Fragmentation channels of relativistic 7Be nuclei in peripheral interactions

At the JINR Nuclotron, ⁷Li nuclei are accelerated. The charge-exchange reaction involving these nuclei at an external target provides a secondary 1.23-A-GeV ⁷Be beam. This beam is used to irradiate emulsion chambers. The mean free path λ_inel(⁷Be) = 14.0 ± 0.8 cm for inelastic ⁷Be interactions in an emulsion coincides within the errors with those for ⁶Li and ⁷Li nuclei. More than 10% of the ⁷Be events are associated with the peripheral interactions in which the total charge of the relativistic fragments is equal to the charge of the ⁷Be nucleus and in which charged mesons are not produced. An unusual ratio of the helium isotopes is revealed in the composition of the doubly charged fragments of the ⁷Be nuclei: the number of the ³He fragments is twice as large as that of the ⁴He fragments. Each of 50% of peripheral interaction events includes two doubly charged fragments. The channels of the ⁷Be fragmentation into charged fragments are presented. In 50% of events, the ⁷Be fragmentation occurs only into charged fragments without the emission of neutrons. The ⁴He + ³He channel dominates, whereas each of the ⁴He + d + p and ⁶Li + p channels constitutes 10%. Two events without neutron emission are observed in the ³He + t + p and ³He + d + d three-body channels. The mean free path for the coherent dissociation of relativistic ⁷Be nuclei into ⁴He + ³He is equal to 7 ± 1 m. The main features of the fragmentation of relativistic ⁷Be nuclei in such peripheral interactions are explained by the ³He + ⁴He two-cluster structure of the ⁷Be nucleus.     

Investigation of Ternary Fission of <Stack><Subscript>98</Subscript><Superscript>252</Superscript></Stack>Cf Using Three-Cluster and Unified Ternary Fission Models

Using three-cluster and unified ternary fission models, the ternary fission of ₉₈²⁵²Cf is studied. We applied collinear and equatorial configurations to study the ternary fission of ₉₈²⁵²Cf when the third fragment is ₃¹⁰Li. The nuclear potential energy in the three-cluster model and unified ternary fission model is calculated respectively, using Yukawa plus exponential and proximity formalisms. The relative yields of different fragmentation channels are calculated. Our results reveal that the ternary fragmentation potential of the three fragments and the relative yields depend on the configuration of three fragments and usedmodel. Two models predict that the lowest driving potential and highest relative yield take place for the fragment combination ₅₁¹³²Sb + ₄₄¹¹⁰Ru + ₃¹⁰Li. Also, the values of driving potential and relative yield are not equal in the three-clustermodel and unified ternary fission model. For fragment combination ₅₁¹³²Sb + ₄₄¹¹⁰Ru + ₃¹⁰Li, the relative yield based on the three-cluster model in collinear configuration is maximum, whereas the unified ternary fission model in equatorial configuration predicts the lowest relative yield.     

Clustering Features of the 7Be Nucleus in Relativistic Fragmentation

Charge topology of fragmentation of 1.2 A GeV ⁷Be nuclei in nuclear track emulsion is presented. The dissociation channels ⁴He + ³He, 2³He+ n, ⁴He + 2¹H are considered in detail. It is established that the events ⁶Be + n amount about to 27 % in the channel ⁴He + 2¹H.     

Measurement of the fragmentation of Carbon nuclei used in hadron-therapy

The increasing use of Carbon nuclei in cancer therapy centres is motivated by their potential advantages as a very precise high LET radiation. The knowledge of the fragmentation of Carbon nuclei when they interact with the human body is important to evaluate the spatial profile of their energy deposition in the tissues, hence the damage to the tissues neighbouring the tumour. We report here a study of the fragmentation with the nuclear emulsion experimental technique. We have designed, built and exposed to a Carbon nuclei beam a chamber made of Lexan plates alternated with nuclear emulsion films. Lexan plates acted as passive material simulating human body tissues while nuclear emulsion films were used as both tracking devices with micrometric accuracy and ionisation detectors. Such a detector allowed the detection of Carbon interactions produced along their path, the identification of the fragments produced and the measurement of their scattering angle. We have measured the Carbon ion survival probability and studied their interactions. We report on the secondary particle multiplicity and the electrical charge distribution. We give results of the scattering angle of final state fragments as well as the range for H and He. Finally we give the total and partial charge-changing cross-sections for Δz=1,2,3,4$\mathrm{\Delta }z=1,2,3,4$ which are compared with previous results when available. The present work aims at providing data required as input to Monte Carlo simulations of Carbon ion interactions in the human body and ultimately of their therapeutic effectiveness.     

Evidence for an isomeric 3/2- state in 53Co

The fragmentation of a 550MeV/u primary beam of ⁵⁸Ni on a ⁹Be target has been used to measure time- and energy-correlated γ decays following the implantation of event-by-event discriminated secondary fragments into a ⁹Be stopper plate. A new isomeric γ decay with T _1/2 = 14( ) ns and E _γ = 646.2(2) keV is observed and attributed to the decay of the yrast 3/2^- state in ⁵³ ₂₇Co₂₆ . This short-lived isomeric state has been populated by means of nuclear reactions during the stopping process of the secondary fragments. The experimental findings are discussed in the framework of large-scale spherical shell model calculations in conjunction with isospin symmetry-breaking residual interactions for the A = 53 , T _z = ±1/2 mirror nuclei ⁵³Co and ⁵³Fe .     

Electromagnetic dissociation of relativistic 8B nuclei in nuclear track emulsion

Experimental data on fragmentation channels in peripheral interactions of ⁸B nuclei in nuclear track emulsions are presented. A detailed analysis made it possible to justify selections of events of the electromagnetic-dissociation process ⁸B → ⁷Be + p and to estimate its cross section. Events of ¹⁰C peripheral dissociation that were observed in the same exposure are described.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

Features of the 9Be → 2He fragmentation in an emulsion for an energy of 1.2 GeV per nucleon

The results of investigation of the fragmentation of relativistic nuclei ⁹Be in an emulsion, which is accompanied by the formation of two 1.2-A-GeV He fragments, are presented. The angular measurements of the ⁹Be → 2He events are analyzed. The ⁹Be → ⁸Be + n fragmentation channel with the decay of ⁸Be from the ground (0⁺) and first excited (2⁺) states into a pair of α particles appears to be dominant.     

Peripheral fragmentation of 8B nuclei in nuclear emulsion at an energy of 1.2 GeV per nucleon

The results obtained by studying the charge topology of fragments produced in the peripheral dissociation of relativistic ⁸B nuclei in emulsion are presented. Fifty-five events of the peripheral dissociation of a ⁸B nucleus in events where there was no production of target-nucleus fragments and mesons (“white stars”) were selected. A leading contribution of the ⁸B → ⁷Be + p mode, which has the lowest energy threshold, was revealed on the basis of these events. Information about the branching ratios for dissociation modes characterized by a higher multiplicity was obtained. The dissociation of the ⁷Be core in ⁸B bears resemblance to the dissociation of a free ⁷Be nucleus. The transverse-momentum distributions of fragments originating from the ⁸B → ⁷Be + p dissociation mode were obtained. For these distributions, a small mean value of 〈P*_T〉 = 52 ± 5 MeV/c in the c.m. frame suggests a low binding energy of the outer proton in the ⁸B nucleus. An indication of a strong azimuthal correlation of the fragments ⁷Be and p was found.     

Measurement of the 11B(11B, 10Be)12C proton transfer reaction at low energies

Differential cross sections for the ¹¹B(¹¹B,¹⁰Be)¹²C proton transfer reaction leading to the ¹⁰Be(g.sO+¹²C(4.43 MeV) $\text{(Q = 0.289}\text{MeV}\text{)}\text{and}{}^{10}\text{(3.37}\text{MeV}\text{) +}{}^{12}\text{C}\text{(g.s.) (Q = 1.36}\text{Me V}\text{)}$ final channels have been measured at E_c.m. = 5.5 MeV by coincident detection of the ¹⁰Be and ¹²C nuclei. The integrated cross sections for the ¹⁰Be + ¹²C(4.43 MeV) channel have been obtained for incident energies between E_c.m. = 2.66 and 3.64 MeV from the yields of the 4.43 MeV γ-ray emitted in the ¹²C 4.43 MeV → g.s. transition. The cross-section magnitudes compare well with the DWBA calculations. The sub-barrier transfer cross sections exhibit an unusual energy dependence: their ratio to the total reaction cross section is decreasing with decreasing incident energy.     

Effect of secondary decay on isoscaling: Results from the canonical thermodynamical model

The projectile fragmentation reactions using ⁵⁸Ni and ⁶⁴Ni beams at 140 MeV/n on targets ⁹Be and ¹⁸¹Ta are studied using the canonical thermodynamical model coupled with an evaporation code. The isoscaling property of the fragments produced is studied using both the primary and the secondary fragments and it is observed that the secondary fragments also respect isoscaling though the isoscaling parameters α and β changes. The temperature needed to reproduce experimental data with the secondary fragments is less than that needed with the primary ones. The canonical model coupled with the evaporation code successfully explains the experimental data for isoscaling for the projectile fragmentation reactions.     

High substitution of Fe for Zr in ZrV1.6P0.4O7 with small amount of FeV0.8P0.2O4 for low thermal expansion

Fe³⁺-doped ZrV_1.6P_0.4O₇ with Fe:Zr molar ratios of 1:9, 2:8, 3:7 and 4:6 was synthesized to reduce phase transition and obtain low thermal expansion. It is shown that the phase transition temperature of Fe-doped ZrV_1.6P_0.4O₇ is reduced obviously with increasing the content of Fe. Fe³⁺ ion with lower valence and smaller radius than that of Zr⁴⁺ favors to extend the bond angle of V–O–V(P) close to 180° in ZrV_1.6P_0.4O₇, which is considered responsible for the normal structure at room temperature and low thermal expansion. The thermal expansion coefficients of Fe-doped ZrV_1.6P_0.4O₇ for Fe:Zr molar ratios from 1:9 to 4:6 are calculated to be from −4.33×10⁻⁶$-4.33\times {10}^{-6}$ to 5.2×10⁻⁷ K⁻¹$5.2\times {10}^{-7}{\text{K}}^{-1}$ by linear thermal expansion measurement. The effect of small amount of FeV_0.8P_0.2O₄ formation with higher content of Fe³⁺ on thermal expansion coefficients of the samples is discussed.     

One-neutron stripping reactions of <Superscript>11</Superscript>Be and <Superscript>19</Superscript>C on light target

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping cross-section with the recently measured one. The effective range for ¹⁹C has been found to be smaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.      

Integrable deformations of nilpotent color Lie superalgebras

In this paper we study the infinitesimal deformations of the _Z3${\mathbb{Z}}_3$-color Lie superalgebra L^n,m,p$L^{n,m,p}$. By means of these deformations all filiform _Z3${\mathbb{Z}}_3$-color Lie superalgebras can be obtained. In particular, we give a method that will allow us to determine the dimension of the subspaces that are composed by linearly integrable deformations.