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.     

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.     

Excess neutron nucleus <Superscript>11</Superscript>Be as a product of reaction (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">p</Emphasis>)

The (t, p) reaction on the ⁹Be nucleus is analyzed using the mechanisms of dineutron stripping and ⁸Li heavy cluster stripping. It is shown that in the shell model, the wave function of the ¹¹Be(1/2⁺) nucleus formed by adding two neutrons to the 9Be nucleus is constructed from a ¹⁰Be(0⁺) core and a 2s-neutron. This concept of the ¹¹Be(1/2⁺) structure allows us to calculate the reduced width of tritium and a dineutron with a relative orbital angular momentum equal to 1. The differential cross section of the (t, p) reaction is calculated with allowance for the contribution from both mechanisms. The agreement between the theoretical and experimental cross sections of dineutron stripping at narrow angles θ_p confirms the shell model can be used to describe the states of nuclei with complex structure and mixed configurations of different shells.     

On the hyperfine structures of the ground state(s) in the <Superscript>6</Superscript>Li and <Superscript>7</Superscript>Li atoms

The hyperfine structure of the ground 2²S-states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus, we determine the hyperfine structure of the ground (doublet) 2²S-state(s) in the ⁶Li and ⁷Li atoms. Our predicted values (228.2058 and 803.5581 MHz, respectively) agree well with the experimental values 228.20528(8) MHz (⁶Li) and 803.50404(48) MHz (⁷Li [R.G. Schlecht and D.W. McColm, Phys. Rev. 142, 11 (1966)]). The hyperfine structures of a number of lithium isotopes with short lifetimes, including ⁸Li, ⁹Li, and ¹¹Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron ⁷Be⁺ and ⁹Be⁺ ions in their ground 2²S-states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet n³S-states of the four-electron atoms and ions.     

Nonempirical quantum-chemical calculation of the electric field gradient at the <Superscript>51</Superscript>V nucleus sites in alkali metavanadates

The electric-field gradient tensor at the vanadium nucleus site was calculated ab initio within a cluster model for chained vanadates XVO₃ (X=Li, Na, K). A comparison with experiment showed that it suffices to consider only small (VO₄)^3? and (V₃O₁₀)^5? clusters in crystals of this type. The calculation scheme stability with respect to increasing cluster size was analyzed.     

Searching for rare cluster configurations of <Superscript>14</Superscript>C nuclei in the pion absorption reaction

Analysis of the two-dimensional Dalitz plot measured in the reaction ¹⁴C(π^–, pd)X allows us to follow the absorption of pions by cluster ³p and identify signs of the configuration ³p + ¹¹Li in the ¹⁴C nucleus. The highly excited state of ^12,13Be beryllium isotopes with excitation energies E* ≈ 30 MeV and which decay with the emission of hydrogen isotopes is observed for the first time: ¹²Be* → p + ¹¹Li and ¹³Be* → d + ¹¹Li.     

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.     

Hyperfine magnetic anomaly in isotopic pairs <Superscript>151, 152</Superscript>Eu and <Superscript>152, 153</Superscript>Eu

High-resolution laser spectroscopy measurements of optical hyperfine splitting on the ^{151, 152, 153}Eu isotopes were performed on the atomic transition 4f ⁷6s ^{2 8} S _7/2 → 4f ⁷6s6p ⁶ P _5/2 at λ ≈ 564.58 nm. Values of the nuclear magnetic dipole and electric quadrupole moments are obtained from the measured hyperfine splitting and the magnetic hyperfine anomalies in the isotope pairs ^{151, 152}Eu and ^{152, 153}Eu are deduced. The absolute values of the hyperfine anomaly in both cases are unusually large: 5 (1)%. The possible sources causing these anomalies are discussed.     

<Superscript>53</Superscript>Cr, <Superscript>17</Superscript>O and <Superscript>14</Superscript>N nuclear quadrupole resonance in ammonium dichromate

The ⁵³Cr resonance frequency in ammonium dichromate has been detected at 4202 kHz giving a Qcc of 8404 kHz (assuming η= 0). Calculations suggest that the value of the ⁵³Cr quadrupole moment is about 84 mB lower that the currently accepted value. The resonance frequencies of two ¹⁷O nuclei have also been detected giving Qcc = 2800, 2890 kHz and η = 0.726, 0.780 respectively. The value for coupling and asymmetry parameter for ¹⁴N has been refined using zero field NQR giving a value Qcc = 78.8 kHz and η= 0.645 the asymmetry value being considerably lower than the value previous reported.     

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.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript>-Li<Superscript>+</Superscript> centers in (Cr,Li): Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> synthetic forsterite

Synthetic single crystals of chromium-and lithium-doped forsterite, namely, (Cr,Li): Mg₂SiO₄, are studied using electron paramagnetic resonance spectroscopy. It is revealed that, apart from the known centers Cr³⁺(M1) and Cr³⁺(M2) (with local symmetries C_i and C_s, respectively), these crystals involve two new types of centers with C₁ symmetry, namely, Cr³⁺(M1)′ and Cr³⁺(M2)′ centers. The standard parameters D and E in a zero magnetic field [zero-field splitting (ZFS) parameters expressed in GHz] and principal components of the g tensor are determined as follows: D=31.35, E=8.28, and g=(1.9797, 1.9801, 1.9759) for Cr³⁺(M1)′ centers and D=15.171, E=2.283, and g=(1.9747, 1.9769, 1.9710) for Cr³⁺(M2)′ centers. It is found that the lowsymmetric effect of misalignment of the principal axes of the ZFS and g tensors most clearly manifests itself (i.e., its magnitude reaches 19°) in the case of Cr³⁺(M2)′ centers. The structural models Cr³⁺(M1)-Li⁺(M2) and Cr³⁺(M2)-Li⁺(M1) are proposed for the Cr³⁺(M1)′ and Cr³⁺(M2)′ centers, respectively. The concentrations of both centers are determined. It is demonstrated that, upon the formation of Cr³⁺-Li⁺ ion pairs, the M1 position for chromium appears to be two times more preferable than the M2 position. Reasoning from the results obtained, the R₁ line (the ²E → ⁴A₂ transition) observed in the luminescence spectra of (Cr,Li): Mg₂SiO₄ crystals in the vicinity of 699.6 nm is assigned to the Cr³⁺(M1)′ center.     

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.     

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.     

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).     

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.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

Structure of the <Superscript>6</Superscript>He nucleus in the three-particle model

The properties of the ⁶He nucleus were investigated in a three-particle approximation (a alpha-particle cluster plus two neutrons) on the basis of the variational approach by using a Gaussian basis. For nn and nα interactions, potentials that make it possible to describe S-wave phase shifts for elastic scattering and, simultaneously, to reproduce faithfully the energy and the size of the ⁶He nucleus were proposed. Characteristic structural features of this nucleus that are manifested in the density distributions, elastic form factor, pair correlation functions, and momentum distributions of particles constituting the ⁶He nucleus in the three-particle model were revealed.     

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.     

Nuclear spin resonance of <Superscript>53</Superscript>Cr in ferromagnetic CuCr<Subscript>2</Subscript>S<Subscript>4</Subscript>: Sb

The influence of variable valence on NSR spectra of ⁵³Cr nuclei in ferromagnetic CuCr_2?xSb_xS₄ (x = 0, 0.02, 0.07) at T = 77 K is considered. For quadrupole nuclei in locally anisotropic positions, the effects of variable valence result in averaging of not only the resonance frequency but also of the quadrupole and magnetic anisotropy constants. The significant difference between the experimental and calculated values of these constants indicates the important role of the intrinsic electronic contribution to the anisotropy of hyperfine fields of compounds containing Cr⁴⁺ ions. Additional lines caused by intrinsic and induced defects in the structure are observed in the spectra of doped and undoped compounds.     

Hyperfine structure of the energy levels of the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript> state of the Li-, B-, and N-like <Stack><Subscript>83</Subscript><Superscript>209</Superscript></Stack>Bi ions

The lowest order corrections, considering the electron-electron interaction, to the hyperfine structure of the energy levels of the Li-, B-, and N-like ₈₃ ²⁰⁹ BI ions in the 2p _3/2 state are calculated. The contributions of the magnetic dipole moment, electric quadrupole moment, and magnetic octupole moment are taken into account. The dynamic proton model is used, in which an electron interacts with a valence proton of a nucleus via photon exchange. In this model, the distribution of the electric and magnetic moments in a nucleus is taken into account automatically.