Breakup Threshold Research Articles

Three particles in a finite volume: The breakdown of spherical symmetry

Lattice simulations of light nuclei necessarily take place in finite volumes, thus affecting their infrared properties. These effects can be addressed in a model-independent manner using Effective Field Theories. We study the model case of three identical bosons (mass m) with resonant two-body interactions in a cubic box with periodic boundary conditions, which can also be generalized to the three-nucleon system in a straightforward manner. Our results allow for the removal of finite volume effects from lattice results as well as the determination of infinite volume scattering parameters from the volume dependence of the spectrum. We study the volume dependence of several states below the break-up threshold, spanning one order of magnitude in the binding energy in the infinite volume, for box side lengths L between the two-body scattering length a and L = 0.25a. For example, a state with a three-body energy of -3/(ma^2) in the infinite volume has been shifted to -10/(ma^2) at L = a. Special emphasis is put on the consequences of the breakdown of spherical symmetry and several ways to perturbatively treat the ensuing partial wave admixtures. We find their contributions to be on the sub-percent level compared to the strong volume dependence of the S-wave component. For shallow bound states, we find a transition to boson-diboson scattering behavior when decreasing the size of the finite volume.

Structure ofHe10Low-Lying States Uncovered by Correlations

The 0+ ground state of the 10He nucleus produced in the 3H(8He,p)10He reaction was found at about 2.1±0.2 MeV (Γ∼2 MeV) above the three-body ^{8}He+n+n breakup threshold. Angular correlations observed for ^{10}He decay products show prominent interference patterns allowing us to draw conclusions about the structure of low-energy excited states. We interpret the observed correlations as a coherent superposition of a broad 1- state having a maximum at energy 4-6 MeV and a 2+ state above 6 MeV, setting both on top of the 0+ state "tail." This anomalous level ordering indicates that the breakdown of the N=8 shell known in 12Be thus extends also to the ^{10}He system.

Resonance States and Alpha Condensation in 12C and 16O

Low density states near the 3α and 4α breakup thresholds in 12C and 16O, respectively, are discussed in terms of the α-particle condensation. Calculations are performed in Orthogonality Condition Model and Tohsaki–Horiuchi–Schuck–Ropke approaches. The \({0_2^+}\) state in 12C and the \({0_6^+}\) state in 16O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

Three-Body Physics in a Finite Volume

Three particles with large two-body scattering lengths display universal properties including a spectrum of three-body bound states called “Efimov trimers”. I calculate the spectrum of three identical bosons inside a finite cubic box below the three-body breakup threshold. The dependence of the spectrum on the box size and the effects of the breakdown of spherical symmetry are investigated using effective field theory. The renormalization of the effective field theory in the finite volume is explicitly verified. The study of the three-nucleon system inside a finite cubic volume provides a tool for the understanding of Lattice QCD results. I study the triton in a finite volume at physical and unphysical pion masses.

Approaching Universality in Weakly Bound Three-Body Systems

Atom-dimer scattering below the three-body breakup threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly bound three-body state are shown to be strongly correlated. An appropriate rescaling of the observables reveals the subtlety of the correlation and serves to identify universal trends in the unitary limit of divergent two-body scattering length. The correlation provides a new quantitative measure of the degree of universality in three-body systems with short-ranged interactions, as well as a consistency check of effective field theories and other theoretical models.

Recent results related to excited states of6Be and10He

The 1H(6Li,6Be)n charge-exchange reaction and the 3H(8He, p)10He two-neutron transfer reaction were recently carried out at the ACCULINNA fragment separator (FLNR, Dubna) to populate the ground and excited states of 6Be and 10He nuclei, respectively. The 6Be ET spectrum (ET is the 6Be energy above its 4He+p+p decay threshold) was obtained with high statistics and described by the well-known 0+ ground state of 6Be at ET = 1.37 MeV, the 2+ state at ET = 3.05 MeV and a broad structure extending from 4 to 16 MeV which could be interpreted as the isovector soft dipole mode associated with the 6Li ground state. In the 10He case the 0+ ground state was found at about 2.1(2) MeV (T ∼ 2 MeV) above the 8He+n+n breakup threshold. Angular correlations observed for 10He decay products show prominent interference patterns allowing to draw conclusions about the structure of low-energy excited states: 1- (E T ∼ 5 MeV) and 2+ (ET > 6 MeV).

Can sonication enhance release from liquid-core capsules with a hydrogel membrane?

The objective is to investigate the influence of sonication on the mechanical and release properties of hydrogel capsules. A new fabrication process is developed to fabricate millimetric capsules made of a highly-viscous liquid core protected by a thin hyperelastic alginate membrane. At high intensities and/or long exposure times, sonication can lead to the capsule rupture, because it induces fatigue in the membrane. Below the breakup threshold, no remnant effect of sonication is, however, measured on the capsule mechanical properties. The release is studied by sonicating capsules filled with blue dextran suspended in an aqueous solution. The mass release that results from sonication is found to be proportional to the sonication duration time and pressure wave amplitude. A possible physical interpretation is that the acoustic streaming flow induced by the ultrasonic wave enhances convection in the vicinity of the capsule membrane and thus mass release. We have finally quantified the passive release subsequent to low-intensity sonications: it is on average identical to the one measured on non-sonicated capsules. Overall the membrane therefore recovers its physical and mechanical properties after sonication. If sonication leads to an increase in porosity of the capsule membrane, the increase is temporary and reverses back at the end of the ultrasonic stimulation.

Woods-Saxon and São Paulo optical model calculations of the threshold anomaly of the 6,7Li+28Si systems near Coulomb barrier energies

Two types of optical model interactions, namely the double-folding density dependent São Paulo potential (SPP) and the Woods-Saxon potential (WSP) are used to study the appearance of the Theshold Anomaly (TA) or the Breakup Threshold Anomaly (BTA) for the nuclear systems 6,7Li+28Si for energies around the Coulomb barrier. In the first case, the presence of the anomaly is determined from the energy dependence of the normalization parameters NR and NI as found from fittings to elastic scattering angular distributions. In the second case, the presence of the anomaly is investigated by the energy variation of the fusion and direct reaction parts of the Woods-Saxon potential. In this case, the parameters of the fusion and direct reaction potentials are calculated by a simultaneous analysis of elastic scattering, fusion and total reaction cross sections. It is found in both cases that the BTA appears for the 6Li+28Si reaction. As for 7Li+28Si, the calculation with the SPP shows that the usual TA appears but the dispersion relation is not satisfied, however the WSP indicates that indeed the BTA shows up.

On the Efimov effect in higher partial waves

Using the framework of effective field theory, we present a detailed study of the Efimov effect in higher partial waves for systems of two identical particles and a third distinguishable particle. Depending on the total angular momentum L, the two identical particles must be bosons or fermions. We derive analytical expressions for the elastic and inelastic atom–dimer scattering cross sections as well as the atom–dimer relaxation rate at the dimer breakup threshold. For the experimentally most relevant case of P-waves, we numerically calculate the atom–dimer scattering cross sections and relaxation rates as a function of the scattering length, three-body parameter and mass ratio for energies below breakup threshold.

Renormalized three-body equations with short-range forces

A three-body problem for a system of three nucleons interacting with short-range forces is discussed following effective field theory. Considering the case of a system of neutron–deuteron scattering, three-body equations are demonstrated such that the eigenvalues greater than unity are removed from the kernel leading to an equation that is renormalization-group invariant. The phase shifts are developed from a unique solution of the case of the doubled channel in neutron–deuteron scattering. The calculated neutron–deuteron phase shifts are well described below the deuteron breakup threshold.

Alpha clustering and condensation in nuclei

Low density states near the 3α and 4α breakup thresholds in 12C and 16O, respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Ropke) approaches. The 0+2 state in 12C and the 0+6 state in 16O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

Evidence for incomplete fusion on the 12C +208Pb and 13C + 207Pb reactions in above-barrier energies

The complete, incomplete and fission cross sections are being measured for 12,13C + 208,207Pb systems to investigate the influence of breakup at above-barrier energies which form the same compound nucleus at the same excitation energies. The α-active heavy reaction products are measured for most dominant reaction xn-channels along with fission cross sections which originate almost exclusively from the complete fusion (CF). The results from the present systems show substantial components from the incomplete fusion in addition to CF. The CF cross section is suppressed by 12 ± 2% for 12C and 3 ± 2% for 13C compared with the single-barrier penetration model calculations. A systematic variation of the suppression of CF for reactions of weakly bound nuclei 6,7Li, 9Be, 10,11 B and 12,13C on targets of 207,208Pb and 209Bi is being found as a function of the breakup threshold energy.

ALPHA CLUSTERING AND CONDENSATION IN NUCLEI

Low density states near the 3α and 4α breakup threshold in 12 C and 16 O , respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Röpke) approaches. The [Formula: see text] state in 12 C and the [Formula: see text] state in 16 O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

CLUSTERS IN THE BETA-DECAY OF LIGHT EXOTIC NUCLEI

The β-decay is a useful tool to study the peculiar features present in light exotic nuclei, such as halos and cluster structures. The large Q-values and low breakup thresholds in the daughter nuclei allow channels with feeding to continuum states and delayed emission of nucleons and light ions. We report experimental results obtained using a technique where the radioactive nuclei are implanted in a finely segmented detector, and the decay channels are identified through the correlation between the implanted nuclei and subsequent decays. Decays involving cluster and halo states in 12 C , 6 He , 11 Li and 11 Be were measured.

Reaction mechanisms involving weakly boundLi6andBi209at energies near the Coulomb barrier

The elastic, inelastic, and transfer cross sections are measured for the ${}^{6}\mathrm{Li}+{}^{209}\mathrm{Bi}$ reaction at energies around the Coulomb barrier. The optical model analysis of elastic scattering shows a breakup threshold anomaly in the energy dependence of the real and imaginary potentials. The observed energy dependence is found to be consistent with the dynamic polarization potential obtained from the coupled-channels calculations that explain the above measured reaction channels simultaneously. A comparison of different reaction probabilities reveals that the relative contribution of breakup starts increasing at energies below the Coulomb barrier, in contrast to the behavior of other reaction channels, which get closed as energy is lowered. The large probability of projectile breakup at sub-Coulomb energies leads to the observation of a nonzero imaginary potential even at ${E}_{\text{lab}}\ensuremath{\leqslant}0.8{V}_{B}$.

Breakup threshold anomaly in the near-barrier elastic scattering ofLi6+Sn116,112

We have measured the elastic scattering of the weakly bound $^{6}\mathrm{Li}$ on the $^{116,112}\mathrm{Sn}$ targets, at energies close to the Coulomb barrier. The energy dependence of the interaction potential has been investigated by two different methods and the presence of the breakup threshold anomaly is observed. We have also derived the total reaction cross sections for the above systems and compared them to those of other systems with halo, weakly bound, and tightly bound projectiles on targets with similar masses. The reaction cross sections are largest for systems with halo nuclei, then the systems with no-halo weakly bound nuclei, and the smallest cross sections are those for tightly bound systems.

Cooper pair insulators and theory of correlated superconductors

The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the $s$-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or $\mathit{XY}$ universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple $s$-wave picture.

R-matrix approach with proper boundary conditions for dissipative and nondissipative collision processes

We develop an $R$-matrix approach to treating collision processes which explicitly takes into account, by means of a simple energy-dependent analytic function, the out-of-phase oscillations of the incident and scattered standing waves in the interior region. Thereby we avoid the use of the Bloch operator. In place of the Bloch operator the incident wave provides the source term in an inhomogeneous equation for the scattered wave. We take those subchannels not treated exactly into account via the optical potential, which is generally non-Hermitian due to dissipation at the boundary. The optical potential is constructed on a real analytic basis using a resolvent that satisfies outgoing-wave boundary conditions. The use of an analytic basis together with the direct determination of the $K$ matrix, rather than the $R$ matrix, at the boundary (this is done by matching the interior wave function to the nearly exact analytic solution beyond the boundary) makes the method particularly well suited to the treatment of ultracold collisions. We have tested our method by applying it to one-photon single-ionization of ($\mathrm{He}1{s}^{2}$) accompanied by excitation to ${\mathrm{He}}^{+}(2s)$ or ${\mathrm{He}}^{+}(2p)$ for photon energies above the complete breakup threshold, where the optical potential is non-Hermitian. Excellent agreement with experiment is obtained for the cross sections for photoionization to both ${\mathrm{He}}^{+} (n=1)$ and to ${\mathrm{He}}^{+} (n=2)$. The $2s$-to-$2p$ branching ratio is strongly influenced by both the optical potential and, at photon energies less than a few tens of eV above the breakup threshold, the nonadiabatic dipole mixing of the $2s$ and $2p$ states.

Effective-Range Expansion of Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.

Dynamic polarization potentials for 6He + 209Bi and 11Li + 208Pb systems at near-barrier energies

The Coulomb dipole induced dynamic polarization potentials for 6He + 209Bi and 11Li + 208Pb systems within the framework of Feshbach’s formalism with a motive to ascertain the presence or absence of threshold anomaly have been studied. As a result of this study, the threshold anomaly has been found to be present for both systems. It has also been found that at deep sub-barrier energies the imaginary part either starts increasing or at least remains unchanged which indicates the presence of the breakup threshold anomaly. In addition, the Coulomb breakup transmission factors for both systems have been found to have maximum value below and near-barrier energies, but at very high energies due to closure of the breakup channel the breakup transmission coefficients quickly becomes zero.