Rm Fm Research Articles

Electric dipole polarizability in208Pb: Insights from the droplet model

We study the electric dipole polarizability $\alpha_D$ in ${}^{208}$Pb based on the predictions of a large and representative set of relativistic and non-relativistic nuclear mean field models. We adopt the droplet model as a guide to better understand the correlations between $\alpha_D$ and other isovector observables. Insights from the droplet model suggest that the product of $\alpha_D$ and the nuclear symmetry energy at saturation density $J$ is much better correlated with the neutron skin thickness $\Delta r_{np}$ of ${}^{208}$Pb than the polarizability alone. Correlations of $\alpha_D J$ with $\Delta r_{np}$ and with the symmetry energy slope parameter $L$ suggest that $\alpha_D J$ is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of thenuclear energy density functional by comparing our theoretical predictions against measurements of both $\alpha_D$ and the parity-violating asymmetry in ${}^{208}$Pb. We find that the recent experimental determination of $\alpha_D$ in ${}^{208}$Pb in combination with the range for the symmetry energy at saturation density $J=[31\pm (2)_{\rm est.}]$\,MeV suggests $\Delta r_{np}({}^{208}{\rm Pb}) = 0.165 \pm (0.009)_{\rm exp.} \pm (0.013)_{\rm theo.} \pm (0.021)_{\rm est.} {\rm fm}$ and $L= 43 \pm(6)_{\rm exp.} \pm (8)_{\rm theo.}\pm(12)_{\rm est.}$ MeV.

Integrated Resonant Optical Readout Applicable to Large Arrays of MEMS Beams

A recent report by the authors presented theoretical studies of a new method of interrogation of the position of arrays of micro-electro-mechanical system (MEMS) cantilever and doubly clamped beams. This letter represents the first experimental evidence of the performance of such an interrogation technique, confirming the modelling and showing noise performance close to the theoretical predictions. Such a technique will be useful in applications such as MEMS-based chemical sensing. Our experimental results show the potential to realize a shot-noise limited component of minimum detectable deflection of 16 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm fm}/\sqrt{\rm Hz}$</tex></formula> .

Lattice QCD at nonzero isospin chemical potential

Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multi-hadron systems. We then use these methods to study systems with the quantum numbers of up to 72 $\pi^+$'s on three ensembles of gauge configurations with spatial extents $L\sim$ 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of {390 MeV}. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three- body interactions amongst $\pi^+$'s. The systems studied correspond to isospin densities of up to $\rho_I\sim 9\ {\rm fm}^{-3}$ and probe isospin chemical potentials, $\mu_I$, in the range $m_\pi\ \lsim \mu_I\ \lsim 4.5\ m_\pi$, allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at $\mu_I\ \gsim m_\pi$.

Anomaly-induced quadrupole moment of the neutron in magnetic field

The neutrons cannot possess a quadrupole moment in the vacuum. Nevertheless, we show that in the presence of an external magnetic field the neutrons acquire a new type of quadrupole moment $Q^{ij}= \chi\,\sigma^i B^j$ involving the components of spin and magnetic field. This "chiral magnetic" quadrupole moment arises from the interplay of the chiral anomaly and the magnetic field; we estimate its value for the neutron in the static limit, and find $\chi \simeq 1.35\cdot10^{-2}\,{\rm fm}^4$. The detection of the quadrupole moment of the neutron would provide a novel test of the role of the chiral anomaly in low-energy QCD and can be possible in the presence of both magnetic and inhomogeneous electric fields. The quadrupole moment of the neutron may affect e.g. the properties of neutron stars and magnetars.

Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions

We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain wall fermions and the Iwasaki gauge action ($\beta = 2.13$). The inverse lattice spacing is $a^{-1} = 1.73$ GeV, and two spatial volumes of ((2.7{\rm fm})^3) and ((1.8 {\rm fm})^3) are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange mass is about 12 % heavier than the physical one. The structure function moments we present include fully non-perturbatively renormalized iso-vector quark momentum fraction, (< x >_{u-d}), helicity fraction, (< x >_{\Delta u - \Delta d}), and transversity, (< 1 >_{\delta u - \delta d}), as well as an unrenormalized twist-3 coefficient, (d_1). The ratio of the momentum to helicity fractions, (< x >_{u-d}/< x >_{\Delta u - \Delta d}), does not show dependence on the light quark mass and agrees well with the value obtained from experiment. Their respective absolute values, fully renormalized, show interesting trends toward their respective experimental values at the lightest quark mass. A prediction for the transversity, (0.7 < < 1 >_{\delta u -\delta d} < 1.1), in the (\bar{\rm MS}) scheme at 2 GeV is obtained. The twist-3 coefficient, (d_1), though yet to be renormalized, supports the perturbative Wandzura-Wilczek relation.

Physical results from2+1flavor domain wall QCD and SU(2) chiral perturbation theory

We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {\rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $\Omega$ baryon, and the $\pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_\pi = 124.1(3.6)_{\rm stat}(6.9)_{\rm syst} {\rm MeV}$, $f_K = 149.6(3.6)_{\rm stat}(6.3)_{\rm syst} {\rm MeV}$ and $f_K/f_\pi = 1.205(0.018)_{\rm stat}(0.062)_{\rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $\bar{\rm MS}$ we find $ m_{ud}^{\bar{\rm MS}}(2 {\rm GeV}) = 3.72(0.16)_{\rm stat}(0.33)_{\rm ren}(0.18)_{\rm syst} {\rm MeV}$ and $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.

Synthesis and Crystal Structure of a Novel A‐Zeolite‐like Copper Complex: [Cu12(SO4)12(3H2O)]·H2O

AbstractThe reaction of CuBr2, N(CH2CH2COOH)3, and Nd(NO3)3·6H2O in water adjusted pH = 5‐6 with H2SO4 at constant 55 °C afforded a novel three‐dimensional coordination complex [Cu12(SO4)12(3H2O)]·H2O, (1), which was characterized by IR, elemental analysis, and X‐ray diffraction. The crystal structure data of 1 as follows: Cubic, ${\rm Fm}{\bar 3}{\rm c}$, a = b = c = 24.018(2) Å, V = 13855 (3) Å3, Z = 968, Dc = 1.905 g/cm3, F(000) = 7712, R1 = 0.0352, wR2 = 0.0866 (I &gt; 2σ(I)), R1 = 0.0449, wR2 = 0.0927 (for all data) and S = 1.075. The analysis of crystal structure indicates that the structure of 1 is similar to that of silicate zeolite (Na12[Al12Si12O48]·27H2O).

Energy loss of a heavy quark produced in a finite size medium

We study the medium-induced energy loss $-\Delta E_0(L_p)$ suffered by a heavy quark produced at initial time in a quark-gluon plasma, and escaping the plasma after travelling the distance $L_p$. The heavy quark is treated classically, and within the same framework $-\Delta E_0(L_p)$ consistently includes: the loss from standard collisional processes, initial bremsstrahlung due to the sudden acceleration of the quark, and transition radiation. The radiative loss {\it induced by rescatterings} $-\Delta E_{rad}(L_p)$ is not included in our study. For a ultrarelativistic heavy quark with momentum $p \gsim 10 {\rm GeV}$, and for a finite plasma with $L_p \lsim 5 {\rm fm}$, the loss $-\Delta E_0(L_p)$ is strongly suppressed compared to the stationary collisional contribution $-\Delta E_{coll}(L_p) \propto L_p$. Our results support that $-\Delta E_{rad}$ is the dominant contribution to the heavy quark energy loss (at least for $L_p \lsim 5 {\rm fm}$), as indeed assumed in most of jet-quenching analyses. However they might raise some question concerning the RHIC data on large $p_{\perp}$ electron spectra.

Raynaud’s vector bundles and base points of the generalized Theta divisor

We study base points of the generalized Θ-divisor on the moduli space of vector bundles on a smooth algebraic curve X of genus g defined over an algebraically closed field. To do so, we use the derived categories Db(Pic0(X)) and Db(Jac(X)) and the equivalence between them given by the Fourier–Mukai transform \({\rm FM}_\mathcal {P}\) coming from the Poincaré bundle. The vector bundles P m on the curve X defined by Raynaud play a central role in this description. Indeed, we show that E is a base point of the generalized Θ-divisor, if and only if there exists a non-trivial homomorphism Prk(E)g+1 → E.

Magnetic properties and 119Sn hyperfine interaction parameters of LiMn6Sn6

We have synthesized LiMn6Sn6, the first RMn6Sn6 compound involving an alkali metal as R element. It crystallizes in the hexagonal (P6/mmm) HfFe6Ge6-type structure. From magnetic measurements and powder neutron diffraction experiments it is found that LiMn6Sn6 magnetically orders at TC = 380 K in a simple easy-plane ferromagnetic structure (mMn = 2.58 μB at 2 K). The 119Sn Mossbauer spectrum recorded at 5 K indicates that the tin nuclei experience huge hyperfine fields (as large as 35 T). Electronic structure calculations are used to gain information about the microscopic origin of both the hyperfine field and electric field gradient at the Sn nuclei. The former arises due to spin-dependent hybridization between the 5s states of Sn and the 3d states of Mn. The latter comes from the 5p charge density close to the nucleus, whose anisotropy is mainly produced through directional interactions with the 3d states of the first Mn neighbors. Comparison between experimental quadrupole splittings and theoretical electric field gradients allows us to propose a value of \(Q = - 11.2 \pm 0.7~{\rm fm}^{2}\) for the quadrupole moment of the first excited state (I= 3/2) of the 119Sn nucleus.

Crystal Structure of Rubidium Tetraiodothallate(III) Dihydrate, RbTlI4·2H2O

AbstractThe crystal structure of RbTlI4·2H2O (cubic, ${\rm Fm}{\bar 3}\rm c$, Nr. 226, Z = 24, a = 1993.5(2) pm, 327 unique reflections with Io &gt; 2σ(Io), R1 = 0.0305, wR2 = 0.0702, GooF = 1.1199, T = 298(2) K) is characterized by an ReO3 analogous arrangement of rubidium centered [TlI4] tetrahedra. The cuboctahedral cavities of this structure are filled with crystal water molecules and additional disordered rubidium cations.

I=2pion scattering length from two-pion wave functions

We calculate the two-pion wave function in the ground state of the I=2 $S$-wave system and find the interaction range between two pions, which allows us to examine the validity of the necessary condition for the finite-volume method for the scattering length proposed by L\"uscher. We work in the quenched approximation employing a renormalization group improved gauge action for gluons and an improved Wilson action for quarks at $1/a=1.207(12) {\rm GeV}$ on $16^3 \times 80$, $20^3 \times 80$ and $24^3 \times 80$ lattices. We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes $L\ge 24$ ($3.92 {\rm fm}$) when the quark mass is in the range that corresponds to $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.

Measurement of the πmeson polarizabilities via the γp → γπ+n reaction

An experiment on the radiative π{+}-meson photoproduction from the proton ( γp → γπ{+}n) was carried out at the Mainz Microtron MAMI in the kinematic region 537MeV < Eγ < 817MeV, 140°≤ $ \theta_{{\gamma \gamma ^{\prime }}}^{{{{\rm cm}}}}$ ≤180°. The π{+}-meson polarizabilities have been determined from a comparison of the data with the predictions of two different theoretical models, the first one being based on an effective pole model with pseudoscalar coupling while the second one is based on diagrams describing both resonant and nonresonant contributions. The validity of the models has been verified by comparing the predictions with the present experimental data in the kinematic region where the pion polarizability contribution is negligible ( s1 < 5mπ2) and where the difference between the predictions of the two models does not exceed 3%. In the region, where the pion polarizability contribution is substantial ( 5 < s1/mπ2 < 15, -12 < t/mπ2 < - 2), the difference $\ensuremath{(\alpha -\beta )_{\pi^{+}}}$ of the electric (α) and the magnetic (β) polarizabilities has been determined. As a result we find $\ensuremath{(\alpha -\beta )_{\pi^{+}}=(11.6\pm 1.5_{{\rm stat}}\pm 3.0_{{\rm syst}}\pm 0.5_{{\rm mod}})\times 10^{-4}{}{\rm fm^{3}}}$ . This result is at variance with recent calculations in the framework of chiral perturbation theory.

Low-energy chiral Lagrangian from the spectral quark model

We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity. The analysis is carried for the SU(3) case. We analyze the pattern of chiral symmetry breaking as well as elaborate on the fulfillment of anomalies. Matching the model results to resonance meson exchange yields the relation between the masses of the scalar, tensor and vector mesons, $M_{f_0}=M_{f_2}=\sqrt{2} M_V= 4 \sqrt{3 /N_c} \pi f_\pi$. Finally, the large-$N_c$ limit suggests the dual relations in the vector and scalar channels, $M_V=M_S= 2 \sqrt{6 /N_c} \pi f_\pi $ and $<r^2 >^{1/2}_S = < r^2 >^{1/2}_V = 2 \sqrt{N_c} / f_\pi = 0.59 {\rm fm} $.

Chiral logarithms in quenched QCD

The quenched chiral logs are examined on a $16^3 \times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi}$ is used to set the lattice spacing, $a = 0.200(3) {\rm fm}$. With pion mass as low as $\sim 180 {\rm MeV}$, we see the quenched chiral logs clearly in $m_{\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory ($\chi$PT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral log parameter $\delta$ together with other low-energy parameters. Only for $m_{\pi} \leq 300 {\rm MeV}$ do we obtain a consistent and stable fit with a constant $\delta$ which we determine to be 0.24(3)(4) (at the chiral scale $\Lambda_{\chi}=0.8 {\rm GeV}$). By comparing to the $12^3 \times 28$ lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to $m_{\pi} \sim 500-600$ MeV. The scale independent $\delta$ is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $\chi$PT\@. We also obtain the low energy constant $L_5$ from $f_{\pi}$. We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300 {\rm MeV}$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $\chi$PT\@.

Multi-flux-tube system in the dual Ginzburg-Landau theory.

We study the system of multi color-flux-tubes in terms of the dual Ginzburg -Landau theory. We consider two ideal cases, where the directions of all the color-flux-tubes are the same in one case and alternative in the other case for neighboring flux-tubes. We formulate the system of multi color-flux -tubes by regarding it as the system of two color-flux-tubes penetrating through a two dimensional sphere surface. We find the multi flux-tube configuration becomes uniform above some critical flux-tube number density $\rho_c = 1.3 \sim 1.7 {\rm fm}^{-2}$. On the other hand, the inhomogeneity on the color electric distribution appears when the flux-tube density is smaller than $\rho_c$. We discuss the relation between the inhomogeneity in the color-electric distribution and the flux-tube number density in the multi-flux-tube system created during the QGP formation process in the ultra-relativistic heavy-ion collision.

The free modular lattice, ${\rm FM}(2+2+2)$, is infinite

The following are known concerning the cardinality of the free modular lattice generated by a set of distinct chains. 1. FM(1+1+1) contains 28 elements [1, p. 68]. 2. FM(2+1+1) contains 138 elements [2, p. 1]; [3, p. 629]. 3. FM(1 + 1 + 1 + 1) contains an infinite chain of distinct elements [4, p. 114]. The proof is due to G. Birkoff. 4. FM(nl+n2), nl, n2 finite, is a finite distributive lattice [1, p. 72]. By a method similar to the one used to prove 3 above, the following theorem is proved. THEOREM. FM(2 + 2 + 2) contains an infinite chain of distinct elements. PROOF. Let G be the free Abelian group (additive) generated by X1, X2, , Xn x c, For k-0, 1, 2, * c . let us define the following. a, [X3k+1 + X3k+2], the subgroup generated by the set of all X3k+1 +X37j+2;