Realistic Two-body Interaction Research Articles

Development of a fully analytical equation of state using ab initio interaction potentials. Application to pure simple fluids: Noble gases Ne, Ar, Kr, and Xe

In this work, we have extended the first-order mean spherical approximation (FMSA) equation of state (EOS) of Tang and Lu [J. Chem. Phys., 99, 9828 (1993)] in order to predict accurately fluid phase diagrams using ab initio potentials. At this level of development, we restricted to simple spherical compounds.The original equation based on hard-core two-Yukawa (HC2Y) was improved by the following:•Adding a new approximate simple correction to include higher orders in the development of Tang and Lu to get an analytical model closer to the full MSA.•Including a term to a better account for the long-range behavior of two-body potentials.•Adding a three-body interaction term (1st order perturbation) based on Axilrod-Teller potential.A general recommendation for setting the hard-sphere diameter value was also given.The predictive capability of the EOS was tested in a systematic manner. First, we checked that various simple theoretical potential (Mie n-6 and Exp n-6) phase diagrams are well reproduced. Second, the EOS was used for predicting fluid phase diagrams of the pure noble gases fluid series Ne, Ar, Kr, and Xe using realistic (i.e. derived from ab initio) two-body and three-body interaction potentials. The model is in good agreement with the experimental phase diagrams.As a conclusion, the simple statistical-mechanics-based fully analytical EOS developed in this work predicts accurately fluid phase diagrams of simple spherical compounds using ab initio potentials. No adjustable parameter was used. This EOS constitutes a strong basis for future development of a predictive model based on ab initio potentials and applicable to more complex compounds.

Nuclear response to supernova neutrino spectra

In current probes searching for rare event processes, appropriate nuclear targets are employed (in the COBRA double-beta decay detector the CdZnTe semiconductor is used). In this work the response of such detectors to various low-energy neutrino spectra is explored starting from state-by-state calculations of the neutrino-nucleus reactions cross sections obtained by using the quasi particle random phase approximation (QRPA) based on realistic two-body residual interactions. As a concrete example, we examine the response of 64Zn isotope to low energy supernova neutrinos.

Nucleon-pair wave functions in a single- j shell

In this work we study approximate and exact solutions for nucleons in a single-$j$ shell, from the perspective of nucleon-pair basis states, i.e., those coupled by pairs with good spins. We find that for four, five, and six particles in the $0{h}_{11/2}$ shell, a selected set of independent nucleon-pair basis states leads to approximate solutions of a realistic two-body interaction, without resorting to the diagonalization. We analytically show that for six particles in the $j=\frac{11}{2}$ shell, two nucleon-pair states with $J=3$ and 11---which are coupled by three pairs of spin 0, 2, and 4 and by pairs of spin 0, 2, and 10, respectively---are eigenstates of any two-body interactions. In particular, we construct general analytic expressions for states of definite seniority numbers $\ensuremath{\nu}=3,4,5$ in terms of nucleon-pair basis states, based on which we further derive exact wave functions for a few eigenstates of any two-body interactions in the midshells of $j=\frac{7}{2},\frac{9}{2},\frac{11}{2}$. The exact wave functions given here should be useful in interpreting electromagnetic moment and transition properties of corresponding nuclei.

Spin-chain model of a many-body quantum battery

Recently, it has been shown that energy can be deposited on a collection of quantum systems at a rate that scales super-extensively. Some of these schemes for `quantum batteries' rely on the use of global many-body interactions that take the batteries through a correlated short cut in state space. Here, we extend the notion of a quantum battery from a collection of a priori isolated systems to a many-body quantum system with intrinsic interactions. Specifically, we consider a one-dimensional spin chain with physically realistic two-body interactions. We find that the spin-spin interactions can yield an advantage in charging power over the non-interacting case, and we demonstrate that this advantage can grow super-extensively when the interactions are long ranged. However, we show that, unlike in previous work, this advantage is a mean-field interaction effect that does not involve correlations and that relies on the interactions being intrinsic to the battery.

Effective operators in a single-j orbital

We present an analysis of effective operators in the shell model with up to three-body interactions in the Hamiltonian and two-body terms in electromagnetic transition operators when the nucleons are either neutrons or protons occupying a single-j orbital. We first show that evidence for an effective three-body interaction exists in the N = 50 isotones and in the lead isotopes but that the separate components of such interaction are difficult to obtain empirically. We then determine higher-order terms on more microscopic grounds. The starting point is a realistic two-body interaction in a large shell-model space together with a standard one-body transition operator, which, after restriction to the dominant orbital and with use of stationary perturbation theory, are transformed into effective versions with higher-order terms. An application is presented for the lead isotopes with neutrons in the orbital.

Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions

Aims. We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods. The EOS is derived using the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Neutron star properties are next computed solving numerically the Tolman–Oppenheimer–Volkov structure equations. Results. Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to ~4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

Quartet correlations in N = Z nuclei induced by realistic two-body interactions

Two variational quartet models previously employed in a treatment of pairing forces are extended to the case of a general two-body interaction. One model approximates the nuclear states as a condensate of identical quartets with angular momentum $J=0$ and isospin $T=0$ while the other let these quartets to be all different from each other. With these models we investigate the role of alpha-like quartet correlations both in the ground state and in the lowest $J=0$, $T=0$ excited states of even-even $N=Z$ nuclei in the $sd$-shell. We show that the ground state correlations of these nuclei can be described to a good extent in terms of a condensate of alpha-like quartets. This turns out to be especially the case for the nucleus $^{32}$S for which the overlap between this condensate and the shell model wave function is found close to one. In the same nucleus, a similar overlap is found also in the case of the first excited $0^+$ state. No clear correspondence is observed instead between the second excited states of the quartet models and the shell model eigenstates in all the cases examined.

Fermionic non-Abelian fractional Chern insulators from dipolar interactions

We study fermions on a triangular lattice model that exhibits topological flatbands characterized by nonzero Chern numbers. Our scheme stems from the well-known Hofstadter model but the next-nearest-neighbor hopping is introduced, which is crucial for tuning the lowest band to be nearly flat. Differing from previous proposals with the necessity of multiparticle interactions, we consider the more realistic long-range dipolar interaction combined with two-body short-range attractions between fermions. We show the realization of the non-Abelian $\nu=1/2$ Moore-Read fractional Chern insulators, and strong evidence for the existence of the more exotic $\nu=3/5$ Read-Rezayi fractional Chern insulators. Our results provide insights for the experimental realization of these exotic states by realistic two-body interactions and thus facilitates the implementation of the universal topological quantum computation.

Gamow–Teller strength distributions in 76Ge, 76,82Se, and 90,92Zr by the deformed proton–neutron QRPA

Abstract The deformed proton–neutron quasiparticle random phase approximation (QRPA) has been developed and applied to evaluate Gamow–Teller (GT) transition strength distributions, including high-lying excited states. The data of high-lying excited states are recently available beyond one or two nucleon threshold by charge exchange reactions using hundreds of MeV projectiles. Our calculations started with single-particle states calculated using a deformed, axially symmetric Woods–Saxon potential. The neutron–neutron and proton–proton pairing correlations are explicitly taken into account at the deformed Bardeen–Cooper–Schriffer theory. Additionally, the ground state correlations and two-particle and two-hole mixing states were included in the deformed QRPA. In this work, we used a realistic two-body interaction, given by the Brueckner G-matrix based on the CD Bonn potential to reduce the ambiguity on the nucleon–nucleon interactions inside nuclei. We applied our formalism to the GT transition strengths for 76Ge, 76,82Se, and 90,92Zr, and compared the results with the available experimental data. The GT strength distributions were sensitive to the deformation parameter as well as its sign, i.e., oblate or prolate. The Ikeda sum rule, which is usually thought to be satisfied under the one-body current approximation, regardless of nucleon models, was used to test our numerical calculations and shown to be satisfied without introducing the quenching factor, if high-lying GT excited states were properly taken into account. Most of the GT strength distributions of the nuclei considered in this work have the high-lying GT excited states beyond one-nucleon threshold, which are shown to be consistent with the available experimental data.

Differential equations in momentum space for the three-body problem in the case of pointlike pair interactions

Corrects schemes for solving equations of three-body dynamics for systems governed by a zerorange two-body interaction are considered. Correlations between spectral features of a three-boson system are obtained. The results are compared with the results obtained by calculating the spectra and scattering lengths in the system of three helium atoms with realistic two-body interaction potentials.

Low-energy electric dipole response of Sn isotopes

We study the low-energy dipole (LED) strength distribution along the Sn isotopic chain in both the isoscalar (IS) and the isovector (IV, or E1) electric channels, to provide testable predictions and guidance for new experiments with stable targets and radioactive beams. We use the self-consistent Quasi-particle Random-Phase Approximation (QRPA) with finite-range interactions and mainly the Gogny D1S force. We analyze also the performance of a realistic two-body interaction supplemented by a phenomenological three-body contact term. We find that from N=50 and up to the N=82 shell closure (132Sn) the lowest-energy part of the IS-LED spectrum is dominated by a collective transition whose properties vary smoothly with neutron number and which cannot be interpreted as a neutron-skin oscillation. For the neutron-rich species this state contributes to the E1 strength below particle threshold, but much more E1 strength is carried by other, weak but numerous transitions around or above threshold. We find that strong structural changes in the spectrum take effect beyond N=82, namely increased LED strength and lower excitation energies. Our results with the Gogny interaction are compatible with existing data. On this basis we predict that a) the summed IS strength below particle threshold shall be of the same order of magnitude for N=50-82, b) the summed E1 strength up to approximately 12 MeV shall be similar for N=50-82 MeV, while c) the summed E1 strength below threshold shall be of the same order of magnitude for N ~ 64 - 82 and much weaker for the lighter, more-symmetric isotopes. We point out a general agreement of our results with other non-relativistic studies, the absence of a collective IS mode in some of those studies, and a possibly radical disagreement with relativistic models.

Adiabatic quantum optimization with the wrong Hamiltonian

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions.

Properties of trapped neutrons interacting with realistic nuclear Hamiltonians

We calculate properties of neutron drops in external potentials using both quantum Monte Carlo and no-core full configuration techniques. The properties of the external wells are varied to examine different density profiles. We compare neutron drop results given by a selection of nuclear Hamiltonians, including realistic two-body interactions as well as several three-body forces. We compute a range of properties for the neutron drops: ground-state energies, spin-orbit splittings, excitation energies, radial densities and rms radii. We compare the equations of state for neutron matter for several of these Hamiltonians. Our results can be used as benchmarks to test other many-body techniques, and to constrain properties of energy-density functionals.

Nuclear Structure of 12,14Be Within Deformed Quasi-Particle Random Phase Approximation (DQRPA)

We developed a deformed quasi-particle random phase approximation (DQRPA) to describe the Gamow–Teller (GT) transitions on even–even neutron-rich nuclei. To describe deformed nuclei, we exploited the deformed axially symmetric Woods–Saxon potential, the deformed BCS, and the deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn CD potential. The deformed single particle states are expanded in terms of the spherical harmonic oscillator basis in order to take the realistic G-matrix stored in the spherical basis. We calculated GT strength distributions, B(GT), of two nuclei 12,14Be for many different deformation parameter β 2 values as a function of the excitation energy E ex w.r.t. the ground state of a parent nucleus. Our results for 12Be predict to prefer a prolate shape and B(GT) results of 14Be turn out to be independent of the β 2 values.

High resolution spectroscopy of112Sn through the114Sn(p,t)112Sn reaction

The ${}^{114}$Sn($p$,$t$)${}^{112}$Sn reaction has been investigated in a high resolution experiment at incident proton energy of 22 MeV. Angular distributions for 28 transitions to levels of ${}^{112}$Sn up to the excitation energy of 3.624 MeV have been measured. The spin and parity identification has been carried out by means of a distorted-wave Born approximation (DWBA) analysis, performed by using conventional Woods-Saxon potentials. A shell-model study of ${}^{112}$Sn nucleus has been performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The energy spectra have been calculated and compared with the experimental ones, while the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, have been used in the microscopic DWBA calculation of the cross-section angular distributions.

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective two-, three- and four-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming two-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length at(0) defined at zero collision energy, which is necessary to obtain both the leading-order effective four-body interaction and consistently include corrections for realistic two-body interactions. The leading-order, effective three- and four-body interaction energies are and , where ω and σ(ω) are the harmonic oscillator frequency and length, respectively, and energies are in units of ℏω. The one-standard deviation error ±0.0001 for the third-order coefficient in U3(ω) is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective three- and four-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range (FR) boson–boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.

Superfluid properties of the inner crust of neutron stars

We investigated the superfluid properties of the inner crust of neutron stars, solving the Hartree-Fock-Bogoliubov equations in spherical Wigner-Seitz cells. Using realistic two-body interactions in the pairing channel, we studied in detail the Cooper-pair and the pairing-field spatial properties, together with the effect of the proton clusters on the neutron pairing gap. Calculations with effective pairing interactions are also presented, showing significant discrepancies with the results obtained with realistic pairing forces. At variance with recent studies on finite nuclei, the neutron coherence length is found to depend on the strength of the pairing interaction, even inside the nucleus. We also show that the spherical Wigner-Seitz approximation breaks down in the innermost regions of the inner crust, already at baryonic densities ${\ensuremath{\rho}}_{b}\ensuremath{\ge}8\ifmmode\times\else\texttimes\fi{}{10}^{+13}$ g/cm${}^{3}$.

Gamow-Teller Transitions for Neutron-Rich Nuclei in the Superburst by the Deformed Quasi-particle RPA(DQRPA)

We developed the deformed quasi-particle random phase approximation (DQRPA) for the Gamow-Teller (GT) transition for even-even deformed nuclei. We started from the deformed axially symmetric Woods-Saxon potential based on the Nilsson basis, and performed deformed BCS and deformed QRPA. In this work, we used a realistic two-body interaction taken by Brueckner G-matrix based on the Bonn potential. For the application, we calculated the GT transition for the deformed nuclei at the surface of the neutron star, where electron captures are important heat sources for the carbon flash.

Theoretical analysis of the possible ultra-low-Q-value decay branch of 135Cs

We have investigated the feasibility of observing an ultra-low-Q-value beta-decay branch of 135Cs by applying the microscopic quasiparticle–phonon model with a realistic two-body nuclear interaction. This work was motivated by an earlier combined experimental and theoretical work on decays of 115In. The inaccuracy of the ground-state-to-ground-state Q value limits our ability to draw definite conclusions, and therefore modern precision measurements for it are called for. We present the computed partial half-lives of each channel for the most likely ranges of Q values.

High-resolution measurement of theSn118,124(p,t)Sn116,122reactions: Shell-model and microscopic distorted-wave Born approximation calculations

The $^{118,124}\mathrm{Sn}$($p$,$t$)$^{116,122}\mathrm{Sn}$ reactions have been investigated in high-resolution experiments at incident proton energies of 24.6 and 25 MeV, respectively. Angular distributions for 55 transitions to levels of $^{116}\mathrm{Sn}$ and 63 transitions to levels of $^{122}\mathrm{Sn}$, up to excitation energies of $~3.850$ and $~4.000$ MeV, respectively, have been measured. The spin and parity identification was carried out by means of a distorted-wave Born approximation (DWBA) analysis, performed by using conventional Woods-Saxon potentials. A shell-model study of $^{116}\mathrm{Sn}$ and $^{122}\mathrm{Sn}$ nuclei was performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly magic nucleus $^{132}\mathrm{Sn}$ was assumed as a closed core, with the 16 and 10 valence neutron holes occupying the five levels of the 50-82 shell. The energy spectra have been calculated and compared with the experimental ones, and the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, have been used in the microscopic DWBA calculation of some cross-section angular distributions of both reactions.