Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

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.     

Reliability of the data on the cross sections of the partial photoneutron reaction for <Superscript>63,65</Superscript>Cu and <Superscript>80</Superscript>Se nuclei

The cross sections of partial photoneutron reactions are evaluated for the ^63,65Cu and ⁸⁰Se isotopes. The cross sections are free of systematic uncertainties from shortcomings of the experimental methods for neutron multiplicity sorting based on measurements of neutron energy used in experiments with quasimonoenergetic annihilation photon beams. An experimental-theoretical method is used to evaluate cross sections σ^eval(γ, in)= F_i^theor σ^exp(γ, xn), where ratios F_i^theor = σ^theor(γ, in)/σ^theor(γ, xn) = σ^theor(γ, in)/σ^theor[(γ, 1n) + 2(γ, 2n) + …] are calculated using a combined model of photonuclear reactions, and σ^exp(γ, xn) is the experimental cross section of the neutron yield reaction free from neutron multiplicity sorting problems. The cross sections are evaluated for reactions (γ, 1n) and (γ, 2n) for the ^63,65Cu and ⁸⁰Se isotopes, and for the total photoneutron reaction σ(γ, Sn) = σ[(γ, 1n) + (γ, 2n) + …]. It is shown that noticeable deviations of the experimental cross sections from the evaluated values result from the unreliable sorting of neutrons between the channels with multiplicities 1 and 2.     

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.     

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.     

Single-electron charge transfer and excitations at collisions between Bi<Superscript>4+</Superscript> ions in the kiloelectronvolt energy range

Pioneering theoretical data for single-electron charge transfer and excitations due to collisions between Bi⁴⁺ ions in the ground (6s) and metastable (6p) states are gained in the collision energy interval 5–75 keV in the center-of-mass frame. The cross sections of the processes are calculated in terms of the close-coupling method in the basis of two-electron quasi-molecular states for the Coulomb trajectory of nuclei. It is found that single-electron capture into the singlet 6s ² states of Bi³⁺ ions makes a major contribution to the charge transfer total cross section for Bi⁴⁺(6s) + Bi⁴⁺(6s) collisions (reaction 1), whereas single-electron capture into the singlet 6s6p states is the basic contributor to the total cross section in Bi⁴⁺(6s) + Bi⁴⁺(6p) collisions (reaction 2). In the collision energy interval mentioned above, the collision cross sections vary between 1.2 × 10^?17 and 1.9 × 10^?17 cm² for reaction 1 and between 3.8 × 10^?17 and 5.3 × 10^?17 cm² for reaction 2. In reaction 1, the 6s → 6p excitation cross sections vary from 0.6 × 10^?16 to 0.8 × 10^?16 cm² for the singlet channel and from 2.2 × 10^?16 to 2.8 × 10^?16 cm² for the triplet channel. The calculation results are compared with the data obtained in experiments with crossed ion beams of kiloelectronvolt energy. The fraction of metastable ions in the beams is estimated by comparing the experimental data with the weighted average theoretical results for the cross sections of reactions 1 and 2. From the data for the charge transfer cross sections, one can estimate particle losses in relativistic beams due to a change in the charge state of the ions colliding with each other in the beam because of betatron oscillations.     

Microscopic description of diffractive deuteron breakup by <Superscript>3</Superscript>He nuclei

A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction ²H(³He, ³Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by ³He nuclei at the projectile energy of 89.4MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated.     

Formation of cumulative nuclei of <Superscript>4</Superscript>He in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The formation of cumulative nuclei of ⁴He in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon was investigated for the first time under conditions of 4π acceptance. The slope parameter of the invariant cross sections for the formation of cumulative nuclei of ⁴He was determined, and new data on the correlations between the yield of these cumulative nuclei and the yield of charged particles and fragments in ¹⁶Op interactions were obtained.     

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.     

Diffractive dissociation of deuterons and exotic nuclei <Superscript>6</Superscript>He and <Superscript>19</Superscript>C

A theory is developed for describing the diffractive dissociation of loosely bound two-cluster nuclei in the nuclear and Coulomb fields of nuclei having a diffuse boundary. The energy spectra of charged products of the breakup of ²H, ⁶He, and ¹⁹C nuclei are calculated on the basis of the proposed approach, and the results are found to be rather sensitive to nuclear structure. For some angles of neutron and proton emission from the reaction ¹²C(d, np)¹²C, the calculated cross sections are in satisfactory agreement with the results of kinematically complete experiments performed recently to study the breakup of intermediate-energy deuterons.     

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.     

Cross sections of the photoneutron reaction for <Superscript>141</Superscript>Pr and <Superscript>186</Superscript>W nuclei,estimated from physical criteria of data reliability

Using objective physical criteria for data reliability, cross sections of partial photoneutron reactions (γ, 1n), (γ, 2n) and (γ, 3n) that are free of the shortcomings of neutron multiplicity sorting methods used on beams of quasimonoenergetic annihilation photons are obtained for ¹⁴¹Pr and ¹⁸⁶W nuclei. Evaluation is performed using the experimental–theoretical method (ETM), based on the experimental cross section of neutron yield reaction σ^exp(γ, xn) = σ^exp(γ, 1n) + 2 σ^exp(γ, 2ⁿ) + 3 σexp(γ, 3n) + … and ratios F _i ^theor= σ^theor(γ, in)/σ^theor(γ, xn) calculated within the combined model (CM) of photonuclear reactions, which stipulates that σ^eval(γ, in) = F _i ^theor σ^exp(γ, xn). It is found that for ¹⁴¹Pr and ¹⁸⁶W, ratios F ^exp _i do not contradict the data reliability criteria only at energies up to ~21 and ~22 MeV, respectively. At the same time, there are notable discrepancies between F _i ^theor and F ^exp _i, and thus between the evaluated and experimental cross sections of reactions. It is shown that the discrepancies between the evaluated and experimental cross sections are due to the assumed unreliable experimental distribution of neutrons in the channels with multiplicities 1, 2, and 3.     

Microscopic multichannel investigation of the <Superscript>6</Superscript>Li + <Emphasis Type="Italic">n</Emphasis> seven-nucleon nuclear system at low energies

The ⁶Li + n seven-nucleon nuclear system is studied at low energies within a microscopic approach based on the multichannel algebraic version of the resonating group model. The partial and total cross sections for the ⁶Li(n, t)⁴He reaction are calculated. The contributions of the various partial cross sections to the energy dependence of the total cross section are considered. The results of the calculations are found to be in a good agreement with experimental data.     

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 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.     

Single Folding Optical Potential for Elastic Scattering of Protons from <Superscript>14</Superscript>N and <Superscript>16</Superscript>O in a Wide Range of Energies

Available experimental data for protons elastically scattered from ¹⁴N and ¹⁶O target nuclei are reanalyzed within the framework of single folding optical potential (SFOP) model. In this model, the real part of the potential is derived on the basis of single folding potential. The renormalization factor N _r is extracted for the two aforementioned nuclear systems. Theoretical calculations fairly reproduce the experimental data in the whole angular range. Energy dependence of real and imaginary volume integrals as well as reaction cross sections are discussed.     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Physical criteria for the reliability of data on the photodisintegration of the <Superscript>89</Superscript>Y nucleus

Experimental photonuclear reaction cross sections obtained in experiments using quasimonoenergetic annihilation, monoenergetic tagged photons, and bremsstrahlung γ-radiation are analyzed using physical criteria for the reliability of data on the ⁸⁹Y nucleus. It is found that the reliability of data on the cross sections of partial reactions (γ, 1n) and (γ, 2n), obtained by means of photoneutron multiplicity sorting, is highly doubtful. Reliable cross sections of reactions (γ, 1n) and (γ, 2n) are obtained using the experimental–theoretical method (ETM) for evaluating using both experimental cross sections of neutron yield reaction σ^exp(γ, xn) that are free of neutron multiplicity problems, and theoretically calculated F _i ^theor ratios of the cross sections of definite (i) partial reactions to cross section σ^theor(γ, xn). It is shown that the evaluated cross sections differ noticeably from the experimental data.     

Suppression of the chain nuclear fusion reaction based on the <Emphasis Type="Italic">p</Emphasis>+<Superscript>11</Superscript>B reaction because of the deceleration of alpha particles

It is shown that a rapid deceleration of alpha particles in matter of electron temperature up to 100 keV leads a strong suppression of the chain nuclear fusion reaction on the basis of the p+¹¹B reaction with the reproduction of fast protons in the α+¹¹B and n+¹⁰B reactions. The statement that the chain nuclear fusion reaction based on the p+¹¹B reaction with an acceleration of ¹¹B nuclei because of elastic alpha-particle scattering manifests itself in experiments at the PALS (Prague Asterix Laser System) facility is analyzed.     

Neutron single-particle structure of <Superscript>48</Superscript>Ca, <Superscript>50</Superscript>Ti, <Superscript>52</Superscript>Cr, <Superscript>54</Superscript>Fe,and <Superscript>56</Superscript>Ni nuclei

The change in the neutron single-particle structure of (1f?2p)-shell magic nuclei near the Fermi energy with an increase in the number of protons in the 1f _7/2 subshell from 0 for ⁴⁸Ca to 8 for ⁵⁶Ni has been investigated. Good agreement of the experimental and estimated values of the single-particle energies E _nlj of the bound states of neutrons in these nuclei with the results of calculations within the dispersive optical model is obtained.