Ab Initio NCSM/RGM for Three-Body Cluster Systems and Application to 4He+n+n

We introduce an extension of the ab initio no-core shell model/resonating group method (NCSM/RGM) in order to describe three-body cluster states. We present results for the ⁶He ground state within a ⁴He+n+n cluster basis as well as first results for the phase shifts of different channels of the ⁴He+n+n system which provide information about low-lying resonances of this nucleus.     

Nuclear spectral energy functions beyond the shell model

We predictl=0 nucleons in¹²C to have a negative (binding) energy centered around –22 MeV with a full width at half-maximum of 5.3 MeV. Thel=1 (P _3/2 nucleons) are predicted to have a much narrower spectral energy function centered around –10.6 MeV. A strongly correlated translational invariant wave function was used to describe the ground state nucleus. A central two-nucleon potential was utilized in the hyperspherical harmonic method to approximately solve the Schrödinger equation for the ground state wave function. Both confirmation and failings of the independent particle shell model are exposed.     

TITAN: An ion trap facility for on-line mass measurement experiments

Precision determinations of ground state or even isomeric state masses reveal fingerprints of nuclear structure. In particular, at the limits of existence for very neutron-rich or -deficient isotopes, one can extract detailed information about nuclear structure from separation energies or binding energies. Mass measurements are important to uncover new phenomena, to test new theoretical predictions, or to refine model approaches. For example, the N?=?28 shell has proven more stable than previously expected; however, the predicted new “magic” number at N?=?34 in the K and Ca isotopes has yet to be confirmed experimentally. For these neutron-rich nuclei, the inclusion of three-body forces leads to significantly better predictions of the ground-state mass. Similarly, halo nuclei present an excellent application for ab-initio theory, where ground state properties, like masses and radii, test our understanding of nuclear structure. Precision mass determinations at TRIUMF are carried out with the TITAN (TRIUMF’s Ion Traps for Atomic and Nuclear science) facility. It is an ion-trap setup coupled to the on-line facility ISAC. TITAN has measured masses of isotopes as short-lived as 9 ms (almost an order of magnitude shorter-lived than any other Penning trap system), and it is the only one with charge breeding capabilities, which allow us to boost the precision by almost 2 orders of magnitude. We recently made use of this feature by measuring short-lived, proton-rich Rb-isotopes, up to ⁷⁴Rb while reaching the 12?+ charge state, which together with other improvements led to an increase in precision by a factor 36.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

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.     

The importance of nucleon substructure in nuclear ground states

Using a potential model, constrained by the hadron spectrum, for the confinement of relativistic quarks we explore the consequences of the substructure of nucleons for the binding energy and ground state wavefunction of ⁴He. In its simplest form, this model gives a binding energy of 19 MeV. Quark wavefunctions differ from those associated with free nucleons by less than 10%, the rms quark radius is 1.34 fm and the resulting structure differs considerably from that of an expansion beginning from the (0s)⁴ shell model. Considerable contributions to the binding energy, attractive from quark delocalization and repulsive from the quark hyperfine interaction, appear unavoidable. We conclude that these effects cannot be excluded from a detailed understanding of the properties of nuclear ground states.     

Effective three-body interactions in the α-cluster model for the <Superscript>12</Superscript>C nucleus

Properties of the lowest 0⁺ states of ¹²C are calculated to study the role of three-body interactions in the α-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the α-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited 0₂⁺ state and the monopole 0₂⁺↦0₁⁺ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the 0₂⁺ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.     

Efimov states in asymmetric three-body atomic clusters

The work is devoted to the investigation of the weakly bound three-body atomic clusters. The calculations on the van der Waals trimer ⁷Li⁴He₂ are carried out using the differential Faddeev equations, which allows us to give accurate binding energies for both the ground and the exited state of the system. The results obtained indicate the Efimov nature of the excited state in this system.     

Properties of proton-rich nuclei in a three-body model

Using a three-body model and realistic two-body potentials, we investigate the properties of the nuclei ¹⁸Ne and ²⁸S near the proton dripline. We figure out the two-proton separation energies, occupation of the valence protons, root-mean-square radii of matter and the valence protons. Besides, the spatial correlation densities are displayed to reflect the correlation between the two valence protons. The first excited 0⁺ state of ¹⁸Ne is most likely to be a halo state according to our calculation. Turning off the Coulomb interactions among the three-body systems, we get the two-neutron separation energies and configuration of the valence neutrons of their corresponding mirror nuclei. The results indicate that the three-body model is proper to describe some proton-rich nuclei and can be used to deduce reliable information.     

Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of ³H and ⁴He , and for the singlet S -wave ³He -neutron scattering length a ₀(³He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a ₀(³He-n) and the ³H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the ³H binding energy and the ³H charge radius, and the Tjon line. With the ³H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of ³H of (1.6±0.2) fm, for the ⁴He binding energy of (28±2.5) MeV, and for Re{a ₀(³He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between ³H and ³He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the ⁴He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.     

Exploring the core deformation properties of 29F halo nucleus using T- and Y-configurations

²⁹F nucleus is a two-neutron halo nucleus with the core (²⁷F) + n + n three-body system. We studied the Jacobi coordinates dependant T-and Y-configurations properties due to the core deformation of this nucleus. For this deformation of the core, the separation energy (S_2n) and the root mean square (RMS) matter radius of this halo nucleus were calculated. This theoretical calculation for investigating T-and Y-configuration properties was accomplished through the MATLAB computational software. A positive core deformation was found, which indicates a prolate shaped halo nucleus. We found an excellent agreement for S_2n and 96.4% and 96% accuracies for the T- and Y-configurations respectively.     

Kinematically complete final state investigations of molecular photodissociation: two- and three-body decay of laser-prepared H 3 3 s ? 2 A 1 '

We have performed kinematically complete investigations of molecular photodissociation of triatomic hydrogen in a fast beam translational spectrometer recently built in Freiburg. The apparatus allows us to investigate laser-induced dissociation of neutral molecules into two, three, or more neutral products. The fragments are detected in coincidence and their vectorial momenta in the center-of-mass frame are determined. We demonstrate the potential of the method at the fragmentation of the 3 s ² A ₁ ^′ ( N = 1, K = 0) state of triatomic hydrogen. In this state, three-body decay into ground state hydrogen atoms H+H+H, two-body predissociation into H+H ₂ (v , J), and photoemission to the H ₃ ground state surface with subsequent two-body decay are competing channels. In the case of two-body predissociation, we determine the rovibrational population in the H ₂ (v , J) fragment. The vibrational distribution of H ₂ is compared with approximate theoretical predictions. For three-body decay, we measure the six-fold differential photodissociation cross-section. To determine accurate final state distributions, the geometric collection efficiency of the apparatus is calculated by a Monte Carlo simulation, and the raw data are corrected for apparatus efficiency. The final state momentum distribution shows pronounced correlation patterns which are characteristic for the dissociation mechanism. For a three-body decay process with a discrete kinetic energy release we have developed a novel data reduction procedure based on the detection of two fragments. The final state distribution determined by this independent method agrees extremely well with that observed in the triple-coincidence data. In addition, this method allows us to fully explore the phase space of the final state and to determine the branching ratios between the two- and three-body decay processes. Received 29 March 2001     

Pairing correlations and soft dipole excitations in nuclei on the neutron-drip line

Paring correlations and soft dipole excitations in weakly bound nuclei on the edge of neutrondrip line are studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei ⁶He and ¹¹Li, as well as a skin nucleus ²⁴O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron-type correlation plays a dominant role in the halo nuclei ⁶He and ¹¹Li having the coupled spin of the two neutrons S = 0, while the correlation similar to the BCS type is important in ²⁴O. Contributions of the spin S = 1 and S = 0 configurations are separately discussed in the low-energy dipole excitations. The calculated results are compared with recent experimental data of ⁶He and ¹¹Li. The text was submitted by the authors in English.     

Molecular binding in the large-N expansion

We apply the large-N expansion to the H⁺₂ ion. An interesting complication occurs in the leading order to yield a degenerate ground state. We also estimate the ground state energy of the hydrogen molecule using the same technique.     

Effect of the three-body force on trinucleon bound systems consideringS andS′-state admixture

We report the calculation of binding energy, charge form factor and point-like proton density of both³H and³He by the hyperspherical harmonics method with the inclusion of two-pion exchange three-nucleon force (Fujita-Miyazawa type). For the two-body force theN-N Afnan-Tang S-3 potential is taken. Coulomb and three-body forces are treated nonperturbatively. In this calculation the mixed symmetryS′-state of the trinucleon ground state is considered along with the space totally symmetricS-state.     

The asymptotic D-state to S-state ratio of triton

At low energies, an effective field theory (EFT) with only contact interactions as well as three-body forces allow a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behaviour. Triton as a three-body system, based on the EFT have been previously shown to provide representative binding energies, charge radii, S-wave scattering amplitude and asymptotic normalization constants for the ³H bound state system. Herein, EFT predictions of the asymptotic D-state to S-state ratio of triton are calculated to more fully evaluate the adequacy of the EFT model. Manifestly model-independent calculations can be carried out to high orders, leading to high precision.     

Λααα cluster model for the Λ 13 C nucleus

The _Λ ¹³ C hypernucleus is treated as a (1/2)⁺ bound state of the Λααα system. The s-wave model is used on the basis of differential equations for the corresponding Yakubovsky components. No account is taken of 2+2 clustering in the system. Phenomenological potentials are used to simulate the αα and αΛ interactions. The system as a whole is bound owing to the additional potential of three-body interaction between the alpha-particle clusters. The differential equations for the Yakubovsky components are solved numerically by the cluster-reduction method. The binding energies are calculated for the ground and the first excited state of the _Λ ¹³ C hypernucleus. It is shown that the dominant type of clustering in the system is (Λαα)α.     

Quantum Monte Carlo calculation for the neutron-rich Ca isotopes

We computed ground-state energies of calcium isotopes from ⁴²Ca to ⁴⁸Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the ⁴⁰Ca core with a mean-field self-consistent potential computed using the Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground state from a wave function built with the single-particle orbitals computed in the self-consistent external potential. The shells considered were the 1F _7/2 and the 1F _5/2 . The Hamiltonian employed is semi-realistic and includes tensor, spin-orbit and three-body forces. While absolute binding energies are too deep if compared with experimental data, the differences between the energies for nearly all isotopes are in very good agreement with the experimental data.