Projectile-target Combinations Research Articles

Possibility to synthesize $Z = 119$ superheavy nuclei with $Z>$ 20 projectiles

Abstract We employed the dinuclear system (DNS) model combined with statistical model to calculate the evaporation residue cross sections for the reaction systems $^{48}$Ca + $^{243}$Am, $^{48}$Ca + $^{248}$Cm, and $^{48}$Ca + $^{249}$Bk. The theoretical results successfully reproduced the experimental trends in the 3$n$ and 4$n$ evaporation channels of these reaction systems. In order to synthesize the new element $Z = 119$, we predicted the evaporation residue cross sections for three reaction systems ($^{54}$Cr + $^{243}$Am, $^{51}$V + $^{248}$Cm, and $^{50}$Ti + $^{249}$Bk) to select the most promising projectile-target combinations. We also noted that the maximum cross sections predicted by our model and other methods appear to be below the detection limits of current experimental facilities, given the projectile-target combinations feasible under current experimental conditions. Therefore, synthesizing superheavy nuclei with $Z = 119$ will require improvements in beam intensity, detection techniques, and effective separation methods.

Coulomb interaction dependence of optimal energy to synthesize superheavy elements

The production of superheavy elements beyond Z = 118 remains unattained through both cold and hot fusion techniques, primarily due to inadequate fusion reaction optimization involving projectile–target combinations and energy. Past efforts employed various theories to optimize these combinations. In our current study, we have successfully identified optimal fusion energies for synthesizing superheavy elements, employing an advance statistical model and dinuclear system models. The establishment of optimal energy governing rule is achieved through a comprehensive examination of the Coulomb interaction parameter, enabling precise determination of the optimal energy for successful fusion reactions in synthesizing superheavy elements. The confidence level of predicting optimal energies using the present formula varies between 97% to 99%. The predicted optimal energy using the present formula for five fusion reactions such as 208Pb(50Ti,1n)257Rf, 208Pb(50Ti,2n)256Rf, 209Bi(50Ti,1n)258Db, 208Pb(58Fe,1n)265Hs, and 244Pu(48Ca,4n)288Fl were studied and are in good agreement with each other. Furthermore, we predicted the Optimal energies for fusion reactions leading to synthesize the superheavy element Z = 119 and 120. The presented empirical rule will certainly bring a revolution in the synthesis of superheavy elements.

A study on the synthesis of superheavy element Mc (Z = 115) using lead, bismuth and actinide targets

The evaporation residue cross sections in synthesizing isotopes of superheavy element Mc (Z = 115) by the hot fusion reactions 48Ca+241,243Am→289,291Mc, 45Sc+240,242,244Pu→285,287,289Mc, 50Ti+236,237Np→286,287Mc, 51V+238U→289Mc, 36S+253Es→289Mc, 46K+248Cm→294Mc, and by the cold fusion reactions 78As+208Pb→286Mc, 76Ge+209Bi→285Mc have been systematically investigated using the phenomenological model for production cross section. We have predicted the most effective projectile-target combinations for synthesizing Mc isotopes among these reactions. Our result shows that the 3n- channel cross section is larger for the reaction 48Ca+243Am→291Mc, and the 4n- channel cross section is larger for the reaction 46K+248Cm→294Mc. This study also examines the effect of the use of mass values and shell corrections by the Möller and Warsaw groups. Using our predicted combinations and the cross section values at a range of excitation energies, we hope these isotopes of Mc can be synthesized in near-future experiments.

Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions. II. Central Pb + Pb collisions

This paper represents a continuation of our investigation into the limitations on total, proton, and neutron particle number densities, as well as the asymmetry of proton and neutron density distributions achievable in central heavy-ion collisions. We explore these aspects at low and medium energies within the framework of the Boltzmann-Uhlenbeck-Uehling (pBUU) transport and time-dependent Hartree-Fock (TDHF) models. Previous studies, focusing on symmetric and asymmetric collisions of Ca and Sn nuclei [1], and initial results on Pb-nuclei collisions [2], emphasized the role of the Coulomb interaction in these events. Our findings indicated that: (i) the highest total densities predicted at Ebeam=800 MeV/nucleon were on the order of ≈2.5ρ0 (ρ0=0.16fm−3), (ii) the proton-neutron asymmetry for maximal densities, δ=(ρnmax−ρpmax)/(ρnmax+ρpmax), did not generally exceed the asymmetry in the initial state of the collision at all beam energies and tended to decrease during the reaction, and (iii) a significant portion of this asymmetry had its microscopic origin in Coulomb forces, masking the pure nuclear contribution. These new findings, particularly relevant in the astrophysical context, are further examined in this work, focusing on the heaviest target-projectile combination Pb212,208 accessible in an experiment. We introduce the SkT3 Skyrme force model, not previously used for the Pb system, and compare it to the SV-bas and SV-sym34 models to explore the symmetry-energy dependence of the results. Contour plots of nucleonic densities are presented, contrasting the time evolution of the density distributions in low (TDHF) and high (pBUU) models. We also present the evolution of normalized maximal proton, neutron, and total nucleon number density with increasing beam energy in the full pBUU model and the Vlasov approximation, aiming to explore the impact of correlations in the reaction. The time evolution of the proton and neutron density distributions in the plane transverse to the beam direction is illustrated at both low and high beam energy. In conclusion, our detailed examination of the Pb system in this work provides further essential evidence that the aforementioned findings (i)–(iii) are only weakly dependent on system size and a symmetry-energy model, and thus, they are of more general importance. Published by the American Physical Society 2024

Systematics of fusion of light nuclei

We have constructed the empirical formula for fusion barrier height (VB), fusion barrier position (RB), and inverted parabola (ħω) of light nuclei with atomic number in the range 2≤ZC≤10. This formula is obtained by studying the fusion barrier characteristics of 333 projectile target combinations. The values produced by the present formula are also compared with experiments. The present semi-empirical formula produces fusion barrier characteristics of light nuclei with the simple inputs of mass number (A) and atomic number (Z) of projectile targets. This semi-empirical formula can be utilized to calculate and interpret fusion barrier characteristics in light nuclear systems.

Analysis of fusion reactions induced by weakly bound nuclei on medium and heavy mass targets

Fusion cross section for reactions induced by weakly bound nuclei 6He, 6,7Li 9,11Be and 10B on targets lying in the mass region 64 ≤ A ≤ 238 have been investigated at around Coulomb barrier energies within the coupled channel formalism. Specifically, the effects of coupling to low-lying excited states of reactants and those arises due to the breakup of projectile have been studied by using Broglia and Winther (BW91), Aage Winther (AW95) and fitted potential (FP) parameterization schemes. Among these the FP scheme is found to be most appropriate in the description of fusion excitation functions of various projectile-target combination. Further, it is observed that in the sub barrier energy region there is an enhancement in the fusion cross section due to coupling to excited states while there occurs fusion suppression at above barrier energies because of the breakup of the projectile.

Semi-empirical parameterization of HI/p L-shell X-ray production cross section ratios in Bi for Heavy Ion PIXE

Quantitative analysis of materials from Heavy Ion PIXE spectra remains impeded by the lack of reliable X-ray production cross section (XPCS) data. Although efforts at experimental Heavy Ion induced XPCS measurements still continue, Multiple Ionisation (MI) effects, which are not fully described by theory, render simulations of heavy ion PIXE data unreliable for large Z1/Z2 collisions, especially at low energies. This is also exacerbated by the random selection of projectile-target combinations for measured and reported experimental data available to validate theory. This study explored heavy ion induced X-ray production cross section deviations from those induced by protons at the same ion velocity. This enabled evaluations of the degree to which cross sections are enhanced through MI effects, with the aim of predicting XPCS due to heavy ion impact. The evaluation was carried out through the scaling of experimental heavy ion to theoretical proton cross section ratios (R), which were then used for the interpolation of XPCS in the same target element for ‘missing’ projectiles within the range of evaluation. Here we present measurements of heavy ion induced total L-shell XPCS in Bi, carried out to determine HI/p MI induced deviations due to C, F, Cl and Ti projectiles at an ion velocity range of (0.2–1.0) MeV/nucleon.

Heavy ion fusion of spherical nuclei

We study the experimental and theoretical fusion reactions of compound nuclei synthesized using different projectile-target systems, among which at least one projectile/target nucleus is spherical. The first part of this study analyses the fusion cross sections obtained using different projectile-target combinations in the synthesis of polonium (Po), thorium (Th), and nobelium (No). In the second part of this study, we suggest the fusion reaction to synthesize the superheavy element Z = 122. We select three nuclei, polonium (Po), thorium (Th), and nobelium (No), which are synthesized using various projectile-target combinations. We also investigate fusion reactions such asZr(Pb, 2n)122 . This study may be a milestone in the synthesis of the superheavy element Z = 122.

Effect of double spin-orbit parameters of spin-orbit strength in reactions involving spherical-prolate, spherical-oblate, oblate-prolate and oblate-oblate configurations

The present work is carried out to see the role of double spin-orbit parameters (W1 and W2) on reactions having spherical-prolate, spherical-oblate, oblate-prolate and oblate-oblate configurations. For the study, semi-classical Skyrme energy density formalism is used by employing SkIx (x=2,3,4) and SAMi Skyrme forces. The calculations suggest that the presence of double spin-orbit strength imparts significant influence on spin-dependent potential (VJ) as maximum barrier height of VJ (VJB) is observed with SAMi force (W1≠W2) and minimum with SkI2 (W1=W2) i.e., VJB(SAMi)>VJB(SkI4)>VJB(SkI3)>VJB(SkI2). The maxima and minima in VJB are further related to the contribution from the isoscalar and isovector parts of the spin-orbit potential. As far as shape of projectile and(or) target is concerned, the higher VJB is obtained for oblate-prolate configuration and lower when spherical-prolate configuration is used. The chosen Skyrme forces also modify the fusion barrier height VB of different target-projectile combinations in the similar way as the spin-orbit barrier height (VJB) does. These Skyrme forces are further applied to address the experimental fusion excitation functions and fusion barrier distributions of the considered reacting partners. The contribution of VJ is also estimated in fusion cross-section of considered reactions.

Unfolding reaction mechanisms in C12 fusion with Zr below 7 MeV/nucleon

Heavy-ion reaction studies in the incident energy regime $\ensuremath{\le}$ 20 MeV/nucleon have suggested multiple signatures of preequilibrium emission during the compound nucleus formation phenomenon and the presence of incomplete fusion, both of which vary with the incident energy and projectile-target combination. However, the available reaction data are insufficient to accurately decipher these contributions as the reports have a finite dependency on the predictions from theoretical models. Therefore, sound data interpretation with robust nuclear models is fundamental to unfolding the underlying processes. We report a new study of excitation functions of residues produced from the $^{12}\mathrm{C}+\mathrm{Zr}$ reactions up to 6.3 MeV/nucleon energy. Cross sections of 16 evaporation residues were measured through off-beam $\ensuremath{\gamma}$-ray spectroscopy. Excitation functions of the evaporation residues are reported at 14 energy points and compared with the reaction model code empire-3.2.2, with variations in nuclear level density. Additionally, the overall contribution of precompound and compound nuclear processes is discussed quantitatively within the realms of empire-3.2.2 model code.

New measurement of the elemental fragmentation cross sections of 218 MeV/nucleon Si28 on a carbon target

Elemental fragmentation cross sections (EFCSs) of stable and unstable nuclides have been investigated with various projectile-target combinations at a wide range of incident energies. These data are critical to constrain and develop the theoretical reaction models and to study the propagation of galactic cosmic rays (GCR). In this work, we present a new EFCS measurement for $^{28}$Si on carbon at 218~MeV/nucleon performed at the Heavy Ion Research Facility (HIRFL-CSR) complex in Lanzhou. The impact of the target thickness has been well corrected to derive an accurate EFCS. Our present results with charge changes $\Delta Z$ = 1-6 are compared to the previous measurements and to the predictions from the models modified EPAX2, EPAX3, FRACS, ABRABLA07, NUCFRG2, and IQMD coupled with GEMINI (IQMD+GEMINI). All the models fail to describe the odd-even staggering strength in the elemental distribution, with the exception of the IQMD+GEMINI model, which can reproduce the EFCSs with an accuracy of better than 3.5\% for $\Delta Z\leq5$. The IQMD+GEMINI analysis shows that the odd-even staggering in EFCSs occurs in the sequential statistical decay stage rather than in the initial dynamical collision stage. This offers a reasonable approach to understand the underlying mechanism of fragmentation reactions.

Theoretical study of superheavy elements 294,297Og using different versions of proximity potential

Formation of superheavy nuclei 294,297Og is studied via calculation of evaporation residue cross section. We investigated the influence of nuclear potential on the evaporation residue cross section using nine versions of proximity potential as Prox77, Prox88, BW91, Bass73, Bass77, Denisov, CW76, GP77 and Guo2013. Calculations are performed for 65 projectile-target combinations with convenient half lives. It is found that the combinations 46Ca+248Cf and 48Ca+249Cf are most favorable for the synthesis of the elements 294,297Og with evaporation cross sections 1395 and 279 fb for the 3n channel in proximity potential Guo2013. The lowest value of evaporation cross section is obtained for Bass73 potential. We have also examined the agreement of the results obtained from different potentials with the experimental data for the systems 48Ca+245Cm, 48Ca+248Cm, and 48Ca+249Bk. The results obtained from potentials Guo2013, GP77 and CW76 show better agreement with the experimental results in comparison with other potentials.

Systematic analysis of the decay of Fl*287,288,290,292 formed in the complete fusion reactions Pu239,240,242,244+Ca48 including Skyrme forces

The fusion evaporation residue cross sections for the decay of the compound nuclear system $^{287,288,290,292}\mathrm{Fl}^{*}$ via $2n$- to $5n$-decay channels, synthesized in $^{239,240,242,244}\mathrm{Pu}+^{48}\mathrm{Ca}$, are studied using the dynamical cluster-decay model (DCM), including quadrupole deformations ${\ensuremath{\beta}}_{2i}$ for compact hot orientations ${\ensuremath{\theta}}_{i}$ at various excitation energies ${E}^{*}=32.5$ to 52.6 MeV. For the nucleus-nucleus interaction potentials, we have employed the Skyrme energy density functional based on the semiclassical extended Thomas-Fermi approach under frozen density approximation. Here, within the DCM, the Skyrme forces used are SLy4, ${\mathrm{SkM}}^{*}$, and, KDE0(v1). The DCM makes use of a single parameter, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ that takes different values for different processes at a given temperature and provides an excellent fit to the measured data, independently of the choice of Skyrme force used. We make predictions of probable fusion-fission and quasifission mass regions of fragments and then calculate the evaporation residue cross sections ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for experimentally unobserved neutron channels. Further, the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$ of compound nucleus (CN) fusion probability ${P}_{\mathrm{CN}}$ and survival probability ${P}_{\mathrm{surv}}$ is calculated to determine the reduced evaporation residue cross section ${\ensuremath{\sigma}}_{\mathrm{ER}}/{\ensuremath{\sigma}}_{\mathrm{fusion}}$, denoted as ${\ensuremath{\sigma}}_{\mathrm{ER}}^{\mathrm{reduced}}$, and we have seen that ${P}_{\mathrm{surv}}$ is the main dominant factor in the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$. To this end, we have analyzed the effects of mass asymmetry and isospin effect of target nucleus on the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ and have found that the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for the production of superheavy element ${\mathrm{Fl}}^{*}$ increases slowly with increasing neutron number of the target nucleus. We have also searched for all possible target-projectile combinations forming the hot compound nucleus ${\mathrm{Fl}}^{*}$ at the excitation energy ${E}^{*}$ for compact-hot configurations and have also calculated the fusion evaporation residue cross sections for the proposed new reactions synthesizing Fl.

Quasifission barriers of heavy ion fusion reaction leading to the synthesis of superheavy nuclei 104 ≤ Z ≤ 126 with actinide targets

Quasifission barriers were studied in the superheavy region [Formula: see text] using different projectile-target combinations. The different entrance channels parameters on quasifission barriers give an insight into the formation of compound nuclei and quasifission process. The quasifission barriers are more systematic for [Formula: see text]. The effect of compound nucleus fissility [Formula: see text] and effective entrance channel fissility [Formula: see text] on quasifission barriers were investigated. The quasifission barriers are strongly influenced by [Formula: see text] and [Formula: see text] entrance channel parameters. The detailed investigations of entrance channel parameters on quasifission barriers provide a thorough understanding of compound nuclei formation in the superheavy element in the region [Formula: see text]. Eventually, this study helps in the selection of projectile-target combinations to synthesis of superheavy nuclei.

Influence of entrance channel on production cross sections of exotic actinides in multinucleon transfer reactions

Within the framework of the dinuclear system model, the influence of mass asymmetry and the isospin effect on the production of exotic actinides have been investigated systematically. The isotopic yields populate in multinucleon transfer reactions of Ca(48), Kr(86), Xe(136), and U(238) bombarding on Cm(248) are analyzed and compared to the available experimental data. Systematics on the production of unknown actinides from Ac to Lr via the available stable elements on the earth (from Ar to U) as projectiles-induced reactions with $^{232}$Th, $^{238}$U and $^{248}$Cm are investigated thoroughly. Potential energy surface and total kinetic energy distribution for the reaction system are calculated and can be used to predict the production cross-section trends. It is found that the heavier projectile leads to the wider isotopic chain distribution for the same target. The heavier target-based reactions prefer to produce plenty of exotic actinides through both mechanisms of deep-inelastic and quasi-fission reactions. Isospin relaxation plays a crucial role in the colliding process, resulting in actinide isotopic distribution tends to shift to the drip lines. Massive new actinides have been predicted at the level of nanobarn to millibarn. The optimal projectile-target combinations and beam energies were proposed for the forthcoming experiments.

Theoretical study on the production of neutron-rich transuranium nuclei with radioactive beams in multinucleon transfer reactions

The production of neutron-rich transuranium nuclei with $Z=93--98$ in multinucleon transfer reactions induced by radioactive beams $^{92}\mathrm{Kr}, ^{132}\mathrm{Sn}$, and $^{144}\mathrm{Xe}$ with actinide target $^{238}\mathrm{U}$ is investigated within the dinuclear system model with decay code gemini$++$. The isotopic distributions for reactions $^{136}\mathrm{Xe}+^{248}\mathrm{Cm}$ and $^{136}\mathrm{Xe}+^{249}\mathrm{Cf}$ are calculated and compared with the available experimental data. Theoretical calculations can reproduce the experimental results well. Both the $N/Z$ ratio equilibration mechanism and driving potential dominate the transfer process of nucleons. Reaction $^{132}\mathrm{Sn}+^{238}\mathrm{U}$ is an optimal projectile-target combination to obtain large production cross sections of neutron-rich isotopes with $Z=93--98$. The corresponding optimal incident energy is also explored. The production cross sections of 41 unknown neutron-rich transuranium isotopes with cross sections greater than 1 nb are predicted. The reaction $^{132}\mathrm{Sn}+^{238}\mathrm{U}$ at ${E}_{\mathrm{c}.\mathrm{m}.}=521.3$ MeV shows huge advantages in producing neutron-rich transuranium nuclei with $Z=93--98$.

Investigation for Suitable Target-Projectile combination for Fusion from the Isotopes of Ti and Nd using Intrinsic Fusion and Fission Barriers Analysis

Background: A configuration is most suitable for the fusion if it corresponds to a minimum intrinsic fusion barrier and maximum fission barrier.Purpose: To find a suitable target-projectile combination from the isotopes of Ti and Nd by analyzing the intrinsic fusion and fission barriers theoretically by including the deformations up to hexadecapole order.Methods: The fragmentation theory has been used for the calculations. Results: The intrinsic fusion barrier is minimum and fission barrier is maximum for the targetprojectile combination: 43Ti+150Nd in belly-belly configuration, and the inclusion of deformation of higher order leads to the decrease of fission barrier for the prolate shaped cases and compactness for most of the cases.Conclusions: The most suitable target-projectile combination from the isotopes of Ti and Nd for the fusion is 43Ti+150Nd.

New experimental evidence for universal odd-even staggering in fragmentation cross sections

About 100 isotopes with $(N\ensuremath{-}Z)$ from 1--9 produced by 300 MeV/nucleon $^{78}\mathrm{Kr}$ projectiles impinging on an ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ target have been separated and identified at the RIBLL2 separator of HIRFL, where their production yields have been measured. The odd-even staggering (OES) in these experimental yields is quantitatively studied by employing a third-order difference formula. Measured data are used to validate the universality of this OES by comparing with other experimental data produced by fragmentation of different krypton projectiles on various targets as well as the OES evaluated from thousands of accurate cross sections measured in many different reactions. These comparisons between experimental data from a large variety of fragmentation reactions provide strong evidence that the OES magnitude almost does not depend on the projectile-target combinations and thus the OES is universal for different reaction systems. The OES magnitudes in these experimental data are also applied to examine the OES predicted by the abrasion-ablation model. There are large discrepancies between the OES magnitudes in predicted and measured cross sections.

Systematic study of probable target-projectile combinations for the synthesis of Z = 120 isotopes using the Skyrme energy density formalism

The synthesis of superheavy elements is an interesting field of research for both theoretical as well as experimental physicists. Till now superheavy element from Z=104 to 118 has been synthesized in various laboratories using cold and hot fusion reactions. Recent predictions of various theoretical models state that Z=120 and N=184 seems most probable doubly magic pair in the island of stability. Hence, we aim to the predict most probable target-projectile combinations of 300,302,304120 superheavy nuclei, so that relevant inputs may be imparted for future synthesis of superheavy nuclei. The target-projectile combinations are taken in reference to the minima's of the fragmentation potential calculated using the Quantum Mechanical Fragmentation Theory (QMFT). In addition, the target-projectile combinations from literature are also considered for which attempts were made for the synthesis of Z=120. The barrier height (VB) of the considered target-projectile combinations are calculated using the spherical and deformed choices of decay fragments. The percentage change in the barrier height ΔVB is explored for the hot and cold fusion approaches. The nuclear interaction potential is obtained within the Skyrme energy density formalism (SEDF) using the GSkI force parameters. For the feasible target-projectile (t-p) combinations, the capture cross-sections of these three isotopes 300,302,304120 are calculated using ℓ-summed Wong model and their comparative analysis is worked out. The probability of formation of compound nucleus (PCN) is determined using the energy dependent function. Among the thirty-six considered target-projectile combinations, the Ti-based reactions with Cf targets and also Cr-based reactions with Cm targets are identified as most suitable combinations for the synthesis of the superheavy element with Z=120. For 300120 isotope are 48Ti+252Cf, 50Ti+250Cf, 50Cr+250Cm, 52Cr+248Cm; whereas 50Ti+252Cf, 54Cr+248Cm, and 54Cr+250Cm form most probable target-projectile pair respectively, for 302120 and 304120 superheavy nuclei.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.