Proton Pairs Research Articles

Mechanism of the transition of solid hydrogen to the conducting state at high pressures

The density functional theory is applied for the calculation of the dependence of pressure and profiles of proton–proton pair correlation function of hydrogen on density in the range 1.14–2.0 g/cm3 at temperature 100 K. The calculated range of pressures is 300–2600 GPa, which corresponds to the solid phase of hydrogen. The transition at pressure 607 GPa is found, which is characterized by a noticeable jump of electrical conductivity and a sharp decrease in the number of molecules of H2. The structural transition is characterized by the first peak of the pair correlation function at a distance of 0.92 Å, which corresponds to the interatomic distance in the ion and does not depend on density. Therefore, the nature of the transition combines ionization with structural changes.

Observation of resonance-like behavior of the pp → {pp}sπ0 reaction around √s = 2.65 GeV

The pp → {pp}sπ0 reaction, where {pp}s denotes a diproton, i.e. an unbound interacting proton pair in the 1S0 state, has been studied in order to obtain the forward differential cross section dσ/dΩ at 11 energy values in the region of 0.8–2.8 GeV. A resonance-like peak with the energy E0 = 2.647 ± 0.005 GeV and the width Γ = 0.26 ± 0.03 GeV has been observed in the energy dependence of the differential cross section dσ/dΩ at zero angle. The slope of the angular dependence for the energies in the peak region is different compared with the energies around it. Possible implications on this phenomenon are discussed.

Resonance behaviour of the reactions pp → {pp}sπ0 and pd → pdππ in the 1-2 GeV region

Resonance peaks observed in the cross sections of the reaction pp → {pp}sπ0, where {pp}s is the 1S0 state of the proton pair, and pd → pdππ in the GeV region are considered in the framework of mechanisms involving known baryon and two-baryon resonances.

Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

A mixture of superconducting and superfluid nuclear liquids of protons coupled to the ultrarelativistic electron gas, and neutrons is considered. In the magnetohydrodynamic (MHD) approximation, the energy-momentum (stress) tensor is derived, and the entrainment contribution is found in the explicit form. It is shown that this contribution generates a force density, when a superfluid velocity lag and the magnetic field are simultaneously present. This force may be important in the nuclear "pasta" phase in neutron stars, if the proton and neutron Cooper pairing in the pasta phase is taken into account. It is found that if the liquid-crystalline matter of the pasta phase is superfluid and superconducting, then magnitude of the forces acting upon element of matter at typical magnetic field and the superfluid velocity lag, under certain conditions may become large enough to induce a critical stress in the neutron star crust. As an application, the necessary conditions for triggering of a starquake are found in the pasta phase of neutron stars, assuming that the nuclei are flat slabs in parallel magnetic field. The present model includes two independent local parameters: the superfluid velocity lag and the magnetic field. Possible links between the entrainment force and the magnetar starquake triggering mechanism, and some open problems are discussed.

The production of charged-kaon pairs in proton–antiproton collisions: The role of higher-twist mechanism

The higher-twist (HT) contribution to the charged-kaon pair production in the high energy proton–antiproton collisions at large transverse momentum [Formula: see text] is investigated by using the frozen coupling constant approach for various kaon distribution amplitudes (DAs), which are predicted by light-cone formalism, the light-front quark model, the nonlocal chiral quark model and the light-front holographic AdS/CFT approach. In the numerics, the dependencies of the HT contribution on the transverse momentum [Formula: see text], the rapidity [Formula: see text], and the variable [Formula: see text] are discussed with special emphasis put on DAs. The HT contribution is also compared with the leading-twist ones. It is shown that the HT contributions are dependent on the kaon DAs and also some other phenomenological parameters such as momentum cutoff parameter [Formula: see text]. Inclusive kaon pair production presents a remarkable test case in which HT terms dominate those of LT in certain kinematic regions. The HT direct production process via gluon–gluon fusion contributes significantly to the inclusive cross-section at large [Formula: see text].

First-Principles Comparison of Proton and Divalent Copper Cation Exchange Energy Landscapes in SSZ-13 Zeolite

The relative proximity of Al atoms substituted in zeolite lattices is an important parameter that influences both hydrothermal stability and catalytic function, but the underlying chemistry that governs Al site proximity is not well understood. Here, we examine relationships between exchanged countercations and different Al–Al arrangements in a chabazite (SSZ-13) zeolite lattice. We report periodic supercell density functional theory (DFT) calculations for structures and energies of SSZ-13 lattices with systematically enumerated and varied Al–Al proximity, both charge-uncompensated and charge-compensated by either proton pairs (H+/H+) or divalent copper cations (Cu2+). Al–Al interactions are electrostatically repulsive without charge compensation, but the relative energies of certain Al–Al site arrangements change upon compensation by countercations. Al–Al interactions are uniformly attractive when compensated by H+/H+ pairs but are attractive at long and repulsive at short Al–Al distances when compensate...

Transport coefficients of leptons in superconducting neutron star cores

I consider the thermal conductivity and shear viscosity of leptons (electrons and muons) in the nucleon NS cores where protons are in the superconducting state. I restrict the consideration to the case of not too high temperatures $T\lesssim 0.35T_{\mathrm{c}p}$, where $T_{\mathrm{c}p}$ is the critical temperature of the proton pairing. In this case, lepton collisions with protons can be neglected. Charged lepton collision frequencies are mainly determined by the transverse plasmon exchange and are mediated by the character of the transverse plasma screening. In our previous works [Shternin \& Yakovlev, Phys. Rev. D {\bf 75} 103004 (2007); {\bf 78} 063006 (2008)] the superconducting proton contribution to the transverse screening was considered in the Pippard limit $\Delta \ll \hbar q v_{\mathrm{F}p}$, where $\Delta$ is the proton pairing gap, $v_{\mathrm{F}p}$ is the proton Fermi velocity, and $\hbar q$ is the typical transferred momentum in collisions. However, for large critical temperatures (large $\Delta$) and relatively small densities (small $q$) the Pippard limit may become invalid. In the present study I show that this is indeed the case and that the older calculations severely underestimated the screening in a certain range of the parameters appropriate to the neutron star cores. As a consequence, the kinetic coefficients at $T\ll T_{\mathrm{c}p}$ are found to be smaller than in previous calculations.

NLO K factors for ZZ double vector boson pairs in proton–proton collisions

The impact of higher-order matrix elements and [Formula: see text] and [Formula: see text] scales on the NLO K factors for ZZ vector boson pairs in proton–proton collisions are presented in this study. All predictions are performed using MCFM-8.0 Monte Carlo generator. First, the QCD predictions of ZZ production at LO and NLO accuracies are obtained using two most recent PDFs, MMHT2014 and CT14. To discuss the impact of higher-order matrix elements on the NLO K factors, both LO and NLO corrections are obtained by LO, NLO and NNLO matrix elements of these two most recent PDFs. Then, the impact of [Formula: see text] and [Formula: see text] scales on the NLO K factors are further discussed by using six different values of [Formula: see text] and [Formula: see text] in a range of [Formula: see text], [Formula: see text], where [Formula: see text] is Z boson mass.

Nuclear properties for astrophysical and radioactive-ion-beam applications (II)

We tabulate the ground-state odd-proton and odd-neutron spins and parities, proton and neutron pairing gaps, one- and two-neutron separation energies, quantities related to β-delayed one- and two-neutron emission probabilities, average energy and average number of emitted neutrons, β-decay energy release and half-life with respect to Gamow–Teller decay with a phenomenological treatment of first-forbidden decays, one- and two-proton separation energies, and α-decay energy release and half-life for 9318 nuclei ranging from 16O to 339136 and extending from the proton drip line to the neutron drip line. This paper is a new and improved version of Atomic Data And Nuclear Data Tables [66 131 (1997)]. The starting point of our present work is the new study (FRDM(2012)) of nuclear ground-state masses and deformations based on the finite-range droplet model and folded-Yukawa single-particle potential published in a previous issue of Atomic Data And Nuclear Data Tables [109–110, 1 (2016)]. The β-delayed neutron-emission probabilities and Gamow–Teller β-decay rates are obtained from a quasi-particle random-phase approximation with single-particle levels and wave functions at the calculated nuclear ground-state shapes as input quantities. A development since 1997 is we now use a Hauser–Feshbach approach to account for (n, γ) competition and treat first-forbidden decay in a phenomenological approach.

α decay preformation probabilities across the N = 126 shell closure based on the single particle energy spectra

We put forward a concise approach to calculate the α decay preformation probabilities by defining the microscopic valence nucleon and hole numbers based on the single particle energy spectra, which is obtained within the relativistic Hartree–Bogoliubov model. The residual interactions including neutron–neutron, proton–proton pairing and proton–neutron correlations could trigger the collective motions among the valence nucleons and holes, along with the independent particle motions under the mean field assumption. Therefore the more the number of valence nucleons and holes, the stronger the collective motions such as α particle clustering. We assume that the valence orbits locate around the Fermi surface obeying a Fermi–Dirac distribution, i.e. nucleons (holes) occupying the orbits with much lower (higher) energies away from the Fermi surface can not be considered as the valence nucleons (holes). The α decay preformation probabilities Pα are calculated within the Np Nn scheme in terms of the valence proton–neutron interaction. As an example, in the case of even–even polonium, radon, radium and thorium isotopes the extracted α decay preformation probabilities , which are obtained within the generalized liquid drop model, can be well reproduced by employing two different formulas to take into account the shell effect at N = 126 shell closure.

Mass Ratios and Proton Pairing for Isotones with N = 20, 50, and 82

Different estimates of the even–odd effect for the nuclear mass surface are discussed. The proton-number dependence of the energy gap is derived from the measured masses of the N = 20, 50, and 82 isotones with closed neutron shells. Its interrelation with the properties of external proton shells is demonstrated, and the effects of proton pairing are considered along with the microscopic nuclear structure.

Isovector plus isoscalar neutron–proton pairing effect on nuclear statistical quantities using a path integral approach

Gap equations at finite temperature are established in the isovector plus isoscalar pairing case [Formula: see text] using a path integral approach. Expressions of the various statistical quantities, i.e., the energy, the entropy and the heat capacity are then deduced. It is shown that they do generalize the ones obtained in the pure isovector ([Formula: see text]) pairing case, as well as those obtained within the conventional finite temperature Bardeen–Cooper–Schrieffer (FTBCS) theory in the pairing between like-particles case. A numerical study is then performed using the schematic one-level model. It is shown that the isoscalar n–p gap parameter [Formula: see text] behaves as a function of the temperature, like its homologues [Formula: see text] and [Formula: see text] in the conventional FTBCS approach. As for the three other gap parameters, i.e., [Formula: see text], [Formula: see text] and [Formula: see text], their behaviors are clearly modified when the isoscalar pairing is taken into account. In particular, one observes a shift of the values of the critical temperatures. Dealing with the statistical quantities, the inclusion of the isoscalar pairing, in addition to the isovector one, leads to a lowering of the energy as well as a change of the shapes of the curves of the energy, the entropy and the heat capacity as a function of the temperature.

Effect of Nucleon Pairing in the Spectra of N = 50 Isotones

The emergence of the pairing effect of identical nucleons in the j = 9/2 state in low-lying excited states of nuclei near 90Zr (N = 50, Z = 40) is discussed. Multiplets of states with seniority s ≥ 2, the splitting of which is determined by the proton pairing energy, are clearly visible in the nuclear spectra for a chain of N = 50 isotones. A comparison of the spectra of ground state multiplets, calculated in the δ-interaction approximation, with experimental data and results from other theoretical calculations shows this approach can be used to describe the structure of spectra and level positions with high J values.

Pairing of Neutrons and Protons in N = Z Nuclei

Values of neutron–proton pairing based on mass relations are estimated. It is shown that substantially different formulas for calculating the np-pairing energy in self-conjugate nuclei yield similar results. Comparison of the obtained values and the structure of ground state multiplet spectra shows that mass relations can be used to describe the isovector (T = 1) component of np-pairing to sufficient accuracy, but provides little or no information on isoscalar component T = 0.

Electron paramagnetic resonance of a 10B-containing heterocyclic radical

Electron paramagnetic resonance measurements for a 10B-containing heterocyclic phenanthrenedione radical, (C6F5)2B(O2C14H8), were made at X-band in 9:1 toluene:dichloromethane from 10 to 293 K and in toluene from 180 to 293 K. In well-deoxygenated 0.1 mM toluene solution at room temperature hyperfine couplings to 10B, four pairs of protons and five pairs of fluorines contribute to a continuous wave spectrum with many resolved lines. Hyperfine couplings were adjusted to provide the best fit for spectra of the radical enriched in 10B and the analogous radical synthesized with 10,11B in natural abundance, resulting in small refinements of the hyperfine coupling constants previously reported for the natural abundance sample. Electron spin relaxation rates at temperatures between 15 and 293 K were similar for samples containing 10B and natural isotope abundance. Analysis of electron spin echo envelope modulation and hyperfine correlation spectroscopy data at 80 K found Axx = −7.5 ± 0.3, Ayy = −8.5 ± 0.3, and Azz = −10.8 ± 0.3 MHz for 11B, which indicates small spin density on the boron. The spin echo and hyperfine spectroscopy data for the 10B –containing radical are consistent with the factor of 2.99 smaller hyperfine values for 10B than for 11B.

Nuclear quantum shape-phase transitions in odd-mass systems

Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -- the number of nucleons -- theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and $E2$ reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuities at neutron number $N=90$, compared to the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared to the corresponding Sm isotopes.

Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

An extended pairing Hamiltonian that describes multi-pair interactions among isospin T=1 and angular momentum J=0 neutron–neutron, proton–proton, and neutron–proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T=1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T=1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron–proton interaction in even–even N∼Z nuclei that can be suitably described in the f5pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

Plasma phase transition in warm dense hydrogen

A new idea is developed that the fluid–fluid phase transition in warm dense hydrogen is related to the partial ionization of molecular hydrogen H2 with formation of molecular ions H and H. Conventional ab initio quantum modelling is applied. The proton–proton pair correlation functions (PCFs) obtained are used for the non‐conventional diagnostics of the phase transition and elucidation of its nature for temperatures in the range 700–1500 K. Short‐ and long‐range changes of PCFs are studied. Ionization of H2 molecules and the appearance of molecular ions H and H are revealed. The validity of the soft sphere model is tested for the long‐range order.

The hydrogen anomaly problem in neutron Compton scattering

Neutron Compton scattering (also called ‘deep inelastic scattering of neutrons’, DINS) is a method used to study momentum distributions of light atoms in solids and liquids. It has been employed extensively since the start-up of intense pulsed neutron sources about 25 years ago. The information lies primarily in the width and shape of the Compton profile and not in the absolute intensity of the Compton peaks. It was therefore not immediately recognized that the relative intensities of Compton peaks arising from scattering on different isotopes did not always agree with values expected from standard neutron cross-section tables. The discrepancies were particularly large for scattering on protons, a phenomenon that became known as ‘the hydrogen anomaly problem’. The present paper is a review of the discovery, experimental tests to prove or disprove the existence of the hydrogen anomaly and discussions concerning its origin. It covers a twenty-year-long history of experimentation, theoretical treatments and discussions. The problem is of fundamental interest, since it involves quantum phenomena on the subfemtosecond time scale, which are not visible in conventional thermal neutron scattering but are important in Compton scattering where neutrons have two orders of magnitude times higher energy. Different H-containing systems show different cross-section deficiencies and when the scattering processes are followed on the femtosecond time scale the cross-section losses disappear on different characteristic time scales for each H-environment. The last section of this review reproduces results from published papers based on quantum interference in scattering on identical particles (proton or deuteron pairs or clusters), which have given a quantitative theoretical explanation both regarding the H-cross-section reduction and its time dependence. Some new explanations are added and the concluding chapter summarizes the conditions for observing the specific quantum phenomena observed in neutron Compton scattering on protons and deuterons in condensed systems.

Search for Higgs boson pair production in events with two bottom quarks and two tau leptons in proton–proton collisions at [formula omitted

A search for the production of Higgs boson pairs in proton–proton collisions at a centre-of-mass energy of 13TeV is presented, using a data sample corresponding to an integrated luminosity of 35.9fb−1 collected with the CMS detector at the LHC. Events with one Higgs boson decaying into two bottom quarks and the other decaying into two τ leptons are explored to investigate both resonant and nonresonant production mechanisms. The data are found to be consistent, within uncertainties, with the standard model background predictions. For resonant production, upper limits at the 95% confidence level are set on the production cross section for Higgs boson pairs as a function of the hypothesized resonance mass and are interpreted in the context of the minimal supersymmetric standard model. For nonresonant production, upper limits on the production cross section constrain the parameter space for anomalous Higgs boson couplings. The observed (expected) upper limit at 95% confidence level corresponds to about 30 (25) times the prediction of the standard model.