Physics of Atomic Nuclei最新文献

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Studies of Yields of ((gamma,{xn})) Reactions on Natural Iridium at the Bremsstrahlung End-Point Energy of 55 MeV ((γ,{xn}))的产率研究天然铱在 55 兆电子伏轫致辐射端点能量下的反应产率
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S106377882470087X
M. V. Zheltonozhskaya, P. D. Remizov, V. D. Pupyshev, V. V. Khankin, A. A. Kuzmenkov, A. P. Chernyaev
{"title":"Studies of Yields of ((gamma,{xn})) Reactions on Natural Iridium at the Bremsstrahlung End-Point Energy of 55 MeV","authors":"M. V. Zheltonozhskaya,&nbsp;P. D. Remizov,&nbsp;V. D. Pupyshev,&nbsp;V. V. Khankin,&nbsp;A. A. Kuzmenkov,&nbsp;A. P. Chernyaev","doi":"10.1134/S106377882470087X","DOIUrl":"10.1134/S106377882470087X","url":null,"abstract":"<p>The article presents the results of the study of the flux-weighted average cross sections of <span>({}^{185-190})</span>Ir and <span>({}^{192})</span>Ir nuclei production in (<span>(gamma,xn)</span>) reactions when a natural mixture of iridium isotopes is irradiated with bremsstrahlung with an end-point energy of 55 MeV. For the first time, the experimental data on the weighted average cross sections of photoneutron reactions with the emission of up to six particles are compared with the theoretical weighted average cross sections calculated in the constant-temperature Fermi gas model and the Gogny–Hartree–Fock–Bogoliubov nuclear mass model using the TALYS1.96 program code. It is shown that the cross sections of the studied reactions are simultaneously successfully described only by the constant-temperature Fermi gas model taking into account the pre-equilibrium processes.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S386 - S391"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unified Description of Elastic Hadron Scattering at Low and High Energies 低能和高能弹性强子散射的统一描述
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S1063778824700960
O. V. Selyugin
{"title":"Unified Description of Elastic Hadron Scattering at Low and High Energies","authors":"O. V. Selyugin","doi":"10.1134/S1063778824700960","DOIUrl":"10.1134/S1063778824700960","url":null,"abstract":"<p>A simultaneous description of different spin independent and spin dependent reactions of nucleon–nucleon elastic scattering is obtained for all existing experimental data at low <span>(sqrt{s}geq 3.6)</span> GeV and high energies up to the last LHC energy. From the point of view of the generalized parton structure of hadrons which unifies parton distributions of the proton, neutron, antiproton and meson the corresponding electromagnetic and gravitomagnetic form factors were obtained. On the base of these form factors, the elastic scattering amplitude is obtained with taking into account the analytical properties such as unitarity, crossing symmetry, polynomial boundedness. As a result, the united description of the existing experimental data of the differential cross sections and spin correlation parameter <span>(A_{N})</span>(<span>(s,t)</span>) is obtained with minimum fitting parameters.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S349 - S362"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Possibility to Record Astrophysical Neutrino with LHAASO Detectors 用LHAASO探测器记录天体物理中微子的可能性
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S1063778824700947
Yu. V. Stenkin, A. V. Butkevich, I. S. Karpikov, D. A. Kuleshov, K. O. Kurinov, X. H. Ma, O. B. Shchegolev
{"title":"On a Possibility to Record Astrophysical Neutrino with LHAASO Detectors","authors":"Yu. V. Stenkin,&nbsp;A. V. Butkevich,&nbsp;I. S. Karpikov,&nbsp;D. A. Kuleshov,&nbsp;K. O. Kurinov,&nbsp;X. H. Ma,&nbsp;O. B. Shchegolev","doi":"10.1134/S1063778824700947","DOIUrl":"10.1134/S1063778824700947","url":null,"abstract":"<p>We propose to use existing LHAASO detectors to study of the flavor composition of UHE astrophysical neutrino. Monte Carlo simulations show that large Water Cherenkov Detector Array (WCDA) is a suitable detector to record high energy near horizontal neutrino interactions, due to its cell structure and rather large size. Signature of such events is very clear thus allows us even to determine the neutrino flavor interacting in the WCDA. The mass of this detector is about 300 kt of water and it is not enough to accumulate many high-energy neutrino events in a near future. Nevertheless, it is running detector and we could develop suitable algorithms for this program and make a search for these events regarding WCDA as a prototype for future full-scale experiment. Moreover, existing of square km EAS array (Km2A) with many muon detectors makes it possible to have a powerful veto against a background flux of near-horizontal atmospheric muons.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S314 - S318"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Data on Photoneutron Reaction Cross Sections for ({}^{{68}})Zn ({}^{{68}}) Zn的光子中子反应截面新数据
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S106377882470090X
V. V. Varlamov, A. I. Davydov, I. A. Mostakov, V. N. Orlin
{"title":"New Data on Photoneutron Reaction Cross Sections for ({}^{{68}})Zn","authors":"V. V. Varlamov,&nbsp;A. I. Davydov,&nbsp;I. A. Mostakov,&nbsp;V. N. Orlin","doi":"10.1134/S106377882470090X","DOIUrl":"10.1134/S106377882470090X","url":null,"abstract":"<p>New data on cross sections of the (<span>(gamma,1n)</span>) and (<span>(gamma,2n)</span>) reactions on the <span>({}^{68})</span>Zn nucleus, for which the neutron yield cross sections of <span>(sigma^{textrm{exp}}(gamma,xn)=sigma(gamma,1n)+2sigma(gamma,2n))</span> and the total photoneutron reaction <span>(sigma^{textrm{exp}}(gamma,sn)=sigma(gamma,1n)+sigma(gamma,2n))</span> have been obtained in two experiments on the beams of bremsstrahlung, were determined using the possibilities of the experimental–theoretical method for the evaluation of cross sections of partial photoneutron reactions based on objective physical criteria. The contributions of partial reaction cross sections <span>(sigma^{textrm{eval}}(gamma,in)=F_{i}^{textrm{theor}}timessigma^{textrm{exp}}(gamma,xn))</span> for <span>(i=1)</span> and <span>(2)</span> to the neutron yield cross section were evaluated using the ratios <span>(F_{i}^{textrm{theor}}=sigma^{textrm{theor}}(gamma,in)/sigma^{textrm{theor}}(gamma,xn))</span> calculated within the combined photonuclear reaction model (CPNRM).</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S264 - S273"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approaches to Optimization of Experimental Design for Cosmic Ray Mass Composition Studies in the 1–1000 PeV Energy Range 1-1000 PeV能量范围内宇宙射线质量组成研究实验设计的优化方法
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S1063778824700959
D. V. Chernov, C. J. Azra, E. A. Bonvech, O. V. Cherkesova, E. L. Entina, V. I. Galkin, V. A. Ivanov, T. A. Kolodkin, N. O. Ovcharenko, D. A. Podgrudkov, T. M. Roganova, M. D. Ziva
{"title":"Approaches to Optimization of Experimental Design for Cosmic Ray Mass Composition Studies in the 1–1000 PeV Energy Range","authors":"D. V. Chernov,&nbsp;C. J. Azra,&nbsp;E. A. Bonvech,&nbsp;O. V. Cherkesova,&nbsp;E. L. Entina,&nbsp;V. I. Galkin,&nbsp;V. A. Ivanov,&nbsp;T. A. Kolodkin,&nbsp;N. O. Ovcharenko,&nbsp;D. A. Podgrudkov,&nbsp;T. M. Roganova,&nbsp;M. D. Ziva","doi":"10.1134/S1063778824700959","DOIUrl":"10.1134/S1063778824700959","url":null,"abstract":"<p>The new SPHERE-3 detector is under development. The main purpose of this experiment is to study the mass composition of primary cosmic rays in the energy range of 1–1000 PeV. The difference between this detector and the previous ones in this series is the registration of not only the Cherenkov light reflected from the snow, but also direct light entering the detector. Several options are being considered for recording direct Cherenkov light. The article presents the estimated parameters of the optical scheme of the detector and the first estimations of its sensitivity to the energy and mass of the primary particle. The first approximations of methods used for energy and mass of the primary particle assessment in each event are given, and their accuracy is considered. At the moment, methods for reflected Cherenkov light and direct Cherenkov light processing are being considered independently of each other.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S319 - S338"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of Monotonic and Non-Monotonic Potentials on the ({}^{{40}})Ca((alpha), ({}^{{3}})He)({}^{{41}})Ca Reaction at 36 and 40 MeV 36和40 MeV下单调和非单调电位对({}^{{40}}) Ca((alpha), ({}^{{3}}) He) ({}^{{41}}) Ca反应的影响
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S1063778824700923
A. Somadder, R. Das, S. K. Das
{"title":"Effect of Monotonic and Non-Monotonic Potentials on the ({}^{{40}})Ca((alpha), ({}^{{3}})He)({}^{{41}})Ca Reaction at 36 and 40 MeV","authors":"A. Somadder,&nbsp;R. Das,&nbsp;S. K. Das","doi":"10.1134/S1063778824700923","DOIUrl":"10.1134/S1063778824700923","url":null,"abstract":"<p>The direct one-nucleon transfer <span>({}^{40})</span>Ca(<span>(alpha)</span>, <span>({}^{3})</span>He)<span>({}^{41})</span>Ca reaction has been investigated at 36 and 40 MeV incident energies. The full finite-range (FFR) distorted-wave Born approximation (DWBA) analysis has been carried out for the angular distributions of the reaction. Two forms of the monotonic potentials namely, Woods–Saxon and Michel, and both the shallow non-monotonic (molecular) and deep non-monotonic (DNM) potentials in the framework of the optical model are used to analyze the transitions to the ground state and to fifteen and twelve excited states in <span>({}^{41})</span>Ca at 36 and 40 MeV, respectively. The extracted spectroscopic factors from all forms of the optical model potentials have been compared with the previous calculations. To estimate the quality of fits, the <span>(chi_{N}^{2})</span> values of the optical model potentials are calculated for the <span>(alpha+{}^{40})</span>Ca elastic scattering and the <span>({}^{40})</span>Ca(<span>(alpha)</span>, <span>({}^{3})</span>He)<span>({}^{41})</span>Ca reaction at two incident energies. The present analysis shows that Michel, molecular, and DNM potentials are able to produce a satisfactory fit to the elastic scattering data, but the Woods–Saxon potential is found to be incompetent. Although, all forms of the monotonic and non-monotonic potentials give an overall good description of the angular distributions in most of the states for the reaction analysis at two incident energies. In this study, it has been also observed that the FFR DWBA analysis is apparently satisfactory for the <span>({}^{40})</span>Ca(<span>(alpha)</span>, <span>({}^{3})</span>He)<span>({}^{41})</span>Ca reaction analysis using all forms of the optical model potentials at 36 and 40 MeV.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S284 - S304"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evolution of Neutron Shell Structure of ({N=14}), ({16}) Isotones ({N=14}), ({16})等音中子壳层结构演化
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-03-03 DOI: 10.1134/S1063778824700844
O. V. Bespalova, A. A. Klimochkina, M. M. Mosunov
{"title":"Evolution of Neutron Shell Structure of ({N=14}), ({16}) Isotones","authors":"O. V. Bespalova,&nbsp;A. A. Klimochkina,&nbsp;M. M. Mosunov","doi":"10.1134/S1063778824700844","DOIUrl":"10.1134/S1063778824700844","url":null,"abstract":"<p>The evolution of the single-particle characteristics of neutron- and proton-rich isotones with the new magic numbers <span>(N=14)</span>, <span>(16)</span> in the <span>(Z)</span> range from 8 to 20 in the dispersive optical model was traced. The calculated energy gaps <span>(N=14)</span> and <span>(16)</span> widened with the increase in excess of protons and neutrons, respectively. At the same time, the deviation of half-sum of the single-particle energies of the last predominantly occupied and the first predominantly unoccupied states from the Fermi energy decreased. The widening of the gaps were enhanced under the assumption of an increase in the diffuseness of the Hartree–Fock component of the dispersive optical model potential with an increase in the neutron excess over the range of <span>(Z)</span> numbers considered. The bubble structure manifests itself clearly in the neutron density distribution of the proton-unstable nucleus <span>({}^{34})</span>Ca.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 2 supplement","pages":"S363 - S371"},"PeriodicalIF":0.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Debuncher for the Formation of a Beam of Light Ions before Injection into the Storage Ring of a Synchrotron 注入同步加速器储存环前形成一束光离子的拆装器
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-02-22 DOI: 10.1134/S1063778824090011
Ya. M. Abakumov, N. F. Drebezova, I. R. Kalieva, A. A. Tumanova
{"title":"Debuncher for the Formation of a Beam of Light Ions before Injection into the Storage Ring of a Synchrotron","authors":"Ya. M. Abakumov,&nbsp;N. F. Drebezova,&nbsp;I. R. Kalieva,&nbsp;A. A. Tumanova","doi":"10.1134/S1063778824090011","DOIUrl":"10.1134/S1063778824090011","url":null,"abstract":"<p>A debuncher for a linear accelerator of protons and light ions with a charge-to-mass ratio <i>A</i>/<i>Z</i> from 1 to 3.5 and a beam energy of 7.5 MeV/nucleon is under development at the National Research Nuclear University MEPhI for scientific research and applications. The electrodynamic, thermal, and mechanical processes and the multipactor discharge have been simulated. Problems of design development of the model taking into account technological equipment that can be used for fabrication have been elaborated.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 11","pages":"1670 - 1675"},"PeriodicalIF":0.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Influence of the Elemental Composition on the Electrical Resistivity of Ti–B–C Coatings Deposited by Magnetron Sputtering 元素组成对磁控溅射沉积的 Ti-B-C 涂层电阻率的影响
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-02-22 DOI: 10.1134/S1063778824090163
Ph. V. Kiryukhantsev-Korneev, A. D. Chertova, V. V. Kuts, Yu. S. Pogozhev
{"title":"Influence of the Elemental Composition on the Electrical Resistivity of Ti–B–C Coatings Deposited by Magnetron Sputtering","authors":"Ph. V. Kiryukhantsev-Korneev,&nbsp;A. D. Chertova,&nbsp;V. V. Kuts,&nbsp;Yu. S. Pogozhev","doi":"10.1134/S1063778824090163","DOIUrl":"10.1134/S1063778824090163","url":null,"abstract":"<p>Ti–B–C coatings of various compositions were obtained by magnetron sputtering using a TiB<sub>2</sub>–TiC heterophase target and were deposited on a Si(111) substrate. The studies were carried out using glow discharge optical emission spectroscopy, X-ray diffraction, and scanning electron microscopy. The electrical resistivity was measured using the four-probe method. The coatings had a dense, low-defect structure based on the hexagonal TiB<sub>2</sub> phase and were characterized by a uniform distribution of elements throughout the thickness. It has been established that the electrical resistivity decreases from 314 to 249 µΩ cm with an increase in the titanium content in coatings from 27 to 42 at %.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 11","pages":"1591 - 1595"},"PeriodicalIF":0.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calibration of the Hyperon+ Gamma-Nuclear Transition Detector with an External Trigger 超子+ γ -核跃迁探测器的外部触发校准
IF 0.3 4区 物理与天体物理
Physics of Atomic Nuclei Pub Date : 2025-02-22 DOI: 10.1134/S1063778824090126
A. M. Gorin, S. V. Evdokimov, A. A. Zaitsev, V. I. Izucheev, D. S. Krinitsyn, B. V. Polishchuk, V. I. Rykalin, S. A. Sadovsky, Yu. V. Kharlov, A. A. Shangaraev
{"title":"Calibration of the Hyperon+ Gamma-Nuclear Transition Detector with an External Trigger","authors":"A. M. Gorin,&nbsp;S. V. Evdokimov,&nbsp;A. A. Zaitsev,&nbsp;V. I. Izucheev,&nbsp;D. S. Krinitsyn,&nbsp;B. V. Polishchuk,&nbsp;V. I. Rykalin,&nbsp;S. A. Sadovsky,&nbsp;Yu. V. Kharlov,&nbsp;A. A. Shangaraev","doi":"10.1134/S1063778824090126","DOIUrl":"10.1134/S1063778824090126","url":null,"abstract":"<p>A calibration procedure with <sup>22</sup>Na radioactive sources for the counters of a gamma-nuclear transition spectrometer, which is fully integrated in the infrastructure of the Hyperon+ setup, including trigger and data acquisition systems, is proposed and implemented.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 11","pages":"1649 - 1657"},"PeriodicalIF":0.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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