEP contribution, agree well with existing systematic data and reveal an “evaporation peak” at the isospin symmetric region where the neutron-to-proton separation energy is close to zero. These results suggest that analysis beyond the Glauber model is crucial for accurately determining nuclear charge radii from CCCSs.

A multi–channel study of the 20Ne + 130Te system within the NUMEN project

The NUMEN project aims to measure specific reaction cross sections to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double beta decay (0νββ). In particular, it was proposed to use heavy – ion induced double charge exchange reactions as tools towards the determination of information on the nuclear matrix elements of 0νββ, strongly motivated by a number of similarities between the two processes. To this extent, the 20Ne + 130Te system was experimentally investigated in a multi-channel approach by measuring the complete net of reactions channels, namely double charge exchange, single charge exchange, elastic and inelastic scattering, one – and two – nucleon transfer reactions, characterized by the same initial projectile and target nuclei. The goal of the study is to fully characterize the properties of the nuclear wavefunctions entering in the 0νββ decay nuclear matrix elements. The experimental setup, the data reduction and some of the obtained results for the 20Ne + 130Te system will be presented and discussed.

Investigations on Coulomb fission time scales and cross sections in inverse kinematics

In inverse kinematics, we explored Coulomb fission cross-sections and time scales. Heavier projectiles such as 238U, 132Xe, and 208Pb on lighter targets such as 16O 26Mg, 27Al, 32S, 35Cl, 40,48Ca, 45Sc, 48,50Ti, 56,58Fe, 64Ni, 89Y, 30Si and 65Zn were looked into. The photofission cross-sections and the number of equivalent photons impinge on the target nuclei are important parameters in cross-section assessment. The anticipated cross-sections increases with increase in atomic number of target nuclei. We also explored the time scale of projectile nuclei at various transition levels. The estimated time scales accord well with the available experimental value, which is in the order of picoseconds. In addition, we predicted time scales of 165Ho nuclei in the transition state from 19/2+→15/2+ to 29/2+→25/2+ for which experimental time scales are not available in literature. As a result, Coulomb fission is one of the causes that has severely hampered in the formation of compound nuclei. Prediction of time scales, in particular, would aid in understanding the structure of various energy levels.

The Effect of the Proton and Neutron as Probe for the Nuclear Fusion Reactions at Near-Barrier Energies

In this study, quantum mechanical calculations and a semi-classical approach were used to determine fusion the probability (Pfus), fusion barrier distribution (Dfus), and fusion cross section (σfus) for the systems 28Si + 90Zr, 28Si + 92Zr, 28Si + 94Zr, 41K + 28Si, and 45K + 28Si. The semiclassical approach involved the use of the WKB approximation to describe the relative motion between the projectile and target nuclei, and the Continuum Discretized Coupled Channel (CDCC) method of Alder-Winther (AW) to describe the intrinsic motion of the nuclei. The importance of the neutron and the proton transfer and exchange on the calculations of Pfus, Dfus, and σfus for the studied systems. The results showed that the consideration of the coupling-channel calculations for quantum mechanics and a semi-classical approach, are very important to be considered specifically around and below the Coulomb barrier. The results were compared with the measured data and found in reasonable agreement.

Number of virtual photons in the Coulomb dipole excitation

In this study, the number of virtual photons obtained through general, relativistic, nonrelativistic, and intermediate methods was investigated, which is an important factor in obtaining the Coulomb dipole strength distribution. The number of virtual photons was studied according to the incident energy ${E}_{\text{lab}}$ using five methods. The general method, which has two different forms (integral and differential), is valid for all energy regions, whereas the relativistic method is effective for regions with high $\ensuremath{\beta}$ values. In addition, the validity of the nonrelativistic approximation was tested by comparing it with the general method in the low-incident-energy region, and the intermediate method was shown to be not effective in the high-excitation-energy region. Further, an investigation was conducted on the dependence of the number of virtual photons on the charges of the projectile and target nuclei. Using the same $R$ value, target nuclei, and incident energy, it was found that the number of virtual photons does not depend on the charge number of the projectile in the relativistic method. With the same $R$ value, projectile, and incident energy, in contrast it can be seen that the number of virtual photon depends on the square of the charge number of target nuclei.

Correlation between the nuclear structure and reaction dynamics of Ar-isotopes as projectile using the relativistic mean-field approach

This theoretical study is devoted to bridging the gap between the nuclear structure and reaction dynamics and unravelling their impact on each other, considering the neutron-rich light mass 30−60Ar isotopes. Using the relativistic mean-field with the NL3⁎ parameter set, several bulk properties such as binding energies, charge radii, quadrupole deformation parameter, two neutron separation energy, and differential two neutron separation energy with the shell closure parameter are probed for the mentioned isotopic chain. For validation, the RMF (NL3⁎) results are compared with those obtained from the finite range droplet model (FRDM), Weizsäcker-Skyrme model with WS3, WS⁎ parameters, and the available experimental data. Most of the participating isotopes are found to be prolate in structure, and neutron shell closures are conspicuously revealed at N=14,20,40 but weakly shown at N=24,28,34. From our analysis, a central depletion in the nucleonic density is identified in 32 Ar and 42−58 Ar, indicating that they are possible candidates for a semi-bubble-like structure. Interestingly, these results are consistent with recent theoretical and experimentally measured data. Furthermore, using the Glauber model, the reaction cross-sections are determined by taking 26−48Ar as projectiles and stable targets such as 12C, 16O, 40Ca, 90Zr, 124,132Sn, 208Pb and 304120. Although there is no experimental evidence for the stability of 304120, it was predicted by Bhuyan and Patra (2012) [115] as a stable nucleus. A relatively higher cross-section value is noticed between 30 Ar and 32 Ar, which infers that 32Ar is the most stable isotope among the considered chain. Moreover, we noticed that the profile of the differential cross-sections and scattering angle are highly influenced by the mass of the target nuclei and the magnitude of the incident energy of the projectile nucleus.

Velocity distributions of forward moving fragments in heavy-ion collisions at Fermi energies

Heavy-ion-induced projectile fragmentation reactions at Fermi energies are of interest to investigate the properties of nuclei far from the valley of stability, nuclear potentials, to get knew knowledge about nuclear equation of state. Isotopes far from stability line can be useful for various applications. It is therefore of interest to predict relative yields of isotopes and their energies with high precision. Here we treat such reactions in a microscopic approach, which consists of several steps: initialization of ground states of the colliding nuclei, dynamical evolution until the freeze-out point where the primary fragments can be identified, calculation of the excitation energy of the primary fragments, and their de-excitation. For the dynamical evolution we use a Boltzmann–Vlasov type transport equation, and for the de-excitation a statistical multi-fragmentation description. We apply this approach to collisions of projectile nuclei 40Ar on target 9Be at energy 36.5 A MeV, obtain isotope distributions and velocity spectra of the produced isotopes and compare the results of our calculations to experimental data obtained at COMBAS set-up in JINR.

Isospin compositions of correlated sources in the Fermi energy domain

Isotopic yield distributions of nuclei produced in peripheral collisions of $^{80}$Kr+$^{40,48}$Ca at 35 MeV/nucleon are studied. Experimental results obtained by the FAZIA Collaboration at the LNS facility in Catania are compared with calculations performed with the statistical multifragmentation model (SMM). The fragments with atomic number $Z=19-24$ observed at forward angles are successfully described with the ensemble method previously established for reactions at higher energy. Using the SMM results, the isotopic compositions of the projectile residues are reconstructed. The results indicate a significant isospin exchange between the projectile and target nuclei, not far from isospin equilibrium, during the initial phase of the reaction. The two groups of light fragments with $Z=1-4$, experimentally distinguished by their velocities relative to coincident heavy projectile fragments, are found to originate from different sources. The isotopic composition of the slower group is consistent with emission from a low-density neck, enriched in neutrons, and satisfactorily reproduced with SMM calculations for a corresponding neck source of small mass.

Effect of deformation dependence and mirror nucleus corrections energy on multinucleon transfer reaction cross sections

Multinucleon transfer reactions are currently a powerful way to synthesize neutron-rich nuclei. To explore the effect of nucleus deformation and mirror nucleus shell correction energy in the nucleus mass model on the calculation of multinucleon transfer reaction cross sections in the dinuclear system (DNS) model, three macroscopic microscopic mass models are selected and the transfer reaction cross sections are calculated for 136Xe+208Pb and 64Ni+238U by improved DNS model+GEMINI++, respectively. The mirror nucleus shell correction energy does not improve the accuracy of the cross section of the transfer reaction. The introduction of a different dependence of the Coulomb and surface energy on the deformation can improve the calculation of the transfer reaction cross section when the projectile and target nuclei are deformed nuclei.

Effect of entrance channel parameters on compound nucleus formation probability in heavy ion fusion reactions

To study the role of entrance channel parameters on compound nucleus formation probability (Pcn), we have picked up 92 heavy ion fusion reactions forming superheavy nuclei and classified them into four categories based on deformation parameters of projectile and target nuclei such as spherical-spherical, spherical-deformed, deformed-spherical, and deformed-deformed. Next, we have examined the role of entrance channel parameters on Pcn for each category and found that the mean fissility parameter plays the strongest role for all the categories. Finally, the effect of the projectile energy in the centre of mass frame has been taken into account to construct four empirical formulae for the four categories. We believe the proposed empirical formulae can be very useful in the planning of experiments in synthesizing the superheavy elements.

Study of Fusion Reactions of some Light projectiles on Medium Targets

Background and objectives: The investigation of heavy-ion (HI) induced fusion processes in order to comprehend the many mechanisms involved in these reactions has long been a focus of nuclear physics. The complicated structure and behavior of projectile and target nuclei with various projectile energy allows us to define the reaction process and may aid in the investigation of the potential of creating superheavy elements (SHE) in the laboratory. Methods: The semiclassical and full quantum mechanical complete fusion cross section calculations and the distribution of the fusion barrier for the systems 12C+50Ti,15N+56Fe,16O+63Cu and 40Ar+27Al. The calculations have been carried out by using SCF code for semiclassical and CC code for quantum mechanical calculations. To account for the target and projectile relative motion, we modified these codes. The fusion barrier distribution to be calculated directly from this code by subroutines written in Fortran language and added to the main code. The coupled-channel is considered by taking two channels only due to the difficulty of solving coupled differential equations. Results: The obtained results for and the for the studied systems were compared to the related measured data and discussed. Conclusion: The semiclassical method used to describe the fusion reaction agrees very well with the quantum method and with the measured data and we can conclude that this semiclassical method can be used as alternative to quantum method to study the fusion reaction.

Fragmentation Measurements in Particle Therapy: status and plans of the FOOT experiment

Due to the advantageous characteristics of the charged particle’s energy deposition in matter, protons or ion beams are used in hadrontherapy to treat deep-seated solid tumors. Using these beams, the maximum of the dose is released to the tumor tissues at the end of the beam range. In this process, nevertheless, fragmentation of both projectile and target nuclei can occur in the nuclear interactions of the beam with the patient tissues and, as showed in recent studies, needs to be carefully taken into account in the delivered dose calculation. Nuclear fragmentation is also extremely relevant for space radioprotection studies, when the exposition of sensors and human crews to solar and galactic particle flows have to be minimized. The goal of the FOOT (FragmentatiOn Of Target) experiment is to estimate target and beam fragmentation performing cross section measurements (with respect to the kinetic energy and direction) with a precision of the order of 5% in the energy range of interest for hadrontherapy (protons in the energy range of 70-230 MeV or ion beams with energy up to 400 MeV/u) and space radioprotection (ion beams with energy up to 800 MeV/u) in order to provide new data for medical physicists, radio-biologists and to improve not only the new generation of oncological Treatment Planning Systems but also the design of shielding elements for the future long duration space missions eventually with human crews. In this paper will be presented the project, the present status of the different detector sub-systems construction and the data-taking plans.

Rules of thumb for synthesizing superheavy elements

Synthesizing any elements in the eighth period using either cold or hot fusion reactions remains a big challenge to date. The quasifission mechanism restricts complete fusion to an indeterminably low evaporation residue (ER) cross-section for superheavy nuclei. The entrance channel parameters of the heavy-ion reaction, the fission barrier of the compound nucleus, the deformation parameters of the projectile and target nuclei, and the kinetic energy of the projectile are mainly responsible for governing the scale of the quasifission. The role of these factors has been examined explicitly by the experimental ER cross-sections. Thorough comparisons lead us to infer that the entrance channel criteria contribute to a much lower extent than the deformation parameters do. The effect of deformation can be categorized into four rules as validated by all the reactions used except one Uue. The null result from this reaction is explained by the improper choice of the projectile energy, as shown theoretically by means of a statistical model approach, which is valid for a system having a large nucleon number so as to intrinsically have a high density of excited states. The optimal selection of the beam energy sets another rule. Therefore, these five rules can be treated as the rules of thumb for synthesizing the superheavy elements. Application of the first four rules can enable us primarily to spot a suitable reaction, and finally, exploitation of the fifth rule chooses the most appropriate reaction at a preferable excited energy to achieve the highest ER cross-section for a superheavy element.