Measurement of the ~2H(~7Be,~6Li)~3He reaction rate and its contribution to the primordial lithium abundance

In the standard Big Bang nucleosynthesis(SBBN) model, the lithium puzzle has attracted intense interest over the past few decades, but still has not been solved. Conventionally, the approach is to include more reactions flowing into or out of lithium, and study the potential effects of those reactions which were not previously considered.~7Be(d,~3He)~6Li is a reaction that not only produces~6Li but also destroys~7Be, which decays to~7Li, thereby affecting~7Li indirectly. Therefore, this reaction could alleviate the lithium discrepancy if its reaction rate is sufficiently high.However, there is not much information available about the~7Be(d,~3He)~6Li reaction rate. In this work, the angular distributions of the~7Be(d,~3He)~6Li reaction are measured at the center of mass energies Ecm = 4.0 Me V and 6.~7Me V with secondary~7Be beams for the first time. The excitation function of the~7Be(d,~3He)~6Li reaction is first calculated with the computer code TALYS and then normalized to the experimental data, then its reaction rate is deduced. A SBBN network calculation is performed to investigate its influence on the~6Li and~7Li abundances. The results show that the~7Be(d,~3He)~6Li reaction has a minimal effect on~6Li and~7Li because of its small reaction rate. Therefore,the~7Be(d,~3He)~6Li reaction is ruled out by this experiment as a means of alleviating the lithium discrepancy.     

Theoretical investigation of the antimagnetic rotation in ~(104)Pd

The particle-number-conserving method based on the cranked shell model is used to investigate the antimagnetic rotation band in ~(104) Pd. The experimental moments of inertia and reduced B(E2) transition probabilities are reproduced well. The J~((2))/B(E2) ratios are also discussed. The occupation probability of each orbital close to the Fermi surface and the contribution of each major shell to the total angular momentum alignment as function of rotational frequency are analyzed. The backbending mechanism of the ground state band in ~(104) Pd is understood clearly and the configuration of the antimagnetic rotation after backbending is clarified. In addition, the crossing of a four quasiparticle state with this antimagnetic rotation band is also predicted. By examining the closing of the angular momenta of four proton holes towards the neutron angular momentum, the "two-shears-like" mechanism for this antimagnetic rotation is investigated and two stages of antimagnetic rotation in ~(104) Pd are clearly seen.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Spectral properties of helical quantum wires

The spectrum of states of a helical quantum wire has been investigated theoretically. Eigenstates were found using an exact method based on alternating-direction implicit (ADI) evolution in imaginary time, for a wavefunction defined at discrete points in occupation number space and a nearest-neighbor interaction. A helical wire is a special case of a one-dimensional superlattice with an infinitesimal glide symmetry and associated glide-momentum quantum number. The continuous symmetry prevents the appearance of band gaps. Energy eigenstates have unquenched angular momentum--angular momentum increases with glide momentum. Band anharmonicity and angular momentum nonlinearity demonstrate effects of centrifugal acceleration.     

Particle-Number Conserving Calculation for Low-Lying Excited High-K Multi-Quasiparticle Bands in 172,174Hf

Using the particle-number conserving method for treating the cranked shell model,the microscopic mechanism of the variation of the kinematic moments of inertia with rotational frequency ω for the rare-earth deformed nuclei ^172,174Hf is investigated. The observed J⁽¹⁾ and angular momentum alignment are reproduced satisfactorily in the PNC calculation,in which no free parameters are involved. The PNC analysis shows that the difference between the variations of J⁽¹⁾ with ω for the high K multi-quasiparticle bands and for ground state band is mainly due to the Pauli blocking effect of high j intruder orbitals near the Fermi surface.     

动量矩定理的统一形式

关于动量矩定理的矩心选取问题已经讨论了几十年^[1,2,8,4]。本文给出动量矩定理的统一形式。特别是导出了相对于速度瞬心的动量矩定理。在一般情况下它被认为是不可行的,然而我们用此定理解决了一个例题。该例通常被认为是相对于速度瞬心的动量矩定理不成立的有力证据。     

The angular momentum dependence of correlations in the ground state rotational spectra of20Ne and22Ne

Multi-Configuration-Hartree-Fock (MCHF) calculations with angular momentum projection before the variation of the internal degrees of freedom have been performed for the nuclei²⁰Ne and²²Ne. This procedure yields different correlated intrinsic states for the different members of a rotational band. Thus the angular momentum dependence of correlations has been studied. Experimentally, the ground state spectra of²⁰Ne and²²Ne show properties similar to the phase transitions observed in some rare earth nuclei which have been well reproduced through the present calculations. The calculated spectra andBE2-values show a significant improvement compared to the ones obtained by variation before the angular momentum projection is effected.     

Positron annihilation in copper

Electron momentum distribution in copper is studied through the angular correlation of positron annihilation radiation, by employing self-consistent linear combination of Gaussian orbitals band structure method. The two-photon momentum density is presented and analysed through three dimensional plots and angular momentum decomposed contributions. Calculation of two-dimensional angular correlation has been carried out in the independent particle approximation. The results for the analysis using Lock, Crisp and West theorem and the reciprocal form factors are also presented. The present theoretical results are compared with the experimental ones wherever possible, and the agreement in general, is good.     

Quasi-free scattering in the 6Li(d,dα)2H reaction at 52 MeV

In order to study the momentum distribution of an α-cluster in ⁶Li we have investigated the quasi-free scattering of deuterons in the ⁶Li(d, dα)²H reaction, using 52 MeV deuterons. The α-particle detector was kept at a fixed position of 30° and the second detector scanned over a range of coplanar angles. The α-cluster momentum distribution has been extracted by means of the plane-wave impulse approximation, using both the energy-sharing method and the angular correlation method. The momentum distributions so obtained are in good agreement with those obtained from other reactions such as (p, pα) and (α, 2α), and are compared with the spectator model. The reasons why the model works well are discussed. For the first time, to our knowledge, quasi-free scattering of deuterons on an α-cluster of a nucleus has been measured and analysed.     

The interaction of aligned 7Li with 58Ni

Elastic and inelastic scattering of aligned ⁷Li on ⁵⁸Ni was studied experimentally for several energies between 14 and 22 MeV. Complete sets of second-rank tensor analyzing powers were measured for two energies, 14.2 and 22.0 MeV. The shape-effect model has been used for a qualitative interpretation of the data. The success of this model indicates the spectroscopic deformation of ⁷Li to be the main source of the observed second-rank tensor analyzing powers. The result enters the formulation of the diffraction as well as the optical model both of which are used to improve the analysis of the data. Besides the parameters which determine the central interaction the spectroscopic deformation was the only adjustable parameter. The deformation was found to be negative, in agreement with the oblate shape of ⁷Li. However the extracted value of the deformation varies within a factor of two when comparing different experiments and/or analyses with different models. The second-rank tensor analyzing powers for projectile excitation are roughly explained by the assumption that the angular momentum transfer is perpendicular to the momentum transfer.     

Atomic-core dynamics and the electronic structure of some endo-and exohedral complexes of fullerenes with light elements

The atomic and electronic structure of some endo-, exo-, and endo-exohedral complexes of the fullerene C₆₀ with various guest atoms and molecules (He_n, H₂, and Li₂) are investigated using semiempirical and nonempirical quantum-chemical methods. The atomic core dynamics is studied by the method of molecular dynamics. It is shown that guest atoms and molecules in fullerene polyhedra acquire an orbital angular momentum due to the correlated motion of nuclei above the low-energy barriers of the potential surface within the carbon polyhedron even at low temperatures (from 4 to 78 K). The emergence of orbital angular momenta of nuclei of guest atoms and molecules is attributed to a change in the contribution of the orbital angular momentum of electrons to the potential surface of the complexes. The motion of Li ions in a polyhedron leads to blurring of the top of the valence band and to the emergence of a charge polarization wave in the carbon polyhedron.     

Direct and sequential processes in the 16O(7Li, 7Be)16N reaction

Calculations are presented for the ¹⁶O(⁷Li, ⁷Be)¹⁶N charge exchange reaction. For the direct reaction, the tensor interaction leads to form factors with large spin and angular momentum transfer which are important for the unnatural parity states. The (⁷Li, ⁶Li)(⁶Li,⁷Be) sequential process exhibits a strong J-dependence and is the dominant contribution to the natural parity states.     

Correspondence between zero angular momentum transfer cross sections of (6Li, 6He) reactions and the Gamow-Teller strength

The (⁶Li, ⁶He) cross sections on targets between ⁶Li and ⁴⁸Ca have been measured. The cross section due to zero angular momentum transfer appears to be correlated with the known Gamow-Teller strength. The reaction mechanism sometimes is dominated by multistep processes.     

Measurement of Angular Distribution for the ^8Li（p,d）^7Li Reaction

The ^8Li（p, d）^7 Li reaction plays an important role in the inhomogeneous Big Bang nucleosynthesis and in the seed-nuclide production phase for the r-process. For the first time, its angular distribution at backward angles was measured in inverse kinematics at Ec.m.=4.0 MeV by using an ^8Li secondary beam. The result of measurement includes the contributions of ^8Li（p, d0）^7Li and ^8Li（p, d1）^7Li^＊. The ^8Li（p, d0）^7Li component is estimated to be 40%-58% in the mixture angular distribution by analysing the measured result.     

Structures and angular distributions of slow and relativistic charged particles produced in 7Li-emulsion interactions at 3 GeV/c per projectile nucleon

Experimental results on the multiplicity distributions of various particles produced in the interactions of ⁷Li with emulsion nuclei at a momentum of 3 GeV/c per projectile nucleon are reported. A comparison with data on collisions induced by other nuclei at a nearly identical momentum per nucleon is presented in order to reveal the dependence on the projectile mass. The internal structure of ⁷Li is explored by studying the projectile fragment. The mean multiplicity of shower particles, 〈n _s〉, induced by ⁷Li is found to be less than that in the case of ⁶Li projectiles. The angular distributions of target fragments and relativistic charged secondaries are investigated. No shock-wave phenomena are observed. Forward-to-backward ratios are calculated for each case. The probability distributions for relativistic secondaries produced per unit rapidity are studied in detail, along with the rapidity densities and their dependence on the projectile and the target mass. A comparison of the angular spectra of shower particles produced in central and peripheral collisions supports the limiting-fragmentation hypothesis. The collisions in question seem to become more central with increasing shower-particle multiplicity.     

Angular momentum and cross sections for fusion with weakly bound nuclei: breakup,a coherent effect

Results for the cross section and average angular momentum for complete fusion at energies around the Coulomb barrier are presented for 7Li with 165Ho. Comparison of the cross sections with a one-dimensional barrier penetration model, using a potential consistent with the measured elastic scattering, showed a reduction above the barrier and an enhancement below it. An increase in the measured average angular momentum, , above the barrier and its consistency with that obtained from the fusion excitation function for weakly bound nuclei, is reported. These results together with a reanalysis of existing data conclusively demonstrate that the effect of breakup on fusion is coherent, like coupling to any nonelastic channel.     

Structure and reactions of the Li and Be halo nuclei

The phenomenon of s-wave intruder orbits is examined for a range of Li and Be isotopes. Whether these states are mixed or stand alone, they contribute distinctively to the properties of these nuclei. For weakly bound states, they accentuate those features of large sizes, narrow momentum widths and low-lying E1 strengths that are associated with halo nuclei.     

Microscopic study of ~7Li-nucleus potential

A microscopic approach is employed to study the optical potential for the 7Li-nucleus interaction system without any free parameters.It is obtained by folding the microscopic optical potentials of the constituent nucleons of 7Li over their density distributions.We employ an isospin-dependent nucleon microscopic optical potential,which is based on the Skyrme nucleon-nucleon effective interaction and derived using the Green's function method,as the nucleon optical potential.The harmonic oscillator shell model is used to describe the internal wave function of 7Li and obtain the nucleon density distribution.The 7Li microscopic optical potential is used to predict the reaction cross-sections and elastic scattering angular distributions for the target range from 27Al to 208Pb and energy range below 450 MeV.Generally,the results can reproduce the measured data reasonably well.In addition,the microscopic optical potential is comparable to a global phenomenological optical potential by fitting the presently existing measured data.     

Investigation of the 58Ni(7Li, 6Li)59Ni reaction with vector polarized 7Li

Angular distributions of the cross section and of the vector analyzing power for the ⁵⁸Ni(⁷$\text{Li}$, ⁶Li)⁵⁹Ni reaction leading to several groups of levels in the final nucleus have been measured at E_Li = 20.3 MeV. The observed Q-value dependence of the vector analyzing power can to a large extent be attributed to a kinematical effect caused by the polarization of the orbital angular momentum of the transferred neutron in ⁷Li.     

Positron angular correlation in copper

The two photon pair momentum density and the angular correlation curves for positron annihilation radiation from copper have been obtained by a band structure calculation, employing Hubbard’s approximation scheme. A comparison of the calculated curve for the long slit geometry with the experimental results shows that the theory rather overestimates the contributions in the high momentum region. An angular correlation curve for a point slit geometry is also calculated.