Structure of light unstable nuclei in continuum energies

The Coulomb breakup reaction of ⁶He into a ⁴He+n+n 3-body system is analyzed by applying the complex scaling method (CSM). We can derive the contributions to El and E2 transitions, not only from resonances, but also 2- and 3-body continuum states, which show the characteristic structure of the many-body unbound states in ⁶He.     

A cluster calculation for 6He spectrum

The ⁶He nucleus is considered as the cluster α + n + n system. The excitation energies of the low-lying levels are calculated using the configuration-space Faddeev equations. The analytical continuation method in a coupling constant is applied for calculation of resonance parameters. The αn interaction is constructed to reproduce the results of R-matrix analysis for αn-scattering data. A realistic AV14 potential describes the nn interaction. Additional three-body potential adjusted by the ground state energy of ⁶He is used. The energies of the low-lying resonances of ⁶He (0 ₁ ⁺ , 0 ₂ ⁺ , 2 ₁ ⁺ ) are reasonably reproduced by the calculations.     

Tests of the discretized-continuum method in three-body dipole strengths

We investigate the ⁶He dipole distribution in a three-body α+n+n model. Two approaches are used to describe the three-body ¹⁻ continuum: the discretized-continuum method, where the scattering wave functions are approximated by square-integrable functions, and the R-matrix formalism, where their asymptotic behaviour is taken into account. We show that some ambiguity exists in the pseudostate method, owing to the smoothing technique, necessary to derive continuous distributions. We show evidence for the important role of the halo structure in the E1 dipole strength. We also address the treatment of Pauli forbidden states in the three-body wave functions.     

Mean field for the p+90Zr system in the energy range −60 MeV<E<+65 MeV and single-particle features of proton states in 90Zr from a dispersive optical-model analysis

Data on the scattering of protons with energies 5 MeV<E<65 MeV by ⁹⁰Zr nuclei and data on the energies of proton particle and hole levels in the A+1 and A?1 systems with A=90 are analyzed within the dispersive optical model. The parameters of the mean proton field for ⁹⁰Zr are determined in the energy range ?60 MeV<E<+65 MeV. The predicted single-particle features of the levels (root-mean-square radii of orbits, occupation numbers, spread widths, spectroscopic factors, and spectral functions) comply well with experimental data obtained in (d, ³He), (³He, d), (n, d), and (d, n) reactions for levels near the Fermi surface and in (e, e′p) and (p, 2p) reactions for deep levels.     

Properties of the He ground state from He neutron knockout

The unbound nucleus ⁷He, produced in neutron-knockout reactions with a 240 MeV/u ⁸He beam in a liquid-hydrogen target, has been studied in an experiment at the ALADIN-LAND setup at GSI. From an R-matrix analysis the resonance parameters for ⁷He as well as the spectroscopic factor for the ⁶He(0⁺) + n configuration in its ground-state have been obtained. The spectroscopic factor is 0.61 confirming that ⁷He is not a pure single-particle state. An analysis of ⁵He data from neutron-knockout reactions of ⁶He in a carbon target reveals the presence of an s  -wave component at low energies in the α+n$\alpha +\mathrm{n}$ relative energy spectrum.     

Electron scattering on two-neutron halo nuclei: The case of 6He

The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core +n + n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on ⁶He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and α knockout by the electron.     

Twenty-parameter eigenfunctions and energy values of the 23 S States of He and He-like Ions

Twenty-parameter calculations of the energies and wave functions of the first excited states 2³ S of He, Li⁺, Be⁺⁺, B⁺⁺⁺, O⁶⁺, Ne⁸⁺, Mg¹⁰⁺, have been carried out using Hylleraas' method. The energy values have been corrected for mass polarization. The coefficients of the best wave functions are listed. Similar calculations for the 2³ S state of the H^? ion yield an energy value which cannot be distinguished from the energy of a free H atom. For He and Li⁺, in addition, forty-parameter calculations have been carried out. The results compare well with the recent calculations of Pekeris using a somewhat different method. Even after the inclusion of the relativistic correction, the theoretical energy values deviate slightly from the observed. The differences, ?0·10±0·05 cm^?1 for He and ?1·07±0·10 cm^?1 for Li⁺, represent observed values of the Lamb shifts in the 2³ S states. These values agree within their uncertainties with the values predicted from quantum electrodynamics.     

Study of the Isospin Mixing in 6Li with α + p + n Three-Body Model

We calculate the isospin mixing probabilities for both T = 0 and T = 1 states of ⁶Li systematically, and compare them to clarify the relation between the structure of ⁶Li and the isospin mixing probabilities. As a result, the effect of halo structure on the isospin mixing cannot be seen clearly. The effect of the coupling to the continuum states such as of ⁵He + p and ⁵Li + n is suggested.     

Resonant structure observed in the 3He(τ, γ)6Be capture reaction

The ³He(τ,γ)⁶Be capture reaction has been studied for ³He bombarding energies from 12 to 27, MeV. Transitions to the first excited state in ⁶Be(T = 1, 2⁺) are readily seen. Transitions to the ground state in ⁶Be (T = 1, 0⁺) are very weak and their presence could not be ascertained. The 90° excitation function for these transitions shows a broad maximum centered at E_τ = 23 ±1 MeV. This is interpreted as a resonance in the compound nucleus ⁶Be at E_x = 23.0±0.5 MeV with a configuration other than ³He+³He. These results are compared with other experimental work as well as with theoretical predictions.     

A radiochemical study on the existence of dineutron

A radiochemical study has been made to search for dineutron² n produced in the simultaneous two-neutron emission of the excited⁶He nuclei,⁶He^*, induced in the reaction of⁹Be+n→-⁶He^*+α with fast neutrons in a reactor. It was attempted to detect the radio-activity of²⁸Mg as a product of the reaction² n+²⁷Al→²⁸Mg+p. The²⁸Mg radioactivity observed in heterogeneous samples composed of the² n-producing target Be and the² n-detecting target Al separately was not found to be more than that of a side reaction,²⁷Al{(n, p)(n _th, γ)+(n _th, γ)(n, p)}²⁸Mg, whereas it clearly exceeded that of the side reaction in alloy samples made of Be and Al metals. The former experiment gives an upper limit of the production rate of the dineutron in the bound state 1×10^?7 per event of the simultaneous two-neutron emission. A tentative explanation for the excessive²⁸Mg radioactivity observed in the latter experiment is the following two-step process,⁹Be+n→⁶He+α and²⁷Al+⁶He→+²⁸Mg+α+p, rather than the process induced by the dineutron in a virtual state.     

Spectroscopy of 7He and superheavy hydrogen isotope 5H

The neutron-transfer reaction d(⁶He, p)⁷He is investigated. The data obtained show that, in the range between 1 and 7 MeV above its ground-state resonance, ⁷He does not have well-pronounced narrow excited states with a single-particle structure. A resonance state of ⁵H with an energy of 2 MeV above the n+n+³H decay threshold is obtained for the first time by making use of the reaction p(⁶He, ²He)⁵H.     

Experimental investigation of highly excited states of the 5,6He and 5,6Li nuclei in the (6Li, 7Be) and (6Li, 7Li) one-nucleon pickup reactions

The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions on ⁶Li and ⁷Li nuclei were investigated in the angular interval 0°–20° in the laboratory system at a ⁶Li energy of 93 MeV. In addition to low-lying states of the ^5,6He and ^5,6Li nuclei, broad structures were observed near the t(³He)+d and t(³He)+t thresholds at the excitation energies of 16.75 (3/2⁺) and ～20 MeV (for ⁵He), 16.66 (3/2⁺) and ～20 MeV (⁵Li), 14.0 and 25 MeV (⁶He), and ～20 MeV (⁶Li). The angular distributions measured in the ⁷Li(⁶Li, ⁷Be)⁶He reaction for transitions to the ground state (0⁺) and excited states at E _x=1.8 MeV (2⁺) and 14.0 MeV of the ⁶He nucleus were analyzed by the finite-range distorted-wave method assuming the 1p-and 1s-proton pickup mechanism. The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions were shown to proceed predominantly through the one-step pickup mechanism, and the broad structures observed at high excitation energies are considered as quasimolecular states of the t(³He)+d and t(³He)+t types.     

Transition energy and dipole oscillator strength of 1s23d-1s2 nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4?n?9) transitions and fine structure splittings of 1s² nf (n?9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n?10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n?9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained.     

Many-body atomic potentials in Thomas-Fermi theory

Many-body atomic potentials, ?, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ?(1, 2) ≡ E(1, 2) ? E(1) ? E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (?1)ⁿ for all coordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ?'s, when truncated at the n-body terms, has the sign (?1)ⁿ⁺¹.     

Almost periodic Schrödinger operators

We discuss the absolutely continuous spectrum ofH=?d ²/dx ²+V(x) withV almost periodic and its discrete analog (hu)(n)=u(n+1)+u(n?1)+V(n)u(n). Especial attention is paid to the set,A, of energies where the Lyaponov exponent vanishes. This set is known to be the essential support of the a.c. part of the spectral measure. We prove for a.e.V in the hull and a.e.E inA, H andh have continuum eigenfunctions,u, with |u| almost periodic. In the discrete case, we prove that |A|≦4 with equality only ifV=const. Ifk is the integrated density of states, we prove thaton A, 2kdk/dE≧π^?2 in the continuum case and that 2π sinπkdk/dE≧1 in the discrete case. We also provide a new proof of the Pastur-Ishii theorem and that the multiplicity of the absolutely continuous spectrum is 2.     

Coupling effects of resonant and discretized non-resonant continuum states in 4He + 6Li scattering at 10 MeV/A

Alpha-particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of ⁶Li is studied at incident energy 10 MeV/A. The α + d breakup continuum part within the excitation energy E _ex = 1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Few-Body Reactions in Nuclear Astrophysics

Nuclear reactions involving light nuclei require few-body models to describe the nuclear structure and the reaction mechanism. The production rates for the α+n+n → ⁶ He+γ and α+n+n+n → ⁶ He+n processes are discussed. Typically only very low relative energies are relevant. For environments with a high density, processes involving more particles could dominate. The use of the adiabatic approach as a method to compute cross sections at very low energies is proposed.     

Low- and medium-spin states in theN=124 isotones208Po and209At

Excited levels in²⁰⁸Po and²⁰⁹At were populated in the reactions (p, 2n) and (³He, 3n), and²⁰⁸Po also in the EC-decay of the²⁰⁸At ground state, which was produced in the²⁰⁹Bi(³He, 4n) reaction. The experimental procedures comprised gamma-ray excitation functions,γ- γ coincidences, as well as gamma-ray angular distribution and conversionelectron measurements, both on- and off-line. The properties of about twenty-five levels in each nuclide were studied. In²⁰⁸Po the energy of the 8⁺→6⁺ transition could be determined to be 4.0±0.2keV and the 8⁺ state thus has an excitation energy of 1,528 keV. The effective quadrupole charge of theh _9/2 proton can be derived ase _eff(τ h _9/2)=1.69(15)e. For the previously reported isomeric half-lives more accurate values are obtained, the systematics of electricL=1, 2 and 3 transition rates are discussed, and their microscopic structure is elucidated. Shell model considerations are used to support the configuration assignments, as are the logft values for the strongest²⁰⁸At(EC)²⁰⁸Po decay branches. The effect of core polarixation on the excitation energies of yrast states is studied in both²⁰⁸Po and²⁰⁹At. Many of the states populated in the²⁰⁸At EC decay are shown to be of core-excited character.     

Microscopic multicluster description of the 7Li7Be, 8Li8B and 9Li9C mirror nuclei

The ⁹Li and ⁹C mirror systems are investigated in a microscopic α+³H+n+n and α+³He+p+p multicluster framework using the stochastic variational method. Possibility of existence of neutron (proton) halo structure is studied. The quadrupole moment of ⁹C is predicted to be −5.04 e fm².