A comparative analysis of the density distributions and the structure models of <Superscript>9</Superscript>Li

In the present study, we have analysed the elastic scattering cross-section data of ⁹Li + ¹²C system at E _lab = 540 MeV and ⁹Li + ²⁰⁸Pb system at E _c.m. = 28.3 MeV for some cluster models and various density distributions of the ⁹Li nucleus. First, we have obtained five different density distributions of the ⁹Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the ⁹Li nucleus consisting of ⁶He + ³H and ⁸Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.     

Momentum distributions of <Superscript>4</Superscript>He nuclei from the <Superscript>6</Superscript>He and <Superscript>6</Superscript>Li breakup

Experimental data on the momentum distributions of ⁴He nuclei originating from ⁶He and ⁶Li breakup on various targets are presented over a wide beam energy range. The experiment with ⁶He was performed at the DRIBs accelerator complex for radioactive beams at the Joint Institute for Nuclear Research (JINR, Dubna). The intensity of the ⁶He beam used was 5 × 10⁶ particles per second and its energy was 10 MeV per nucleon. The momentum distributions of breakup products were measured by means of the MSP-144 magnetic spectrometer. The distribution width was shown to be virtually independent of the target mass. A small value of this width, σ ～ 28 MeV/c, confirms the presence of a halo in ⁶He. The measurements performed with ⁶Li beams of energy 18 and 46 MeV per nucleon at the U-400M accelerator yielded a width value of σ ～ 50 MeV/c for the momentum distributions of ⁴He nuclei, which is intermediate between that for ⁶He and those for stable nuclei. A compilation of the widths of the momentum distributions of fragments originating from the breakup of various nuclei is presented versus the binding energy of one or two neutrons in these nuclei, the target mass and the projectile energy.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Elastic and inelastic scattering of 800-MeV protons on <Superscript>16</Superscript>O and <Superscript>20</Superscript>Ne nuclei

Differential cross sections and polarization observables for the elastic and inelastic scattering of 800-MeV protons on ¹⁶O and ²⁰Ne nuclei are calculated on the basis of the theory of multiple diffractive scattering and the α-cluster model involving dispersion. The single-particle nucleon-density distributions obtained within the α-cluster model involving dispersion are used in the calculations. The differential cross sections and polarization calculated for elastic and inelastic p¹⁶O and p²⁰Ne scattering are compatible with available experimental data. The spin-rotation functions calculated for elastic p¹⁶O and p²⁰Ne scattering within the independent-nucleon model differ qualitatively from their counterparts calculated within the α-cluster model involving dispersion.     

Magnetic resonances in the electroexcitation of the <Superscript>26</Superscript>Mg nucleus

On the basis of spectroscopic information about direct pickup reactions, the multipole magnetic resonances M2, M4, and M6 of the ²⁶Mg nucleus are calculated within the particle-core coupling version of the multiparticle shell model. The excitation-energy distribution of the form factors for the multipole magnetic 1? ω resonances is obtained for momentum transfers to a nucleus up to 2 fm^?1. A comparison of the results of the calculations for the M6 form factors with corresponding experimental data confirms that the adopted model approximations are realistic.     

Structure of neutron-rich Isotopes <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li and allowance for it in elastic scattering

The differential cross sections for elastic proton scattering on the unstable neutron-rich nuclei ⁸Li and ⁹Li at E = 700 and 60 MeV per nucleon were considered. The ⁸Li nucleus was treated on the basis of the three-body α-t-n model, while the ⁹Li nucleus was considered within the α-t-n and ⁷Li-n-n models. The cross sections in question were calculated within Glauber diffraction theory. A comparison of the results with available experimental data made it possible to draw conclusions on the quality of the wave functions and potential used in the calculations.     

Role of the nuclear and electromagnetic interactions in the coherent dissociation of the relativistic <Superscript>7</Superscript>Li nucleus into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

The differential cross section in the transverse momentum Q and a total cross section of (31 ± 4) mb for the coherent dissociation of a 3-A-Ge V/c ⁷Li nucleus through the ³H + ⁴He channel have been measured on emulsion nuclei. The observed Q dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction (Q ≤ 400 Me V/c) and Coulomb (Q ≤ 50 Me V/c) dissociations are calculated to be 40.7 and 4 mb, respectively.     

Scattering of protons by <Superscript>9</Superscript>B and <Superscript>10</Superscript>B isotopes at intermediate energies in the diffraction theory

Differential cross sections of the elastic scattering of protons of intermediate energies by ⁹B and ¹⁰B nuclei are calculated within the Glauber theory. The matrix elements of elastic scattering are derived with a wave function in the three-particle 2αp-model (for ⁹B) and with an oscillatory wave function (for ¹⁰B). The differential cross-sections are calculated with allowance for the triple collisions on ⁹B nuclei and in the approximation of double collisions on ¹⁰B nuclei. The sensitivity of the differential cross-section to the ⁹B nucleus structure is analyzed. The differential cross section of ¹⁰B at E = 197 MeV is compared to the results from calculations using the distorted wave method.     

Search for superheavy hydrogen isotopes <Superscript>4,5</Superscript>H in reactions of pion absorption by <Superscript>10,11</Superscript>B nuclei

The results of searching for production of superheavy hydrogen isotopes ^4,5H in reactions of absorption of stopped π^? mesons by ^10,11B nuclei are reported. A peak near 3 MeV was observed in the missing mass spectra measured in the reactions ^10,11B(π^?, t⁴He)X, ¹⁰B(π^?, d⁴He)X, and ¹⁰B(π^?, t³He)X. A structure caused by two ⁵H states with the resonance energies E _R = 5.2 and 10.4 MeV was observed in the missing mass spectra measured in the reactions ¹¹B(π^?, d⁴He)X, ¹¹B(π^?, t³He)X, and ¹⁰B(π^?, d³He)X.     

Studying the ejection of light charged particles induced by 50 MeV <Superscript>3</Superscript>He ions upon interacting with a <Superscript>112</Superscript>Sn nucleus

Experimental double-differential and integral spectra of (³He, xp), (³He, xd), (³He, xt), (³He, x³He) and (³He, xα) reactions on ¹¹²Sn nuclei induced by 50 MeV 3He ions are presented. Theoretical calculations of the experimental inclusive spectra of the reactions are performed using the exciton model of preequilibrium decay. The corresponding mechanisms of reactions are determined. The experimental results can be used to develop new approaches in the theory of nuclear reactions, and to design safe and wasteless hybrid nuclear power plants.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.     

Structure of the spatial periphery of the <Superscript>11</Superscript>Li and <Superscript>11</Superscript>Be isobars

On the basis of the shell model with an extended basis, the structure of ⁹Li-⁹Be to ¹¹Li-¹¹Be nuclei is examined with allowance for the competition of ^jj coupling and Majorana exchange forces via considering the sequential addition of neutrons, and the respective wave functions are determined. A formalism for calculating the spectroscopic factor for a dineutron and for individual neutrons in nuclei whose wave functions incorporate the mixing of shell configurations is developed. The reactions ⁹Li(t, p)¹¹Li and ⁹Be(t, p)¹¹Be treated with allowance for the mechanisms of dineutron stripping and a sequential transfer of two neutrons are considered as an indicator of the proposed structure of lithium and berylliumisotopes. The parameters of the optical potentials, the wave functions for the bound states of transferred particles, and the interaction potentials corresponding to them are determined from a comparison of the theoretical angular distribution of protons from the reaction ⁹Be(t, p)¹¹Be with its experimental counterpart. It is shown that a dineutron periphery of size about 6.4 fm is present in the ¹¹Li nucleus and that a single-neutron periphery of size about 8 fm is present in the ¹¹Be nucleus.     

Study of fusion and nucleon transfer channels in the <Superscript>197</Superscript>Au + <Superscript>6</Superscript>He reaction in an energy range of <Superscript>6</Superscript>He to 20 Mev/A

New data on the cross sections of reactions occurring during the interaction of ⁶He nuclei with ¹⁹⁷Au at energies of ⁶He from 40 to 120 MeV are presented. The experiments were performed in the ACCULINNA secondary beam separator of the Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. To identify the reaction products, the activation method for measuring the gamma activity of the target assembly of thin foils was used. The excitation functions for fusion reactions involving the evaporation of up to ten neutrons from the compound nucleus as well as reactions with the emission of charged particles and nucleon transfer in the investigated energy region are obtained. Data analysis was carried out using two codes: ALICE-MP and NRV. The cross sections for the (⁶He, xn) reactions occurring through the compound nucleus are mostly in agreement with the results of model calculations based on the statistical approach. It is shown that, up to the energies of 114 MeV, the cross-section drop in the complete fusion reactions is negligible. The experimental excitation functions of reactions leading to the formation of isotopes of mercury and gold (transfer reaction) indicate that the main contribution to their formation is made by direct processes and that evaporation reactions (⁶He, pxn) and (⁶He, αxn) play a minor role, as is evidenced by a comparison of the measured cross sections with the calculation results.     

Prompt-fission-neutrons spectra of <Superscript>238</Superscript>U

The spectra of prompt fission neutrons from the reaction ²³⁸U(n, F) for neutrons of energy in the range E _n ≤ 20 MeV are interpreted within the statistical model. It is shown that exclusive spectra of prefission neutrons emitted in (n, xnf) reactions play a decisive role in describing the observed promptfission-neutron spectra and determine the average energies of prompt-fission neutrons. The dependence of the effect of prefission neutrons on the fissility of a target nucleus is demonstrated for the reactions ²³²Th(n, F), ²³⁵U(n, F), and ²³⁹Pu(n, F).     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Adiabatic elastic moduli in ZnSe : Mn<Superscript>2+</Superscript> and ZnSe : V<Superscript>2+</Superscript> crystals

The temperature dependences of the elastic moduli C ₄₄ (C ₁₁ ? C ₁₂)/2 and C _l = (C ₁₁ + C ₁₂ + 2C ₄₄)/2 of ZnSe : V²⁺ (impurity concentration, 6 × 10¹⁸ cm^?3) and ZnSe : Mn²⁺ (9.4 × 10²⁰ cm^?3) are measured in the temperature range 1.4–100.0 K at frequencies of 52 and 156 MHz. The temperature dependences of the adiabatic elastic moduli are derived. It is established that softening of the symmetry modules is observed only in the crystal with an impurity having orbitally degenerate states.     

Study of the Involvement of <Superscript>8</Superscript>Be and <Superscript>9</Superscript>B Nuclei in the Dissociation of Relativistic <Superscript>10</Superscript>C, <Superscript>10</Superscript>B,and <Superscript>12</Superscript>C Nuclei

The results obtained by estimating the contribution of 8Be and 9B nuclei to the coherent dissociation of ¹⁰C, ¹⁰B, and ¹²C relativistic nuclei in nuclear track emulsions (“white” stars) are presented. The selection of white stars accompanied by 9B leads to a distinct peak appearing in the distribution of the excitation energy of 2α2p ensembles and having a maximum at 4.1 ± 0.3 MeV. A 8Be nucleus manifests itself in the coherent-dissociation reaction ¹⁰B → ²He + H with a probability of (25 ± 5)%, (14 ± 3)% of it being due to 9B decays. The ratio of the branching fractions of the ⁹B + n and ⁹Be + p mirror channels is estimated at 6 ± 1. An analysis of the relativistic dissociation of ¹²C nuclei in a nuclear track emulsion revealed nine 3α events corresponding to the Hoyle state.     

Coherence and recombination in two-dimensional atomic hydrogen on the surface of superfluid <Superscript>4</Superscript>He

Experimental results on the achievement of high degrees of quantum degeneration in two-dimensional atomic hydrogen (2D H↓) by the magnetic-compression method are analyzed by taking into account current data on the binding energy E _a = 1.14(1) K of hydrogen atoms with the ⁴He surface and the constant K _ab of the two-particle exchange recombination of adsorbed H atoms. The behavior of pair and three-particle correlation functions, as well as the transverse delocalization of the wavefunction of adsorbed atoms due to their interaction with each other, is taken into account self-consistently. A new mechanism of cooling of the compression region by means of the flow of H atoms on the helium surface with the subsequent evaporation and emission from a magnetic trap is proposed. This mechanism prevails at high densities, whereas the heat transfer at low densities occurs owing mainly to the interaction of ripplons with the phonons of the helium film. Existing data corroborate the achievement of the phase density σλ² ? 10, which is certainly higher than the density necessary for both the arrangement of local coherence in 2D H↓ and its transition to the superfluid state. The results agree with the representations on quasi-condensation; however, direct evidence of this phenomenon is not revealed. The probability of three-particle dipole recombination that is corrected for the quantum correlation and delocalization is equal to 7(2) × 10^?26 cm⁴ s^?1 (T = 0.15, …, 0.21 K, B = 6.6 T, and σλ² = 1, …, 9). The results are compared with other theoretical and experimental data.