Diffractive scattering of <Superscript>7</Superscript>Be and <Superscript>8</Superscript>B nuclei by <Superscript>12</Superscript>C nuclei

A theory of the diffractive scattering of loosely bound three-cluster nuclei by nuclei was developed with allowance for Coulomb interaction. The differential cross sections for the scattering of projectile exotic nuclei ⁷Be and ⁸B by ¹²C nuclei at an energy of 40 MeV per nucleon were calculated within the proposed formalism. The results describe satisfactorily relevant experimental data.     

Polarization phenomena in the intermediate energy elastic deuteron scattering from <Superscript>16</Superscript>C and <Superscript>16</Superscript>O nuclei

A model based on the multiple diffraction scattering theory and the α-cluster model with dispersion of target nuclei is proposed for describing the behavior of observables for the elastic deuteron scattering from ¹²C and ¹⁶O nuclei at intermediate energies. Differential cross-sections and analyzing powers calculated within this approach for incident-deuteron energies of 400 and 700 MeV are in a reasonable agreement with experimental data.     

Coupled-channels analysis of K<Superscript>+</Superscript> scattering from <Superscript>6</Superscript>Li and <Superscript>12</Superscript>C using the Watanabe superposition model

Coupled-channels calculations for the elastic and inelastic scattering of K⁺ at 715 MeV/c by ⁶Li and ¹²C at 635, 715 and 800 kaon Lab momenta have been analysed. The optical potentials of ¹²C and ⁶Li are calculated in terms of the alpha-particle and deuteron optical potentials. Good fits to the experimental data and phenomenological calculations are obtained for ⁶Li and ¹²C nuclei.     

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.     

Nuclear rainbow in the elastic scattering of <Superscript>16</Superscript>O nuclei on carbon isotopes

An investigation of refractive effects in heavy-ion scattering is continued. For the elastic scattering of ¹⁶O nuclei on a ¹³C target at E(¹⁶O) = 132 MeV, the differential cross sections are measured for the first time in addition to previous measurements for targets from the carbon isotopes ¹²C and ¹⁴C. Airy structures that are similar for all isotopes and which have close cross sections are observed and are found to be consistent with the energy systematics of Airy minima that were obtained previously. The volume integrals of the real and imaginary parts of the optical potentials found in the present study are nearly identical for all of the isotopes considered here and are also in good agreement with the systematics obtained previously.     

Semiclassical description of the <Superscript>6</Superscript>He+<Superscript>12</Superscript>C elastic scattering

The results of the elastic scattering of ⁶He+¹²C systemat E _Lab = 18 MeV by using the barrier and internal wave decomposition of the S-matrix element within the framework of the WKB method are presented. This is the first detailed study for the interaction of the exotic ⁶He nucleus on different stable nuclei by using a semiclassicalmethod. In this paper, we show that in order to obtain the elastic scattering cross section of the ⁶He+¹²C systemat energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling effects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum-mechanical one.     

Calculation analyzing power in the elastic scattering of protons on <Superscript>15</Superscript>C and <Superscript>15</Superscript>N nuclei in the diffraction theory

Shell-model wave functions are used to calculate the vector analyzing power in the elastic scattering of 0.2, 0.6, and 1 GeV protons on ¹⁵C and ¹⁵N nuclei within the Glauber diffraction theory. Single and double collisions are allowed for upon the decomposition of multiple scattering. It is shown that the number of oscillations and the amplitude of the analyzing power increase with rising energy in the same angular range.     

Nuclear rainbow in elastic scattering of <Superscript>9</Superscript>Be nuclei

A systematic investigation of the elastic scattering of the ⁹Be nucleus, which is among themost loosely bound stable nuclei was performed.Differential cross sections for elastic ⁹Be + ¹⁶O scattering were measured at a c.m. energy of 47.5 MeV (beam of 132-MeV ¹⁶O nuclei). Available data at different energy values and data for neighboring nuclei were included in our analysis. As a result, the very fact of rainbow scattering was reliably established for the first time in systems involving ⁹Be. In addition, the analysis in question made it possible to identify Airy minima and to determine unambiguously the nucleus-nucleus potential with a high probability.     

Interaction of intermediate-energy protons with <Superscript>20</Superscript>Ne and <Superscript>24</Superscript>Mg nuclei within the multiple-scattering model

Observables of the elastic and inelastic scattering of 800- and 250-MeV protons on ²⁰Ne and ²⁴Mg nuclei were calculated on the basis of the theory of multiple diffractive scattering and the dispersive α-cluster model. The ²⁰Ne and ²⁴Mg nuclei were assumed to consist of a core (¹⁶O nucleus) and additional alpha-particle clusters, which could be situated with the highest probability both in the vicinity of the center of mass of the core and outside the core. The multiparticle densities of these nuclei and single-particle nucleon-distribution densities as obtained from the dispersive α-cluster model were used in the calculations. The differential cross sections and polarizations for elastic and inelastic p ²⁰Ne and p ²⁴Mg scattering at the energy of 800 MeV are in better agreement with experimental data than the analogous calculations at the energy of 250 MeV. The spin-rotation functions calculated in the singleparticle approximation for elastic p ²⁰Ne and p ²⁴Mg scattering at these two energy values differ qualitatively from their counterparts calculated on the basis of the dispersive α-cluster model.     

Charge topology of the coherent dissociation of relativistic <Superscript>11</Superscript>C and <Superscript>12</Superscript>N nuclei

The charge topology of coherent-dissociation events is presented for ¹¹С and ¹²N nuclei of energy 1.2 GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for ⁷Be, ^8,10B, ^9,10C, and ¹⁴N nuclei.     

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.     

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.     

Raman spectroscopy of isotopically pure (<Superscript>12</Superscript>C, <Superscript>13</Superscript>C) and isotopically mixed (<Superscript>12.5</Superscript>C) diamond single crystals at ultrahigh pressures

The Raman scattering by isotopically pure ¹²C and ¹³C diamond single crystals and by isotopically mixed ^12.5C diamond single crystals is studied at a high accuracy. The studies are performed over a wide pressure range up to 73 GPa using helium as a hydrostatic pressure-transferring medium. It is found that the quantum effects, which determine the difference between the ratio of the Raman scattering frequencies in the ¹²C and ¹³C diamonds and the classical ratio (1.0408), increase to 30 GPa and then decrease. Thus, inversion in the sign of the quantum contribution to the physical properties of diamond during compression is detected. Our data suggest that the maximum possible difference between the bulk moduli of the ¹²C and ¹³C diamonds is 0.15%. The investigation of the isotopically mixed ^12.5C diamond shows that the effective mass, which determines the Raman frequency, decreases during compression from 12.38 au at normal pressure to 12.33 au at 73 GPa.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

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.     

Unexpected transparency in the scattering of fragile <Superscript>6</Superscript>Li and <Superscript>6</Superscript>He Nuclei

It is found that the scattering of the fragile nucleus ⁶Li from ¹²C and ¹⁶O is unexpectedly transparent. It is shown that the internal-wave contribution is significantly large in the scattering, which suggests that some transparency could persist in the scattering involving the fragile nucleus ⁶He.     

Interference effects in proton scattering on <Superscript>15</Superscript>N nuclei at intermediate energies

The differential cross section for proton scattering on ¹⁵N nuclei is calculated within Glauber diffraction theory at energies of 0.2, 0.6, and 1.0 GeV. Use is made of the shell-model wave function for the ¹⁵N nucleus. The contribution of single and double collisions to the Glauber operator Ω is taken into account. The sensitivity of the differential cross sections to the contributions of scattering on nucleons from different shells, to the parameters of the elementary pN amplitude, and to the energy of projectile protons is investigated. It is shown that the interference between amplitudes corresponding to different collision multiplicities, as well as between the amplitudes for scattering on nucleons from different shells, determines special features of the cross section.     

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.     

Shell-model structure of exotic nuclei beyond <Superscript>132</Superscript>Sn

We report on a study of exotic nuclei around doubly magic ¹³²Sn in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the bare potential is renormalized by constructing a smooth low-momentum potential, V_low-k, that is used directly as input for the calculation of the effective interaction. In this paper we focus attention on the nuclei ¹³⁴Sn and ¹³⁵Sb which, with an N/Z ratio of 1.68 and 1.65, respectively, are at present the most exotic nuclei beyond ¹³²Sn for which information exists on excited states. Comparison shows that the calculated results for both nuclei are in very good agreement with the experimental data. We present our predictions of the hitherto unknown spectrum of ¹³⁶Sn.