Two-nucleon System Research Articles

Second-order perturbation theory for and pd scattering in pionless EFT

This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second-order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, including two-photon contributions at next-to-next-to-leading order. After fixing a three-nucleon force to the binding energy at this order, proton–deuteron scattering in the doublet S-wave channel is calculated for moderate center-of-mass momenta.

Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.

Combining Few-Body Cluster Structures with Many-Body Mean-Field Methods

Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of $^{22}$C ($^{20}$C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied.

Two-nucleon higher partial-wave scattering from lattice QCD

We present a determination of nucleon-nucleon scattering phase shifts for l >= 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For l > 0, this is the first lattice QCD calculation using the Luscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to m_pi = m_K ~ 800 MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V ~ (3.5 fm)^3 and V ~ (4.6 fm)^3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.

Low-energy theorems for nucleon-nucleon scattering atMπ=450MeV

We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of $M_\pi\simeq 450$ MeV obtained by the NPLQCD collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^3S_1$ and $^1S_0$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation.

Classical and Mexican hat-type potential energy curve for the hydrogen molecule from a confined Kratzer oscillator

We review harmonic oscillator theory for closed, stable quantum systems. The H2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg–Klein–Rees (RKR) H2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H2, HF, I2, N2 and O2 to a single one. The equal probability for H2, originating either from [Formula: see text] or [Formula: see text], is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields.

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m_{π}∼450 and 806MeV in uniform, time-independent magnetic fields of strength |B|∼10^{19}-10^{20} G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems.

Experimental setup for studying N–N correlations in reaction d + 2H → n + n + p + p

An experimental setup for studying the effects of N–N correlations in reaction d + 2H → n + n + p + p is described. It is planned to determine the energies of quasibound singlet states of two-nucleon systems (nn, pp, and np) under identical experimental conditions. The experiment is modeled numerically. The setup allows us to detect simultaneously the two nucleons (n + n, p + p, or n + p) resulting from the breakup of a quasi-bound state and a third particle (n or p). The characteristics of the setup’s detectors are investigated. A test experiment was carried out on reaction d + 2H → (pp) + (nn), with two protons and a neutron being detected.

Ab initio Calculation of the np→dγ Radiative Capture Process.

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np→dγ, and the photo-disintegration processes γ^{(*)}d→np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m_{π}~450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m_{π}~806 MeV, using only lattice QCD inputs, a cross section σ^{806 MeV}~17 mb is found at an incident neutron speed of v=2,200 m/s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ^{lqcd}(np→dγ)=334.9(+5.2-5.4) mb is obtained at the same incident neutron speed, consistent with the experimental value of σ^{expt}(np→dγ)=334.2(0.5) mb.

Investigation of the reaction d + d → 2He + 2 n at the deuteron energy of 15 MeV

An experimental setup for studying the reaction d + d → 2He + 2 n is described, and the first preliminary results of measurements at a deuteron energy of 15 MeV are presented. The experiment was aimed at determining the energies of quasibound singlet states of two-nucleon systems (nn and pp), these energies being important features of nucleon–nucleon (NN) interaction. The measurements in question were performed at a deuteron beamfrom the U-120 cyclotron of the Skobeltsyn Institute ofNuclear Physics (Moscow State University). Two protons and one of the neutrons fromthe breakup of the dineutron system were detected in the experiment. A simulation of the reaction in question and preliminary experimental results reveal the possibility of determining the energy of quasibound singlet states on the basis of the form of the energy spectra of particles originating from their breakup.

The dynamical Casimir effect in two-nucleon systems

Arguments for registering at JINR synchrophasotron a quantum phenomenon similar to theoretically predicted but still unobserved experimentally Hawking effect are given. Here an analogue of the Hawking radiation is a generalized coherent state corresponding to the dynamical symmetry group SU(1, 1), which describes Bose condensate of pions in a strong external field.

The Two-Nucleon and Three-Nucleon System in Three Dimensions

The Two-Nucleon and Three-Nucleon System in Three Dimensions

Core excitation in three-body nuclear reactions: Improved nucleon-core potential

Three-body nuclear reactions in two-nucleon plus core systems are described in the framework of exact scattering equations including the core excitation. A nucleon-core optical potential is constructed that can be easily adjusted to the reference potential and thereby to the experimental two-body data, if available. This constitutes an important improvement over the simple deformation of the potential used previously that violated the original fit to the data. Predictions for elastic, inelastic, and transfer reactions involving $^{10}{Be}$ and $^{24}{Mg}$ nuclear cores are obtained. The new optical potential leads to a moderate increase of cross sections.

Inclusive and Exclusive Scatterings from Tensor Polarized Deuteron

The possibility of using a tensor polarized deuteron target in electroproduction reactions creates new opportunities for studying different phenomena related to the short-range hadronic and nuclear physics. The use of the tensor polarized deuteron allows us to isolate smaller than average inter-nucleon distances for the bound two-nucleon system. In this report we consider several high Q2 reactions which are particularly sensitive to the short-range two- nucleon configurations in the deuteron. One is the relativistic dynamics of electron-bound- nucleon scattering, which can be studied in both inclusive and exclusive reactions, and the other is the strong final state interaction in close proximity of two nucleons that can be used as a sensitive probe for color-transparency phenomena.

From nucleon-nucleon interaction matrix elements in momentum space to an operator representation

Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the partial waves with low angular momentum. As a first application we use this method to obtain an operator representation for the Argonne potential transformed by means of the unitary correlation operator method and discuss the necessity of including momentum-dependent operators. The resulting operator representation leads to the same results as the original momentum space matrix elements when applied to the two-nucleon system and various light nuclei. For applications in fermionic and antisymmetrized molecular dynamics, where an operator representation of a soft but realistic effective interaction is indispensable, a simplified version using a reduced set of operators is given.

Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory

We calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave decomposition. Deuteron form factors are extracted by applying the Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation function of deuteron interpolating fields and the electromagnetic current operator. Numerical results of a leading-order calculation with removed cutoff regularization agree well with experimental data.

Implicit Versus Explicit Renormalization of the NN Force: An S-Wave Toy Model

We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.

Differential cross section and vector analysing power of the p pol p → {pp} s π0 reaction at 353–700 MeV

The reaction ppolp → {pp}sπ0 was studied with the ANKE spectrometer at COSY-Julich using a polarized beam with energies 353, 500, 550 and 700 MeV. The proton pairs {pp}s were detected at low excitation energy Epp < 3 MeV, where S-wave dominates. The angular dependences of vector analysing power Ay and differential cross section dσ/dΩ of the reaction have been obtained for the most of the angular range at 353 MeV and forward angles at the higher beam energies. The partial wave amplitude analysis, done with the 353 MeV results, is important for Chiral Perturbation Theory tests at this energy. The data at higher energies detalize the energy dependence of dσ/dΩ(0°) obtained earlier. It allows to learn about the dynamics of the Δ(1232) resonance excitation in two-nucleon systems.

Two-nucleon systems in a finite volume. II.S13−D13coupled channels and the deuteron

The energy spectra of two nucleons in a cubic volume provide access to the two phase shifts and one mixing angle that define the S-matrix in the 3S1-3D1 coupled channels containing the deuteron. With the aid of recently derived energy quantization conditions for such systems, and the known scattering parameters, these spectra are predicted for a range of volumes. It is found that extractions of the infinite-volume deuteron binding energy and leading scattering parameters, including the S-D mixing angle at the deuteron pole, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with 10 fm <~ L <~ 14 fm. The viability of extracting the asymptotic D/S ratio of the deuteron wavefunction from Lattice QCD calculations is discussed.

Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry

The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L \sim 3.4 fm, 4.5fm and 6.7 fm, and with a lattice spacing of b \sim 0.145 fm. With determinations of the energies of the two-nucleon systems (both of which contain bound states at these up and down quark masses) at rest and moving in the lattice volume, Luscher's method is used to determine the low-energy phase shifts in each channel, from which the scattering length and effective range are obtained. The scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) = 9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) = {4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1) = 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) = 3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes exact in the limit of large-N_c. In both spin channels, the phase shifts change sign at higher momentum, near the start of the t-channel cut, indicating that the nuclear interactions have a repulsive core even at the SU(3)-symmetric point.