Analysis of α-7Li elastic and inelastic scattering at low energy with a simple model of the pauli principle effects

The elastic and inelastic scattering of α on ⁷Li are calculated at different low energies in the framework of the resonating group method in which the ⁷Li is supposed to be comprised of two clusters, α and t. To reduce the time of calculation, the effects of the Pauli principle due to the exchange of two nucleons belonging to two different clusters are approximated with an effective nucleon-nucleon potential which has been determined previously in order to reproduce correctly the scattering and bound states of the nuclear systems comprised of two particles, 2α or α + t. This calculation takes into account the exchange of the incoming a with the a belonging to ⁷Li as well as the coupling with the ⁸Be + t channel. Without any free parameter, the model calculation reproduces correctly the main features of the experimental data when the projectile energy is less than 5 MeV (lab). It appears that the coupling with the ⁸Be + t channel cannot be neglected.     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.     

Study of the 8Be first T = 2 state with 4He + α and 7Li + p initiated excitation functions

In a high resolution study of the ⁴He + α initiated excitation functions in the region of the ⁸Be first T = 2 state, weak resonance excursions have been observed in some reaction channels yielding the total width Γ = 14.7 ± 4.0 keV. No resonance excursion has been observed in the ⁴He + α elastic scattering yielding the branching ratio Γ_α/Γ ≦ 0.003 for the decay of the ⁸Be first T = 2 state into two α-particles. For the decay to the low-lying states of ⁶Li and ⁷Li lower limits of the branching ratio are given. The reinvestigation of the ⁷Li+p initiated excitation functions revealed no resonance anomaly in the region of the ⁸Be first T = 2 state. The upper limit Γ_p/Γ ≦ 0.023 has been derived for the proton decay to the ⁷Li_g.s.. The results are compared with previous measurements and with shell-model calculations.     

Three-body analysis of<Superscript>11</Superscript>Li and its<Emphasis Type="Italic">β</Emphasis>-decay to deuteron channel and to halo analog state<Superscript>11</Superscript>Be* (18.3 MeV)

The ground state wave function of¹¹Li obtained in a three-body model proposed earlier (S Kumar and V S Bhasin,Phys. Rev. C65, 034007 (2002)) has been employed to study the probability distributions, momentum distributions and n−n correlation. Complex scaling method has been used to find the energy positions and widths of the three resonant states of¹¹Li above the breakup threshold. The formalism is extended further to study the β-decay of¹¹Li to two channels. One is the β-transition of¹¹Li into a high lying excited state of¹¹Be at 18.3 MeV, i.e.,¹¹Be* and the second is the decay to deuteron +⁹Li channel. The¹¹Be* state has been considered as a halo analog state identified as a bound three-body (⁹Li + n + p) system. The n-⁹Li interaction incorporates both the virtual state and the p-wave resonance observed experimentally. For p-⁹Li interaction, a Coulomb corrected separable interaction is constructed using charge indepedendence for strong interaction part. The n-p interaction is operative only in³S₁ state corresponding to the isotopic spin T^h =0. As a result the¹¹Be* state has the same isotopic spin as that of⁹Li core, i.e.,T = 3/2. Using these realistic parameters as input and without invoking any other free parameter, the model has been used to predict the strength of the Gamow-Teller β-decay of¹¹Li to¹¹Be*, i.e.,Bgt = 1.5 and the value of the branching ratio to⁹Li + deuteron channel to be 1.3 × 10^-4. These results are found to be in rather good agreement with the recent experimental findings.     

Structure of 10Li and 11Li

Recent two-body nuclear reaction measurements of the struture of ¹⁰Li and ¹¹Li are reviewed. The mass of ¹¹Li is now well known, but the situtation for ¹⁰Li is not so clear. However recent evidence presented at this conference seems to confirm the existence of a slightly unbound s-wave ground state.     

Double spectator poles observed in a double coincidence study of the 6Li + 6Li → 2α + 2d reaction

Enhancements in yield, due to double spectator poles, have been observed in d-d and α-α, but not α-d, double coincidence spectra from ⁶Li + ⁶Li double breakup at 36 to 47 MeV incident energy. The peak locations agree well with those predicted by kinematics but their widths are much smaller than can be explained from the momentum distribution of α + d clusters in ⁶Li. The enhancements do not result from phase space, a final-state interaction, or sequential decay of levels in ⁴He, ⁶Li, or ⁸Be.     

Characteristics of elastic proton scattering from <Emphasis Type="Italic">A</Emphasis> = 9 Li,Be, and C isobars

Differential cross sections and analyzing powers (A _y ) for elastic proton scattering from ⁹Be at 220 MeV and 1.0 GeV and from ⁹Li and ⁹C at 60 and 700 MeV/nucleon are calculated in the context of the Glauber diffraction theory with the three-body wave functions for the ⁹Be, ⁹Li, and ⁹C nuclei described by the α + α + n, ⁷Li + n + n, and ⁷Be + p + p models. Comparison with the available experimental data is made, which allows some conclusions about the quality of the model wave functions.     

Population of high spin states of160Dy in the (7Li, α 2n)-reaction

In-beam gamma spectra have been measured during the bombardment of¹⁵⁹Tb with⁷Li of 28, 34, and 37 MeV incident energy. Levels with spin up to 12? in¹⁶⁰Dy were strongly populated through the (⁷Li, α 2n) channel.     

Nuclear magnetic resonance on the 10−, 0.88 ms state in 206Bi

Alpha-particle reduced widths for the 8⁺ state at 11.95 MeV, obtained from analysis of both ¹⁶O + α resonant scattering data and ¹⁶O(⁶Li, d)²⁰Ne reaction data are consistent with expectation for the 8⁺ member of the ground-state rotational band.     

Halo structure of 11Li in proton scattering: A folding model description with isospin,density and momentum dependent effective interaction

Recent ¹¹Li+p elastic scattering data at 62, 68.4, and 75 MeV and inelastic scattering data at 68.4 MeV, taken at RIKEN, are analysed with an isospin, density and momentum dependent finite range effective interaction (SBM) and M3Y interaction in a single folding model. The M3Y folded ¹¹Li+p potentials are found to be almost similar to the folded ⁹Li+p potentials. But the SBM folded ¹¹Li+p potentials are distinctly different, causing small but significant change in the angular distribution. Folded potentials need appreciable reduction factors indicating possible effects of strong breakup channel coupling. No significant change in results is found if ⁹Li core + Gaussian two-neutron halo density is used instead of the COSM density of ¹¹Li although the radial extent of the latter is much larger. The angular distribution of the recently discovered excited state at 1.3 MeV, well reproduced by the SBM folded potential, is found to be predominantly dipole in nature.     

Generator-coordinate study of inelastic α + 12C scattering

A multi-channel calculation performed with the generator coordinate method is presented for α + ¹²C scattering. The inelastic channel α + ¹²C(2⁺) is included. Bound-state and resonance energies are determined for J^π = 0⁺ up to 6⁺. For the negative parity levels, the results are very similar to those obtained with a single-channel calculation. The positive parity resonances are more numerous and in better qualitative agreement with experiment in the multi-channel calculation. However, an incorrect value for the threshold energy α + ¹²C(2⁺) channel prevents one from obtaining a quantitative agreement with experiment.     

Polarized deformed spin−32 projectile scattering and complex folded potentials

A formalism is presented where polarization observables of all ranks for deformed spin ?$\text{case3}\text{2}$ projectiles are calculated in a parameter-free fashion. Complex optical potentials for the available ⁷$\text{Li}$ + ⁵⁸Ni elastic scattering data at E_lab = 20.3 MeV are obtained from single folding calculations, taking the ⁷Li ground state to be an α + t cluster in relative p-state. The expansion of the hamiltonian in spin-space generates tensor terms of ranks 2 (T_R) and 3 (T₃) apart from the usual central and spin-orbit terms. The T_R potential fits the second-rank tensor analysing powers quite well without being able to resolve discrete ambiguities of input optical parameters. The T₃ term generates a J · L contribution, making the spin-orbit interaction three-component. The ⁷Li vector analysing power so obtained is negative, but the magnitude is not fully reproduced. Modification of parameters to account for absorption modes not included in the superposition model indicates the need for properly handling dynamical polarization effects due in particular to the low-lying first excited state of ⁷Li.     

Nature of halo in light nuclei

A feature peculiar to light neutron-rich nuclei is that their lowest decay thresholds are only slightly above their ground states. Among them, ⁶He and ¹¹Li are two most striking examples. The energy needed to break ⁶He (¹¹Li) into an alpha particle (⁹Li) and two neutrons is about 1 MeV (300 keV). So small a value prompts one to construct their theory by analogy with the zero-range-nuclear-force approximation previously applied to the deuteron. A more detailed analysis shows, however, that the simple version of this approximation applied to systems that decay through a three-particle channel does not take into account some important features of these systems and requires significant improvements. First, with increasing distance between three particles, the potential energy decreases, in contrast to what is observed for binary systems, in inverse proportion to the hyperradius cubed. Second, the Pauli exclusion principle adds complexity even in the asymptotic domain, and we meet its demands in constructing the ⁶He and ¹¹Li wave functions in the continuum. An approach is proposed to analyze weakly bound three-cluster systems that takes into account the aforementioned features and which describes correctly the experimentally observed structure of bound and unbound states above the threshold for three-particle decay.     

High-lying excited states in <Superscript>10</Superscript>Be from the <Superscript>9</Superscript>Be(<Superscript>9</Superscript>Be,<Superscript>10</Superscript>Be)<Superscript>8</Superscript>Be reaction

A transfer-reaction experiment of ⁹Be(⁹Be, ¹⁰Be)⁸Be was performed at a beam energy of 45 MeV. Excited states in ¹⁰Be up to 18.80 MeV are produced using missing mass and invariant mass methods. Most of the observed high-lying resonant states, reconstructed from the α + ⁶He and t + ⁷Li decay channels, agree with the previously reported results. In addition, two new resonances at 15.6 and 18.8 MeV are identified from the present measurement. The 18.55 MeV state is found to decay into both the t + ⁷Li_g.s. and t + ⁷Li* (0.478 MeV) channels, with a relative branching ratio of 0.93 ± 0.33. Further theoretical investigations are encouraged to interpret this new information on cluster structure in neutron-rich light nuclei.     

Analytic Continuation of Scattering Function and Asymptotic Normalization Constants for 6Li

A new method of determining asymptotic normalization coefficients (ANC) corresponding to the two-channel virtual process A → B +  C is suggested. The method makes use of the Coulomb-modified effective range (ER) expansion for the two-channel elastic BC scattering. The coefficients of the ER expansion are found using the results of the phase-shift analysis of the BC scattering. Then the ER expansion is analytically continued in energy to the pole corresponding to the bound state A. The ANC is directly related to the residue of the BC scattering amplitude at that pole. The method suggested is applied to the ⁶Li nucleus in the α +  d channel. The ANCs for the S and D states of the relative αd motion are evaluated.     

Nuclear field theory predictions for 11Li and 12Be: Shedding light on the origin of pairing in nuclei

Recent data resulting from studies of two-nucleon transfer reaction on ¹¹Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of ⁹Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon-mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5-ms-lived ¹¹Li nucleus. In other words, the ground state of ¹¹Li can be viewed as a neutron Cooper pair bound to the ⁹Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two-particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t, p) data on ⁷Li, suggest the existence of a pairing vibrational band based on ⁹Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of ¹¹Li(p, t)⁹Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper-pair nuclear pairing, let alone specific information concering the “rigidity” of the N = 6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections σ _abs associated with the reactions ¹²Be(p, t)¹⁰Be(g.s.) and ¹²Be(p, t)¹⁰Be(pv) (≈¹⁰Be(p, t)⁸Be(g.s.)). In particular, concerning this last reaction, predictions of σ _abs can change by an order of magnitude depending on whether the halo properties associated with the d _5/2 orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.     

Possibility of Studying Neutron–Neutron Correlations in Halo Nuclei

An experimental investigation of the reaction of core pickup from ⁶He and ¹¹Li two-neutronhalo nuclei is proposed. In such experiments, neutron–neutron correlations in a halo nucleus will be assessed on the basis of the energy of a neutron–neutron quasibound state. A detailed kinematical simulation of the reaction ⁶He + ²H → ⁶Li + (nn) →⁶ Li + n + n is performed. It is shown that the energy of the quasibound state in question can determined from the shape of the energy spectrum of neutrons originating from the breakup of this state. In the proposed exclusive experiment, a beam of ⁶He (¹¹Li) nuclei with an energy of about 5 to 10 MeV per nucleon interacts with a deuterated-polyethylene target. This will permit detecting charged particles (⁶Li and ¹¹Be) and a neutron. On the basis of determining the energy of the neutron–neutron quasibound state, it will become possible to estimate the effective attraction between the valence neutrons in the field of the third particle (core).     

The role of configurations of neutron halo in the formation of the model vertex function for description of the two-neutron transfer reaction

The nuclear vertex functions for virtual decay of halo nuclei ⁶He → α + n + n (¹¹Li-⁹Li + n + n) for dineutron and cigarlike configurations of the neutron halo have been analytically investigated using the diagram method of direct nuclear reactions. These vertex functions describe the one-step process of two-neutron transfer. It is shown that the angular and energy distributions of the reaction products (α particles, ⁹Li, etc.) in different ranges of variables correspond to different structural elements of the halo. The vertex function describing the two-step process of halo neutron transfer has also been analyzed.     

Investigation of the radiative capture reaction t + α → 7Li + γ in the algebraic version of the resonating group method

The radiative capture reaction t + α → ⁷Li + γ is investigated in the framework of the algebraic version of the resonating group method at low energies. The Hasegawa-Nagata nucleon-nucleon potential is used in calculations. The lowest compatible with the Pauli exclusion principle wave functions of a translationally invariant shell model are adopted as the internal wave functions for α and t clusters. The obtained results are in reasonable agreement with the experimental data.