Excitation functions of <Superscript>6</Superscript>Li incomplete fusion reactions with Pt nuclei

Experimentally determined excitation functions of the transfer reactions producing ^194–199Au and ^197m Hg isotopes during the interaction of ⁶Li with Pt nuclei are presented. An analysis of the experimental data as compared to EMPIRE-2.18 model calculations and experimental results on the d + ^natPt and α + ^natPt reactions allow determination of the interaction channels of d- and α-clusters in ⁶Li with the target nucleus. The results from model calculations of the reaction cross sections appear considerably lower than the experimental data. This discrepancy in describing the reactions with weakly bound nuclei is probably associated with the incomplete consideration of various interaction channels in the EMPERE-2.18 software. It is clear that a complete understanding of the interaction pattern in these processes requires consideration of the direct channels of ⁶Li nucleus cluster transfer during ⁶Li breakup near the Coulomb barrier.     

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.     

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.     

Deuteron scattering on <Superscript>6</Superscript>Li at an energy of 25 MeV

At an energy of 25 MeV and in the angular range 7°−175° in the laboratory frame, angular distributions were measured for elastic deuteron scattering on ⁶Li nuclei and for the respective inelastic-scattering processes accompanied by the transitions to the ground state (1+) of the ⁶Li nucleus and to its excited state at E _x = 2.186 MeV (J ^π = 3⁺). The resulting data were analyzed on the basis of the optical model of the nucleus and the coupled-reaction-channel method with allowance for the mechanism of alpha-particle-cluster exchange. It is shown that only upon including, in the analysis, channel coupling and the exchange mechanism can the experimental cross sections for elastic and inelastic scattering be reproduced over the entire range of angles.     

<Superscript>4</Superscript>He<Superscript>3</Superscript>H<Superscript>2</Superscript>H three-body model of the <Superscript>9</Superscript>Be nucleus

Within the framework of the single-channel approximation, an {αtd} model of the ⁹ Be nucleus is presented. A comparative analysis of the t ⁶ Li wave functions describing relative motion of bound states constructed in {ααn} and {αtd} cluster representations is carried out on the example of calculations of the ⁹ Be(γ,t₀)⁶ Li process characteristics. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 85–89, January, 2008.     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

Production of the (<Emphasis Type="Italic">I</Emphasis> = 19/2) high-spin isomer <Superscript>135</Superscript>Cs in photonuclear reactions

The yields of ¹³⁵Cs nuclei in a high-spin (19/2) isomeric state and of nuclei neighboring it were measured for photonuclear reactions of the (γ, f) and (γ, α) types. The experiments in question were performed by using bremsstrahlung from a microtron at the maximum electron energy of 25 MeV. The product nuclei were identified by their half-lives and by the lines of gamma radiation emitted in their decay, and the reaction yields R were determined by the ratios of the intensities of these lines to the bremsstrahlung flux. The cross sections for isomer production were calculated, and the angular momenta of product nuclei immediately before the cascade of gamma transitions populating the ground or an isomeric nuclear state were evaluated on the basis of these results. An enhanced yield of the high-spin isomer of ¹³⁵Cs in the fission reaction in relation to the respective (γ, α) reaction and in relation to the results of the calculations is found.     

Peculiarities in total cross sections of reactions with weakly bound nuclei <Superscript>6</Superscript>He, <Superscript>9</Superscript>Li

The energy dependence of the total cross sections for the ⁶He + Si and ⁹Li + Si reactions was measured at beam energies between 5 and 20 MeV per nucleon. The results agree with experimental data published for the ⁶He + Si reaction. New data are obtained for the ⁹Li + Si reaction in the vicinity of a local enhancement of the total cross section. A theoretical analysis of the possible reasons behind the appearance of this peculiarity in the case of collisions of ⁶He and ⁹Li nuclei with silicon target nuclei is performed. In particular, the enhancement may owe its origin to the effect of loosely bound projectile nucleons.     

Fragmentation of <Superscript>7</Superscript>Li relativistic nuclei on a proton into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

In a track nuclear photoemulsion exposed to a beam of ⁷Li nuclei accelerated to a momentum of 3 GeV/c per nucleon at the synchrophasotron of the Joint Institute for Nuclear Research (JINR, Dubna), 13 events in which ⁷Li nuclei interacting with protons break up into ³H and ⁴He fragments were detected among 3730 inelastic-interaction events. For this fragmentation channel, the cross section was found to be 8 ± 2 mb. The average value of the fragment total transverse momentum was 214 ± 5 MeV/c. This value exceeds markedly the average value of the transverse-momentum transfer in the coherent dissociation of ⁷Li nuclei on track-emulsion nuclei (166±5MeV/c). The recoil-proton transverse momentum was on average 98% of the total proton momentum. The longitudinal-momentum distribution of protons was characterized by a variance of 16 MeV/c and a mean value of 37 ± 2MeV/c.     

Analyzing the p(<Superscript>6</Superscript>He,n gamma)<Superscript>6</Superscript>Li reaction

The differential cross section of the charge-exchange reaction p(⁶He, n)⁶Li(0⁺, 3.56 MeV) is calculated within the context of direct mechanisms: the stripping of a heavy ⁵He cluster, replacing a virtual neutron with a proton in the 5He cluster field, and the mechanism of consecutive transfer of a neutron and an α particle. The spatial structure of initial and final nucleus is determined from the dependence of various direct mechanisms contributions from spatial configurations.     

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.     

Three-body structure of <Emphasis Type="Italic">A</Emphasis> = 9 isobars (Be,Li, and C) and elastic proton scattering

Density profiles and static features (radii, magnetic moments, and quadrupole moments) are calculated with the wave functions found for A = 9 isobars on the basis of the α + α + n three-body model for the ⁹Be nucleus, the ⁷Li + n + n three-body model for the ⁹Li nucleus, and the ⁷Be + p + p three-body model for the ⁹C nucleus. The differential cross sections and analyzing powers for elastic proton scattering on ⁹Be at E = 220 MeV and 1.0 GeV and on ⁹Li and ⁹C at E = 700 and 60 MeV/nucleon (in inverse kinematics) are calculated within Glauber diffraction theory. All of the results are compared with available experimental data and with the results of the calculations performed by other authors.     

Measurement of the excitation function for the <Superscript>7</Superscript>Li(t,p)<Superscript>9</Superscript>Li reaction using detection of delayed neutrons

The excitation function for the ⁷Li(t, p)⁹Li reaction is measured at the EGP-10 electrostatic tandem accelerator (VNIIEF) at the incident triton energies E _t = 5–11.3 MeV. The measurements were based on detection of delayed neutrons resulting from the decay of ⁹Li nuclei. The neutrons were detected by the 4π detector consisting of ³He counters enclosed in a polyethylene moderator. A pulsed mode was used for irradiating the LiF target (210 μg cm^?2) of natural isotopic composition on the tantalum backing. Absolutization of the excitation function was performed against the ⁷Li(p, n) reaction cross sections.     

Nuclear deformation and the two-neutrino double- β decay in <Superscript>124, 126</Superscript>Xe , <Superscript>128, 130</Superscript>Te , <Superscript>130, 132</Superscript>Ba and <Superscript>150</Superscript>Nd isotopes

The two-neutrino double-beta decay of ^{124, 126}Xe , ^{128, 130}Te , ^{130, 132}Ba and ¹⁵⁰Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2ν β^-β^- half-lives of ^{128, 130}Te , and ¹⁵⁰Nd isotopes, and 2ν β⁺β⁺ , 2ν β⁺ EC and 2ν ECEC for ^{124, 126}Xe and ^{130, 132}Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2 : 0⁺ → 2⁺) , static quadrupole moments and g -factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element M _2ν is confirmed.     

New approximations to the energy dependences of the total cross sections for the proton-induced fission of <Superscript>197</Superscript>Au, <Superscript>203</Superscript>Tl, <Superscript>nat</Superscript>Pb,and <Superscript>209</Superscript>Bi nuclei

The total cross sections for ¹⁹⁷Au and ²⁰³Tl fission induced by protons of energy varied from about 200 to 1000 MeV with a step of about 100 MeV are measured. New approximations to the energy dependences of the cross sections for the proton-induced fission of ¹⁹⁷Au, ²⁰³Tl, natPb, and ²⁰⁹Bi nuclei are presented and discussed. For all of these nuclei, exponential functions are used as approximations.     

Heavy lithium isotope <Superscript>11,12</Superscript>Li production in pion absorption reactions on a <Superscript>14</Superscript>C radioactive target

The results from an experimental search for the production of heavy lithium isotopes ^11,12Li in stopped π⁻-meson absorption reactions on a ¹⁴C radioactive target are presented. A pronounced peak is observed in the missing mass spectrum of the ¹⁴C(π⁻, pp)X reaction, which is associated with the formation of a nucleon-unstable ¹²Li state with the following resonance parameters: E _R = 4.0 ± 0.2 MeV and Γ = 1.1 ± 0.2 MeV. Resonance parameters of three low-lying ¹¹Li excited states were determined in the ¹⁴C(π⁻, pd)X, reaction.     

Spectroscopy of the <Superscript>9</Superscript>Li isotope in stopped-pion absorption reactions

The origin of the ⁹Li isotope is sought in missing-mass spectra measured in ¹¹B(π⁻, d)X, ¹²C(π⁻, pd)X, and ¹⁴C(π⁻, dt)X stopped-pion absorption reactions. The parameters of the three observed low-lying excited states coincide with the literature data. A state with excitation energy E _x = 9.1 ± 0.1 MeV, lying above the threshold of ⁹Li decay into ⁶He + t, is observed for the first time.     

Evaluation of the <Superscript>52</Superscript>Cr–<Superscript>52</Superscript> Cr Interaction via Spin-Flip Scattering

In order to evaluate g ₀, the interaction strength of a pair of ⁵²Cr atoms with total spin S = 0, a specially designed s-wave scattering of the pair has been studied theoretically. Both the incident atom and the target atom trapped by a potential are polarized previously but in reverse directions. Due to spin-flips, the outgoing atom may have spin component μ ranging from −3 to 3. The outgoing channels are classified by μ. The effect of g ₀ on the s-wave cross sections of each of these μ- channels has been predicted. In particular, when the parameters of the trapping potential are given around their optimal values so that the cross sections can be maximized, distinguished features of the dependence of the cross sections on g ₀ are found. These features are helpful for evaluating g ₀.     

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.     

Spectroscopy of the <Superscript>10</Superscript>Li isotope in stopped pion absorption reactions on a <Superscript>14</Superscript>C radioactive target

A search for the ¹⁰Li formation was performed in missing mass spectra measured in stopped pion absorption reactions ¹⁴C(π ⁻, pt)X and ¹⁴C(π ⁻, dd)X. Three excited states of ¹⁰Li were found. The broad state with a resonance energy of E _R = 6.13 ± 0.11 MeV has the highest excitation energy in comparison with levels observed earlier.