arXiv subjects
Publications and source records attributed to Nir Barnea.
Here we summarize how the LIT and CC methods can be coupled, in order to allow for ab initio calculations of reactions in medium mass nuclei. Results on 16O are reviewed and preliminary calculations on 40Ca are presented.
We illustrate how nuclear polarization corrections in muonic atoms can be formally connected to inelastic response functions of a nucleus. We first discuss the point-nucleon approximation and then include finite-nucleon-size corrections. As an example, we compare our ab-initio calculation of the third Zemach moment in the muonic Helium-4 ion to previous phenomenological results.
Stimulated by the proton radius conundrum, measurements of the Lamb shift in various light muonic atoms are planned at PSI. The aim is to extract the rms charge radius with high precision, limited by the uncertainty in the nuclear polarization corrections. We present an ab-initio calculation of the nuclear polarization for mu-4He+ leading to an energy correction in the 2S-2P transitions of $δ_{pol}=-2.47$ meV $\pm$ 6%. We use two different state-of-the-art nuclear Hamiltonians and utilize the Lorentz integral transform with hyperspherical harmonics expansion as few-body methods. We take into account the leading multipole contributions, plus Coulomb, relativistic and finite-nucleon-size corrections. Our main source of uncertainty is the nuclear Hamiltonian, which currently limits the attainable accuracy. Our predictions considerably reduce the uncertainty with respect to previous estimates and should timely serve the mu-4He+ experiment planned for 2013.
{\it Ab initio} calculation of the total cross section for the reactions $^{4}\rm{He}(γ,p)^3\rm{H}$ and $^{4}\rm{He}(γ,n)^3\rm{He}$ is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics (EIHH) method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.
The photoassociation of Efimov trimer, composed of three identical bosons, is studied utilizing the multipole expansion. For identical particles the leading contribution comes from the r^2 s-mode operator and from the quadrupole d-mode operator. Log-periodic oscillations are found in the photoassociation response function, both near the energy threshold for the leading s-wave reaction, and in the high frequency tail for all partial waves.
We present an ab-initio calculation of the giant dipole resonance in 16O based on a nucleon-nucleon (NN) interaction from chiral effective field theory that reproduces NN scattering data with high accuracy. By merging the Lorentz integral transform and the coupled-cluster methods, we extend the previous theoretical limits for break-up observables in light nuclei with mass numbers (A<=7), and address the collective giant dipole resonance of 16O. We successfully benchmark the new approach against virtually exact results from the hyper-spherical harmonics method in 4He. Our results for 16O reproduce the position and the total strength (bremsstrahlung sum rule) of the dipole response very well. When compared to the cross section from photo-absorption experiments the theoretical curve exhibits a smeared form of the peak. The tail region between 40 and 100 MeV is reproduced within uncertainties.
We present an estimate of the nuclear electric polarizability of the 6He halo nucleus based on six-body microscopic calculations. Wave functions are obtained from semi-realistic two-body interactions using the hyperspherical harmonics expansion method. The polarizability is calculated as a sum rule of the dipole response function using the Lanczos algorithm and also by integrating the photo-absorption cross section calculated via the Lorentz integral transform method. We obtain alpha_E=1.00(14) fm^3, which is much smaller than the published value 1.99(40) fm^3 extracted from experimental data. This points towards a potential disagreement between microscopic theories and experimental observations.
The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et al.. The extension consists in the inclusion of spin and isospin degrees of freedom such that a calculation with more realistic NN potential models becomes possible, whereas the modification allows a much simpler determination of the fermionic ground state. The approach is applied to four- and six-body nuclei (4He, 6Li) with various NN potential models. It is shown that the results for ground-state energy and radius agree well with those from the literature.
Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process where the atomic spins are conserved the reaction rate is governed by the monopole $r^2$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra $k^4$ factor in comparison to the spin-flip process. Comparing the relative strength of the $r^2$ and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a limiting case of a bound state with vanishing binding energy, emerging for a particular set of critical potential parameters. In this work we study the properties of these critical parameters for short range central potentials. To this end we develop two exact methods and also utilize the first and second order WKB approximations. Using these methods we have calculated the critical parameters for several widely used central potentials. The general analytic expressions for the asymptotic representations of the critical parameters were derived for cases where either the orbital quantum number $l$ or the number $n$ of bound states approaches infinity. The above mathematical models enable us to answer the following physical (quantum mechanical) questions: i) what is the number of bound states for a given central potential and given orbital quantum number $l$; ii) what is the maximum value of $l$ which can provide a bound state for the given central potential; iii) what is the order of energy levels for the given form of the central potential. It is revealed that the ordering of energy levels depends on the potential singularity at the origin.
We investigate the generalized Hubbard model of $(2n+1)$ Fermion species interacting via a symmetric contact attraction potential. We prove that the ground state of such system is a gapless superfluid, where a full Fermi surface coexists with a superfluid. Moreover, doing so we prove the existence of a free mode in a strongly interacting system, regardless of the potential strength. This proof holds at the mean field level. A Grassmannian Gaussian integration technique is used to deal with the problem. Our predictions may be relevant to future high-spin cold atoms experiments.
A detailed study of the 4He longitudinal response function R_L(ω,q) is performed at different kinematics, with particular emphasis on the role of three-nucleon forces. The effects shown are the results of an ab initio calculation where the full four-body continuum dynamics is considered via the Lorentz integral transform method. The contributions of the various multipoles to the longitudinal response function are analyzed and integral properties of the response are discussed in addition. The Argonne V18 nucleon-nucleon interaction and two different three-nucleon force models (Urbana IX, Tucson-Melbourne') are used. At lower momentum transfer (q<= 200$ MeV/c) three-nucleon forces play an important role. One even finds a dependence of R_L on the three-nucleon force model itself with differences up to 10%. Thus a Rosenbluth separation of the inclusive electron scattering cross section of 4He at low momentum transfer would be of high value in view of a discrimination between different three-nucleon force models.
We present a microscopic calculation of the 6He beta-decay into the ground state of 6Li. To this end, we use chiral perturbation theory at next-to-next-to-next-to-leading order to describe the nuclear weak-currents. The nuclear wave functions are derived from the J-matrix inverse scattering nucleon-nucleon potential (JISP), and the Schroedinger equation is solved using the hyperspherical-harmonics expansion. Our calculation brings the theoretical decay-rate within 3% of the measured one. This success is attributed to the use of chiral-perturbation-theory based mesonic currents, whose contribution is qualitatively different compared to standard nuclear physics approach, where the use of meson exchange currents worsens the comparison to experiment. The inherent inconsistency in the use of the JISP potential together with chiral-perturbation-theory based is argued not to affect this conclusion, though a more detailed investigation is called for. We conclude that any suppression of the axial constant in nuclear matter is included in this description of the weak interaction in the nucleus.
We present an ab-initio calculation of the longitudinal electron scattering response function off 4He with two- and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasi-elastic peak by 10% for q between 300 and 500 MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100 MeV/c. At very low q, however, data are missing.
An ab-initio calculation of the 4He(e,e') inelastic longitudinal response function R_L is presented. Realistic two- and three-body forces are used. The four-body continuum dynamics is treated rigorously with the help of the Lorentz integral transform. The three-nucleon force reduces the quasi-elastic peak height by about 10% for momentum transfers q between 300 and 500 MeV/c. Experimental data are well described, but not sufficiently precise to resolve this effect. The reduction due to the three-nucleon force increases significantly at lower q reaching up to about 40% at q=100 MeV/c. However, at such q values data are missing.
We present a microscopic calculation of the 6He beta-decay into the ground state of 6Li. To this end we use the impulse approximation to describe the nuclear weak current. The ground state wave functions are obtained from the solution of the nuclear 6-body problem. The nucleonnucleon interaction is described via the J-matrix inverse scattering potential (JISP), and the nuclear problem is solved using the hyperspherical-harmonics approach. This approach results in numerical accuracy of about 2 per mil in the transition matrix element. Bearing in mind that the contribution of meson-exchange currents to the transition matrix element is about 5%, these results pave the way for accurate estimation of their effect.
We study the evolution of the energy gap in a unitary Fermi gas as a function of temperature. To this end we approximate the Fermi gas by the Hubbard lattice Hamiltonian and solve using the dynamical mean-field approximation. We have found that below the critical temperature, Tc, the system is a superfluid and the energy gap is decreasing monotonously. For temperatures above Tc the system is an insulator and the corresponding energy gap is monotonously increasing.
Dynamical mean-field approximation with explicit pairing is utilized to study the properties of a two-component Fermi gas at unitarity. The problem is approximated by the lattice Hubbard Hamiltonian, and the continuum limit is realized by diluting the lattice. We have found that at zero temperature the predictions of this theory for the energy and the pairing gap agree remarkably well with the results of full numerical Monte-Carlo simulations. Investigating the evolution of the system with temperature we identify the existence of a second order phase transition associated with a jump in the heat capacity and the collapse of the pairing gap.