Breakup Fragments Research Articles

Reaction dynamics of proton drip-line nuclei at energies around the Coulomb barrier

This work briefly introduces our recent studies on reactions induced by proton drip-line nuclei, 8B and 17F, at energies around the Coulomb barrier. Using detector arrays with large solid-angle coverage, the complete kinematics measurements were performed for systems of 8B+120Sn and 17F+58Ni. For the 8B+120Sn, the coincident measurement of the breakup fragments was achieved for the first time for a proton-halo nuclear system. The correlations between the breakup fragments reveal that the prompt breakup occurring on the outgoing trajectory dominates the breakup dynamics of 8B. For 17F+58Ni, the complete reaction channel information, such as quasi-elastic scattering, breakup and total fusion, was derived for the first time. An enhancement of the fusion cross section of 17F+58Ni was observed at the energy below the Coulomb barrier. Theoretical calculations indicate that this phenomenon is mainly due to the couplings to the continuum states. Moreover, different direct reaction dynamics were found in 8B and 17F systems, suggesting the influence of proton-halo structure on the reaction dynamics.

Effect on incomplete fusion of breakup fragments of the weakly bound projectile 8B in reactions with targets 27Al, 28Si, 208Pb and 209Bi

Calculations of total, complete and incomplete fusion cross sections are presented as function of the incident energy of the weakly bound projectile 8B in reactions with light 27Al, 28Si and heavy 208Pb and 209Bi mass targets. In particular, the relative effect of the breakup fragments; proton and 7Be of 8B on incomplete fusion is determined. Also, the effect of an additional proton to the nuclear potential of the targets 28Si, 209Bi respect to 27Al and 208Pb is determined as a function of the incident energy. It is found that the proton absorption becomes more important than for 7Be for light targets for energies around and above the barrier, however, the inverse occurs for heavy targets. The calculations are performed with two different methods. The CDCC to determine the relative projectile-target radial wave functions which subsequently are used in the angular momentum-dependent model of fusion probabilities to calculate complete, incomplete and total fusion.

Statistical Characteristics of Droplets Formed due to the “Bag Breakup” Fragmentation Event at the Interface between Water and High-Speed Air Flow

Abstract Recent studies indicate that the dominant mechanism for generating sprays in hurricane winds is a “bag breakup” fragmentation. This fragmentation process is typically characterized by inflation and consequent bursting of short-lived objects, referred to as “bags” (sail-like pieces of water film surrounded by a rim). Both the number of spray droplets and their size distribution substantially affect the air–sea heat and momentum exchange. Due to a lack of experimental data, the early spray generation function (SGF) for the bag breakup mechanism was based on the assumed similarity with resembling processes. Here we present experimental results for the case with a single isolated bag breakup fragmentation event. These experiments revealed several differences from similar fragmentation events that control the droplet sizes, such as secondary disintegration of droplets in gaseous flows and bursting of bubbles. In contrast to the bubble bursting, the film thickness of the bag canopy is not constant but is random with lognormal distribution. Additionally, its average value does not depend on the canopy radius but is determined by the wind speed. The lognormal size distribution of the canopy droplets is observed in conjunction with the established mechanism of liquid film fragmentation. The rim fragmentation results in two types of droplets, and their size distribution has been found to be lognormal distribution. The constructed SGF is verified by comparing it with experimental data from the literature. The perspectives of transferring the results from laboratory to field environment have also been discussed. Significance Statement The “bag breakup” fragmentation is the dominant mechanism for generating spray in hurricane winds. The number and the sizes of the spray droplets substantially affect the heat transport from the ocean to the atmosphere and, thereby, the development of hurricanes. This paper presents experimental data and analysis that demonstrate how droplet formation occurs during bag breakup fragmentation. It also shows analysis of the quantity and size of droplets formed during a single fragmentation event. This work demonstrates how obtained experimental results can be applied to real field conditions in the context of hurricane prediction models.

Proton halo effects in the 8B+64Zn collision around the Coulomb barrier

The 8B+64Zn reaction at 38.5 MeV has been studied at HIE-ISOLDE CERN to investigate proton halo effect on the reaction dynamics. For the first time it was used the only existing post-accelerated 8B beam. The measured elastic scattering angular distribution showed a small suppression of the Coulomb-nuclear interference peak, opposite to what observed for the one-neutron halo nucleus 11Be on the same target where a large suppression was observed instead. Inclusive angular and energy distributions of breakup fragments were also measured showing that, both, elastic and non-elastic breakup contribute. The presence of the additional Coulomb interactions halo-core and halo-target in 8B makes the reaction dynamics in this proton-halo nucleus different than the neutron-halo case.

Characterization of the breakup channel in the asymmetric systems Ca40,48+C12 at 25 and 40 MeV/nucleon

An analysis of the asymmetric reactions $^{40,48}$Ca+$^{12}$C at 25 and 40 MeV/nucleon is presented. Data have been collected with six modules of the FAZIA array. The analysis is focused on the breakup channel of sources produced in dissipative collisions, partially corresponding to incomplete fusion processes. The study has been performed both on detected fragments and on some resonances reconstructed by means of particle-fragment correlations, with a focus on the evolution of the breakup channel with the beam energy and the neutron content of the system, looking in particular at the relative velocity between the breakup fragments. Results show that also Carbon fragments reconstructed by means of particle correlations can be in large part interpreted as the light partner of a scission.

Cluster structure of C11 investigated with a breakup reaction

The excitation spectra above the breakup threshold of C11 were measured using the invariant mass method with a 25.0-MeV/nucleon beam bombarding a carbon target for the first time. This measurement was performed with a zero-degree double-sided silicon strip detector together with four CsI(Tl) detectors, which could detect breakup fragments with low relative kinetic energy. Some resonances in C11 were clearly observed in the excitation energy range of 8–14 MeV proceeding through the Be7 + α channel. Among them, a resonance with the largest yield was observed around 8.10 MeV. We assign it as the head of the Kπ=3/2− rotational band, and suggest the 9.38-MeV state as the second member of this band.1 MoreReceived 3 May 2022Revised 16 September 2022Accepted 11 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.014320©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsNuclear structure & decaysProperties6 ≤ A ≤ 19Nuclear Physics

Breakup of the proton halo nucleus 8B near barrier energies

The dynamics of a nuclear open quantum system could be revealed in the correlations between the breakup fragments of halo nuclei. The breakup mechanism of a proton halo nuclear system is of particular interest as the Coulomb polarization may play an important role, which, however, remains an open question. Here we use a highly efficient silicon detector array and measure the correlations between the breakup fragments of 8B incident on 120Sn at near-barrier energies. The energy and angular correlations can be explained by a fully quantum mechanical method based on the state-of-the-art continuum discretized coupled channel calculations. The results indicate that, compared to the neutron halo nucleus 6He, 8B presents distinctive reaction dynamics: the dominance of the elastic breakup. This breakup occurs mainly via the short-lived continuum states, almost exhausts the 7Be yield, indicating the effect of Coulomb polarization on the proton halo state. The correlation information reveals that the prompt breakup mechanism dominates, occurring predominantly on the outgoing trajectory. We also show that, as a large environment, the continuum of 8B breakup may not significantly influence elastic scattering and complete fusion.

Improved Quantum Molecular Dynamics Model and Its Application to Ternary Breakup Reactions

Collisions of very heavy nuclei 197Au+197Au at the energy range of 5–30 A MeV have been studied within the improved quantum molecular dynamics (ImQMD) model. A class of ternary events satisfying a nearly complete balance of mass numbers is selected and we find that the probability of ternary breakup depends on the incident energy and the impact parameter. It is also found that the largest probability of ternary breakup is located at the energy around 24 A MeV for the system 197Au+197Au. The experimental mass distributions and angular distributions for the system 197Au+197Au ternary breakup fragments can be reproduced well by the calculation with the ImQMD model at the energy of 15 A MeV. The modes and mechanisms of ternary and quaternary breakup are studied by time-dependent snapshots of ternary events. The direct prolate, direct oblate, and cascade ternary breakup modes, are manifested and their production probabilities are obtained. The characteristic features in ternary breakup events, three mass-comparable fragments, and the very fast, nearly collinear breakup, account for the two-preformed-neck shape of the composite system. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary breakup with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.

Relative probabilities of breakup channels in reactions of 6,7Li with 209Bi at energies around and above the Coulomb barrier * *Supported by National Natural Science Foundation of China (11635015, U1832130, 11975040), State Key Laboratory of Software Development Environment (SKLSDE-2020ZX-16), the Continuous Basic Scientific Research Project (WDJC-2019-13) and the Leading Innovation Project (LC192209000701, LC202309000201)

Coincidence measurements of breakup fragments in reactions of with at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array. Through the Q values along with the relative energies of the breakup fragments, different breakup components (prompt breakups and delayed breakups) and different breakup modes ( , , , and ) are distinguished. A new breakup mode, , is observed in -induced reactions at energies above the Coulomb barrier. Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated. The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion, particularly for the above-barrier energies.

Progress on reaction mechanisms of the proton drip-line nucleus <sup>17</sup>F at energies around the Coulomb barrier

<p indent=0mm>The reaction mechanism of proton drip-line nuclear systems at energies around the Coulomb barrier is one of the most popular topics in the field of nuclear physics. The present status of reactions induced by ¹⁷F at energies around the Coulomb barrier is reviewed in this paper. To make a further investigation of the reaction mechanisms of ¹⁷F, our group performed the measurements of elastic scattering of ¹⁷F+¹²C, ⁸⁹Y and ²⁰⁸Pb, as well as the complete kinematics of ¹⁷F+⁵⁸Ni at energies around the Coulomb barrier. For the elastic scattering, the excitation to the first excited state of ¹⁷F cannot be distinguished, hence the results have to be considered as the quasi-elastic scattering. The continuum-discretized coupled-channels (CDCC) calculations were performed to investigate the couplings to the continuum states on the elastic scattering. Both the calculations with and without the couplings to the continuum states can describe the quasi-elastic scattering data properly. The results indicate that, in a wide target-mass range, the couplings to the continuum states of ¹⁷F are not significant. For the breakup mechanism, breakup fragments of ¹⁷F+⁵⁸Ni and ²⁰⁸Pb were measured at energies above the Coulomb barrier. CDCC calculation could reproduce the breakup angular distribution of ¹⁷F+⁵⁸Ni well. However, it significantly overestimated the results of ¹⁷F+²⁰⁸Pb. The possible reason is that the excitation of the core, ¹⁶O, was not taken into account in the calculation. However, the underlying physics needs a further study. Within the energy region close to the Coulomb barrier, the breakup reactions of ¹⁷F+⁵⁸Ni were measured in single and in coincidence. The CDCC and the newly developed three-body model (the IAV model) were adopted to analyze the breakup data. The coincident data could be described well by the CDCC calculations. The sum of CDCC and IAV, which is referred to be as the total breakup, can reproduce properly the angular distributions of ¹⁶O. Moreover, the results also indicate that the non-elastic breakup dominates the ¹⁶O production. For the fusion measurement, only the results of ¹⁷F+⁵⁸Ni and ²⁰⁸Pb have been reported so far. The total fusion cross section of ¹⁷F+⁵⁸Ni was derived by measuring the fusion-evaporated protons and alphas. Compared with ¹⁶O+⁵⁸Ni, an obvious enhancement was observed at the energy below the Coulomb barrier. CDCC calculation indicates that such an enhancement is mainly due to the couplings to the continuum states. While for ¹⁷F+²⁰⁸Pb, the total fusion cross section was deduced by measuring the fusion-fission fragments in coincidence. The fusion excitation function of ¹⁷F+²⁰⁸Pb is almost identical with the stable system ¹⁹F+²⁰⁸Pb, indicating that the weakly bound nature of ¹⁷F does not play an important role in the fusion of ¹⁷F+²⁰⁸Pb. The underlying physics of the difference between ¹⁷F+⁵⁸Ni and ²⁰⁸Pb strongly deserves a further investigation. Furthermore, to establish the systematics of the reaction dynamics of ¹⁷F, reaction measurements of ¹⁷F on a range of targets at energies around and below the Coulomb barrier will be valuable. The results of ¹⁷F further indicate that the complete kinematics measurement could be the only promising approach to understand the reaction mechanisms of weakly bound nuclear systems comprehensively and provide the convincing data to promote the development of nuclear reaction theory.

Fragmentation analysis of 105Ag∗ nucleus governed via complete and incomplete fusion channels at Ec.m. = 89MeV

A systematic study of dynamical aspects associated with heavy-ion-induced [Formula: see text] reaction is carried out at center-of-mass energy [Formula: see text] MeV. The complete fusion (CF) and incomplete fusion (ICF) contributions are estimated by using the dynamical cluster-decay model (DCM). The incomplete fusion component is examined by normalizing the incident beam energy for each of the breakup fragment. The fusion evaporation cross-sections that emerged from CF and ICF channels are duly addressed using the optimized value of neck-length parameter [Formula: see text]. Further, the mass yield of compound nuclei (CN) formed in the CF and ICF processes is analyzed with respect to angular momentum [Formula: see text] values. The DCM-based calculations indicate the possible contribution of deep inelastic collision (DIC) in the decay of [Formula: see text] at higher [Formula: see text] values, and DIC cross-sections are predicted which call for future validation.

Detailed investigation of bag-breakup process in the context of spray of droplets generation within wind-wave interaction

The main mechanism responsible for the generation of spume droplets in marine atmospheric boundary layer was investigated at the experiments carried out at the high-speed wind-wave flume of IAP RAS. Strong wind tears off water from the crest of the waves during bag breakup fragmentation of small-scale disturbances that arise at the air-water interface. Separate bag-breakup event forced to occur in a dried high-speed wind-wave flume was investigated qualitatively and quantitatively using multiperspective shadowgraph high-speed video recording.

Study of continuum excitation by light weakly bound projectiles on proton target

Elastic scattering and breakup angular distribution measurements for the systems 6,7Li + p were performed at the MAGNEX facility of the Istituto Nazionale di Fisica Nucleare-Laboratori Nazionali del Sud (INFN-LNS) in Catania, in the energy range of (2.3–5.4)AMeV. The breakup channel was identified and quantified adopting the algorithm MULTIP.Within this algorithm which is a Monte Carlo simulation code, the history of the breakup fragments can be tagged from the rest frame of the decay nucleus itself to the laboratory frame. Angular distribution data of both elastic scattering and breakup were analyzed under the same theoretical model and the influence of continuum on the elastic channel was investigated.

Interpretation of coincidence data from strip detectors and extraction of absolute cross section using 3-body Monte Carlo simulation method

Accurate knowledge of the response of the detection system is very crucial for unambiguous interpretation of the experimental data. A simulation code has been developed using the Monte Carlo technique involving 3-body kinematics for the analysis of data obtained with segmented large area Si Δ E−E detector telescopes in nuclear reaction measurements. Care was taken in the analysis to maximize the angular coverage and statistics. The emphasis is placed to extract the absolute cross sections of the different reaction processes, for which coincident measurements are unavoidable. The estimated detection efficiency of different coincidence events are found to depend on various parameters, e.g., the relative energy of the breakup fragments, incident beam energy of the projectile, ground state Q-value of the reaction, the excitation of the ejectile as well as target like nuclei, mass asymmetry of the breakup fragments, detection threshold, and geometric solid angle of the detection setup. The interpretation of the various observables from the exclusive measurements of breakup and transfer breakup reactions is reported.

Measurement of droplet breakage in a pump-mixer

The direct experimental data for droplet breakage frequency and daughter droplet size distribution is urgently required for the application of the population balance model. To meet this requirement, a method to directly measure the droplet breakage in the pump-mixer was developed using a high speed online camera. Two typical breakup patterns, tensile breakup and revolving breakup were observed and the number of the breakup fragments was determined. The multiple breakage was treated as a series of binary breakups. In order to precisely describe the daughter size distribution, these binary breakups were divided into three different types, i.e. the original tensile breakup, intermediate tensile breakup, and revolving breakup. The influences of the rotating speed and interfacial tension on the droplet breakup frequency and daughter droplet size distribution were then quantitatively investigated. Empirical correlations were proposed and good agreement was found between the prediction results and the experimental data.

The “Bag Breakup” Spume Droplet Generation Mechanism at High Winds. Part I: Spray Generation Function

AbstractThis paper describes the results of an experimental and theoretical investigation into the mechanisms by which spume droplets are generated by high winds. The experiments were performed in a high-speed wind-wave flume at friction velocities between 0.8 and 1.5 m s−1 (corresponding to a 10-m wind speed of 18–33 m s−1 under field conditions). High-speed video of the air–water interface revealed that the main types of spray-generating phenomena near the interface are “bag breakup” (similar to fragmentation of droplets and jets in gaseous flows at moderate Weber numbers), breakage of liquid ligaments near the crests of breaking surface waves, and bursting of large submerged bubbles. Statistical analysis of these phenomena showed that at wind friction velocities exceeding 1.1 m s−1 (corresponding to a wind speed of approximately 22.5 m s−1), the main mechanism responsible for the generation of spume droplets is bag breakup fragmentation of small-scale disturbances that arise at the air–water interface under the strong wind. Based on the general principles of statistical physics, it was found that the number of bags arising at the water surface per unit area per unit time was dependent on the friction velocity of the wind. The statistics obtained for the bag breakup events and other data available on spray production through this type of fragmentation were employed to construct a spray generation function (SGF) for the bag breakup mechanism. The resultant bag breakup SGF is in reasonable agreement with empirical SGFs obtained under laboratory and field conditions.

Dynamics of complete and incomplete fusion of 6,7Li, 15N and 16O with a 209Bi target

The dynamics of complete and incomplete fusion of 6,7Li, 15N and 16O with a common target (209Bi) around the Coulomb barrier are analyzed within the context of the coupled channel formulation and the energy dependent Woods-Saxon potential (EDWSP) model. The calculated results are compared with experimental fusion cross-sections and it has been shown that complete fusion (CF) data of weakly bound projectile with a heavy target (209Bi) gets suppressed at above barrier energies. In the case of the 6Li + 209Bi (7Li + 209Bi) reaction, the CF data at above barrier energies is reduced by 34% (26%) with reference to the expectations of the coupled channel approach. However, the theoretical estimations due to the EDWSP model can minimize the suppression factor by 9% with respect to the reported value and consequently the portion of above barrier CF cross-section data of 6Li + 209Bi (7Li + 209Bi) reaction is suppressed by 25% (17%) when compared with the present model calculations. This fusion inhibition can be correlated with the low breakup threshold of projectile which in turn breaks up into two fragments in the entrance channel prior to fusion barrier. The total fusion (TF) data, which is sum of complete fusion (CF) data and incomplete fusion (ICF) data, is not suppressed when compared with the predictions of the theoretical approaches and thus breakup channel has very little influence on the total fusion cross-sections. Although the breakup fragments appeared in both reactions, the enhanced suppression effects observed for the lighter projectile can be correlated with its low binding energy associated with the $\alpha$ -breakup channel. Further the outcomes of the EDWSP model reasonably explained the ICF contribution appeared in the fusion of 6,7Li + 209Bi reactions. In contrast to this, the observed fusion dynamics of 15N + 209Bi and 16O + 209Bi reactions, wherein the collective excitations such as two phonon, three phonon vibrational states contribute to produce below barrier fusion enhancement, has been adequately explored by the adopted models, and henceforth ensures the stability of well bound nuclei against breakup effects.

Projectile-breakup-induced fission-fragment angular distributions in the Li6+Th232 reaction

Background: Experimental anisotropy in fission-fragment (FF) angular distribution in reactions involving weakly bound stable projectiles with actinide targets are enhanced compared to statistical saddle-point model (SSPM) predictions. Contributions from breakup- or transfer-induced fission to total fission are cited as possible reasons for such enhancement.Purpose: To identify the breakup- or transfer-induced fission channels in $^{6}\mathrm{Li}$+$^{232}\mathrm{Th}$ reaction and to investigate their effects on FF angular anisotropy.Methods: The FF angular distributions have been measured exclusively at three beam energies (28, 32, and 36 MeV) around the Coulomb barrier in coincidence with projectile breakup fragments like $\ensuremath{\alpha}, d$, and $p$ using Si strip detectors. The angular anisotropy obtained for different exclusive breakup- or transfer-induced fission channels are compared with that for total fission. SSPM and pre-equilibrium fission models have been employed to obtain theoretical FF angular anisotropy.Results: Angular anisotropy of the fission fragments produced by different transfer- or breakup-induced fission reactions have been obtained separately in the rest frame of respective recoiling nuclei. Some of these anisotropies were found to be stronger than those of the inclusive fission. Overall angular distributions of transfer or breakup fission, integrated over all possible recoil angles with weight factor proportional to differential cross section of the complementary breakup fragment emitted in coincidence in all possible directions, were obtained. It was observed that the overall FF angular anisotropy for each of these fission channels is less than or equal to the anisotropy of total fission at all the measured energies. Assuming isotropic out-of-plane correlations between the fission fragments and light-charged particles, the overall breakup- or transfer-induced fission fragment angular distributions do not explain the observed enhancement in FF anisotropy of total fission. Pre-equilibrium fission model provides a reasonable explanation of the enhanced experimental anisotropy of total fission.Conclusions: Angular anisotropies for different breakup or transfer fission channels involving emission of $\ensuremath{\alpha}, d$, and $p$ in the reaction plane have been measured for the $^{6}\mathrm{Li}+^{232}\mathrm{Th}$ reaction. The overall FF angular anisotropies of breakup- or transfer-induced fissions do not explain the enhanced anisotropy of total fission at near-barrier energies. A measurement of out-of-plane correlation is necessary to confirm the above observation and obtain a complete picture on the effect of transfer or breakup on total fission.

Study of the cluster structure of10Be and16C neutron-rich isotopes by means of intermediate energies breakup reactions

We describe the results of a new experiment aimed to investigate the possible existence of cluster structures in10Be and16C isotopes. They have been investigated at the FRIBs facility of INFN-LNS by means of an invariant mass analysis on correlated projectile breakup fragments carried out with the CHIMERA 4π detector. From the analysis of the6He+4He channel we found evidence of a new state in10Be at 13.5MeV excitation energy. Concerning16C, we investigated6He+10Be correlated fragments and we found a non-vanishing yield at about 20.5MeV in the corresponding excitation energy spectrum. Finally, we describe few details of a new experiment performed at the FRIBs facility where the CHIMERA detector was coupled to the FARCOS hodoscope, with the aim to improve the presently obtained results.

Revisiting the collision risk with cataloged objects for the Iridium and COSMO-SkyMed satellite constellations

After two decades of slightly declining growth rate, the population of cataloged objects around the Earth increased by more than 56% in just a couple of years, from January 2007 to February 2009, due to two collisions in space involving the catastrophic destruction of three intact satellites (Fengyun 1C, Cosmos 2251 and Iridium 33) in high inclination orbits. Both events had occurred in the altitude range already most affected by previous launch activity and breakups. In 2011 a detailed analysis had been carried out to analyze the consequences of these fragmentations, in particular concerning the evolution of the collision risk for the Iridium and COSMO-SkyMed satellite constellations. Five years after such first assessment, the cataloged objects environment affecting the two constellations was revisited to evaluate how the situation had evolved due to the varying contribution of the above mentioned breakup fragments and the space activities carried out in the meantime. Being distributed, at 778km, over six nearly polar orbit planes separated by just 30° at the equator, the Iridium satellites represent a very good gauge for checking the evolution of the environment in the most critical low Earth region. In approximately five years, from May 2011 to June 2016, the average flux of cataloged objects on the Iridium satellites increased by about 14%, to 1.59×10−5m−2 per year. The cataloged fragments of Fengyun 1C, Cosmos 2251 and Iridium 33 still accounted for, on average, 54% of the total flux. More than 39% of the latter was associated with the Fengyun 1C fragments, about 11% with the Cosmos 2251 fragments and less than 4% with the Iridium 33 fragments. Specifically concerning the mutual interaction among the Iridium 33 debris and the parent constellation, the progressive dispersion and rather fast decay of the fragments below the Iridium operational altitude, coupled with a slow differential plane precession and low average relative velocities with respect to four of the six constellation planes, determined in five years, on average, a decline of the flux by about 31%, i.e. to about 5.75×10−7m−2 per year. The decrease occurred in each constellation plane, even though with different rates and percentages, due to the varying relative orbit geometry. From May 2011 to June 2016, the mean flux of cataloged objects on the COSMO-SkyMed satellites, at 623km, increased by about 26%, to 7.24×10−6m−2 per year. The Fengyun 1C, Cosmos 2251 and Iridium 33 cataloged fragments accounted for, on average, about 1/4 of the total, with 12% due to Fengyun 1C, 8% to Cosmos 2251 and 4% to Iridium 33.