Spin-0 Nuclei Research Articles

New Measurements of the Beam-Normal Single Spin Asymmetry in Elastic Electron Scattering over a Range of Spin-0 Nuclei.

We report precision determinations of the beam-normal single spin asymmetries (A_{n}) in the elastic scattering of 0.95 and 2.18GeV electrons off ^{12}C, ^{40}Ca, ^{48}Ca, and ^{208}Pb at very forward angles where the most detailed theoretical calculations have been performed. The first measurements of A_{n} for ^{40}Ca and ^{48}Ca are found to be similar to that of ^{12}C, consistent with expectations and thus demonstrating the validity of theoretical calculations for nuclei with Z≤20. We also report A_{n} for ^{208}Pb at two new momentum transfers (Q^{2}) extending the previous measurement. Our new data confirm the surprising result previously reported, with all three data points showing significant disagreement with the results from the Z≤20 nuclei. These data confirm our basic understanding of the underlying dynamics that govern A_{n} for nuclei containing ≲50 nucleons, but point to the need for further investigation to understand the unusual A_{n} behavior discovered for scattering off ^{208}Pb.

Beam-normal single-spin asymmetry in elastic scattering of electrons from a spin-0 nucleus

We study the beam-normal single-spin asymmetry (BNSSA) in high-energy elastic electron scattering from several spin-0 nuclei. Existing theoretical approaches work in the plane-wave formalism and predict the BNSSA to scale as $\ensuremath{\sim}A/Z$ with the atomic number $Z$ and nuclear mass number $A$. While this prediction holds for light and intermediate nuclei, a striking disagreement in both the sign and the magnitude of BNSSA was observed by the PREX collaboration for $^{208}\mathrm{Pb}$, coined the ``PREX puzzle.'' To shed light on this disagreement, we go beyond the plane-wave approach which neglects Coulomb distortions known to be significant for heavy nuclei. We explicitly investigate the dependence of BNSSA on $A$ and $Z$ by (i) including inelastic intermediate states' contributions into the Coulomb problem in the form of an optical potential, (ii) by accounting for the experimental information on the $A$-dependence of the Compton slope parameter, and (iii) giving a thorough account of the uncertainties of the calculation. Despite of these improvements, the PREX puzzle remains unexplained. We discuss further strategies to resolve this riddle.

Flavor-dependent radiative corrections in coherent elastic neutrino-nucleus scattering

We calculate coherent elastic neutrino-nucleus scattering cross sections on spin-0 nuclei (e.g. 40Ar and 28Si) at energies below 100 MeV within the Standard Model and account for all effects of permille size. We provide a complete error budget including uncertainties at nuclear, nucleon, hadronic, and quark levels separately as well as perturbative error. Our calculation starts from the four-fermion effective field theory to explicitly separate heavy-particle mediated corrections (which are absorbed by Wilson coefficients) from light-particle contributions. Electrons and muons running in loops introduce a non- trivial dependence on the momentum transfer due to their relatively light masses. These same loops, and those mediated by tau leptons, break the flavor universality because of mass-dependent electromagnetic radiative corrections. Nuclear physics uncertainties significantly cancel in flavor asymmetries resulting in subpercent relative errors. We find that for low neutrino energies, the cross section can be predicted with a relative precision that is competitive with neutrino-electron scattering. We highlight potentially useful applications of such a precise cross section prediction ranging from precision tests of the Standard Model, to searches for new physics and to the monitoring of nuclear reactors.

Impact of Triaxiality on the Emission and Absorption of Neutrons and Gamma Rays in Heavy Nuclei

For many spin-0 target nuclei neutron capture measurements yield information on level densities at the neutron separation energy. Also the average photon width has been determined from capture data as well as Maxwellian average cross sections for the energy range of unresolved resonances. Thus it is challenging to use this data set for a test of phenomenological prescriptions for the prediction of radiative processes. An important ingredient for respective calculations is the photon strength function for which a parameterization was proposed using a fit to giant dipole resonance shapes on the basis of theoretically determined ground state deformations including triaxiality. Deviations from spherical and axial symmetry also influence level densities and it is suggested to use a combined parameterization for both, level density and photon strength. The formulae presented give a good description of the data for low spin capture into 124 nuclei with 72<A<244 and only very few global parameters have to be adjusted when the predetermined information on ground state shapes of the nuclei involved is accounted for.

Two component charged condensate in white dwarfs

The possibility of the formation of a condensate of charged spin-0 nuclei inside white dwarf cores, studied in [G. Gabadadze, R.A. Rosen, JCAP 0810 (2008) 030, arXiv:0806.3692] and [G. Gabadadze, D. Pirtskhalava, JCAP 0905 (2009) 017, arXiv:0904.4267], is pursued further. It has been shown, for cores composed mainly of one element (helium or carbon), that after condensation phonons become massive and the specific heat drops by about two orders of magnitude. In this Letter we extend that analysis by considering the coexistence of the nuclei of both types (helium and carbon), whose condensation points are generically different. An effective field theory is developed to describe the system when both elements are condensed. The spectrum of fluctuations of this two component charged condensate possesses a collective massless mode with ω∝k2. Assuming that the fraction of the less abundant element is greater than ∼1/100, the thermal history changes as follows: There is a softer discontinuity in the average specific heat after the condensation of first sector, resulting in slower cooling and a milder drop in luminosity function. The specific heat remains almost constant until the condensation of the second sector, then starts to declines as T3/2.

Effective field theory for quantum liquid in dwarf stars

An effective field theory approach is used to describe quantum matter at greater-than-atomic but less-than-nuclear densities which are encountered in white dwarf stars. We focus on the density and temperature regime for which charged spin-0 nuclei form an interacting charged Bose-Einstein condensate, while the neutralizing electrons form a degenerate fermi gas. After a brief introductory review, we summarize distinctive properties of the charged condensate, such as a mass gap in the bosonic sector as well as gapless fermionic excitations. Charged impurities placed in the condensate are screened with great efficiency, greater than in an equivalent uncondensed plasma. We discuss a generalization of the Friedel potential which takes into account bosonic collective excitations in addition to the fermionic excitations. We argue that the charged condensate could exist in helium-core white dwarf stars and discuss the evolution of these dwarfs. Condensation would lead to a significantly faster rate of cooling than that of carbon- or oxygen-core dwarfs with crystallized cores. This prediction can be tested observationally: signatures of charged condensation may have already been seen in the recently discovered sequence of helium-core dwarfs in the nearby globular cluster NGC 6397. Sufficiently strong magnetic fields can penetrate the condensate within Abrikosov-like vortices. We find approximate analytic vortex solutions and calculate the values of the lower and upper critical magnetic fields at which vortices are formed and destroyed respectively. The lower critical field is within the range of fields observed in white dwarfs, but tends toward the higher end of this interval. This suggests that for a significant fraction of helium-core dwarfs, magnetic fields are entirely expelled within the core.

STRONGLY COUPLED CONDENSATE OF HIGH DENSITY MATTER

Arguments are summarized, that neutral matter made of helium, carbon, etc., should form a quantum liquid at the above-atomic but below-nuclear densities for which the charged spin-0 nuclei can condense. The resulting substance has distinctive features, such as a mass gap in the bosonic sector and a gap-less spectrum of quasifermions, which determine its thermodynamic properties. I discuss an effective field theory description of this substance, and as an example, consider its application to calculation of a static potential between heavy charged impurities. The potential exhibits a long-range oscillatory behavior in which both the fermionic and bosonic low-energy degree of freedom contribute. Observational consequences of the condensate for cooling of helium-core white dwarf stars are briefly discussed.

Quantum liquid signatures in dwarf stars

We develop further the proposal of arXiv:0806.3692 that a new state of matter — charged condensate of spin-0 nuclei — may exist in helium-core dwarf stars. The charged condensate and its fluctuations are described by an effective field theory Lagrangian. The spectrum of bosonic fluctuations is gapped, while electrons, at temperatures of interest, give rise to gapless excitations near the Fermi surface. These properties determine the evolution of the dwarfs with condensed cores. In particular, we show that such dwarf stars would cool significantly faster than their crystallized counterparts. As a result, the luminosity function for the helium-core dwarfs will have a sharp drop-off after the condensation. It is tempting to interpret the recently discovered abrupt termination of a sequence of 24 helium-core dwarf candidates in NGC 6397 as a signature of the charged condensation.

Retarded Boson-Fermion interaction in atomic systems

The retarded interaction between an electron and a spin-0 nucleus, that has been derived from electro-dynamical perturbation theory is discussed here. A brief account of the derivation is given. The retarded form is correct through order v 2/c 2. Use of the relative coordinates leads to an effective one-electron operator that can be used through all orders of perturbation theory. A few unitary transformations give rise to the interaction that is valid in the non-relativistic limit.

Retarded boson-fermion interaction in atomic systems

The retarded interaction between an electron and a spin-0 nucleus is derived from electrodynamical perturbation theory. The contribution of retardation at order v(2)c(2) mimics the Breit interaction [Phys. Rev. 34, 553 (1929); 36, 388 (1930); 39, 616 (1932)] with the Dirac matrix alpha(2) being replaced by p(2)m(2)c where p(2) is the linear momentum operator for the nucleus. An effective one-electron retardation operator is obtained in relative coordinates, and this can be used through all orders in perturbation theory without any problem of infinite degeneracy. A few steps of unitary transformation lead to the nonrelativistic limit. The leading terms in retardation corrections to energy are of order (m(e)m(n))alpha(2)Z(4)(alpha(2)m(e)c(2)). The implications for atomic systems are discussed.

On the A-dependence of nuclear generalized parton distributions

We perform a microscopic evaluation of nuclear generalized parton distributions (GPDs) for spin-0 nuclei in the framework of the Walecka model. We demonstrate that the meson (non-nucleon) degrees of freedom dramatically influence nuclear GPDs, which is revealed in the non-trivial and unexpected A-dependence of deeply virtual Compton scattering (DVCS) observables. In particular, we find that the first moment of the nuclear D-term dA(0) ∝ A2.26, which confirms the earlier prediction of Polyakov. We find that in the HERMES kinematics, contrary to the free proton case, the nuclear meson degrees of freedom in large nuclei enhance the nuclear DVCS amplitude which becomes comparable to the Bethe–Heitler amplitude and, thus, give the non-trivial A-dependence to the DVCS asymmetries: as a function of the atomic number, the beam–charge asymmetry increases whereas the beam–spin asymmetry decreases slowly.

Microscopic description of deeply virtual Compton scattering off spin-0 nuclei

We evaluate within a microscopic calculation the contributions of both coherent and incoherent deeply virtual Compton scattering from a spin-0 nucleus. The coherent contribution is obtained when the target nucleus recoils as a whole, whereas for incoherent scattering break-up configurations for the final nucleus into a an outgoing nucleon and an $A-1$ system are considered. The two processes encode different characteristics of generalized parton distributions.

Spectroscopic Tests of Spin-Statistics Connection and Symmetrization Postulate of Quantum Mechanics

Recent experiments searching for violations of the spin-statistics connection and of the symmetrization postulate of quantum mechanics are reviewed. Spectroscopic tests on O2 and CO2 molecules are described in detail and it is shown that these should be considered as tests of the spin-statistics connection for the spin-0 oxygen nuclei. The possibility of new experiments to test the spin-statistics connection and the symmetrization postulate is discussed.

Salient features of scattering amplitudes in intermediate energy nucleon-nucleus scattering.

Phenomenological relativistic optical models for scattering of nucleons from a spin-0 nucleus mainly use two different approaches. In the first, one essentially uses the Schroedinger equation incorporating appropriate relativistic kinematical terms. In the second approach, which is superior especially in reproducing spin observables, one starts with the Dirac equation and obtains an equivalent Schroedinger equation which forms a convenient basis for the calculation of experimental observables. Adopting a mathematical procedure developed earlier within the framework of potential scattering, we calculate the regionwise contribution to the reaction cross section for spin-1/2--spin-0 systems using both these types of relativistic optical models. The relative importance of different regions of intermediate energy optical potential in generating the total reaction cross section is examined using the method of regionwise absorption and it is found that reaction process is surface dominant. These findings are further elaborated by depicting the general features of [ital S] matrix and scattering amplitudes as a function of angular momentum.

Magnetic-monopole spin resonance

The magnetic monopole of charge $g$ is given an intrinsic spin \textonehalf{} and is bound to a spin-0 nucleus with a repulsive core potential. Bound-state energies are calculated. Speculation regarding the existence of magnetic-monopole spin resonance is examined.

Nuclear recoil effects on the polarization of spin-1/2 particles

In this paper the effects of nuclear scattering on the polarization of a beam of spin-\textonehalf{} particles are calculated. These first-order results include the effects of nuclear recoil and apply to elastic scattering by light, spin-0 nuclei at moderate energies. The net effect of the scattering is that the polarization vector is rotated through an angle $\ensuremath{\beta}$ about the normal to the scattering plane, in the same direction in which the momentum is rotated. The rotation of the polarization vector is less than that of the momentum by an angle given by $cos (\ensuremath{\theta}\ensuremath{-}\ensuremath{\beta})=\frac{[1\ensuremath{-}{(\frac{m}{\ensuremath{\epsilon}})}^{2}{tan}^{2}(\frac{\ensuremath{\theta}}{2})]}{[1+{(\frac{m}{\ensuremath{\epsilon}})}^{2}{tan}^{2}(\frac{\ensuremath{\theta}}{2})]}$, where $\ensuremath{\theta}$ is the scattering angle and $\ensuremath{\epsilon}=E+\frac{({E}^{2}\ensuremath{-}{m}^{2})}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}}$, with $m$ and $E$ denoting the mass and energy of the scattered particle and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{E}$ the energy of the recoiling nucleus. The magnitude of this effect is illustrated for the scattering of muons from helium at several incident energies.

Semi-leptonic weak and electromagnetic interactions in nuclei:: Parity violations in electron scattering and weak neutral currents

A general result for the difference in differential cross sections for electron scattering between any two nuclear levels with incident longitudinally polarized right- and left-handed electrons is derived. This difference must involve the parity-violating weak interaction at least linearly and can be used to study weak neutral currents as pointed out by Feinberg. A V — A structure for the weak neutral currents is assumed with a semi-leptonic current-current interaction, and the electromagnetic interaction is treated in the one-photon-exchange approximation. The result is expressed in terms of the same set of reduced matrix elements of the multipoles of the nuclear currents which govern all electromagnetic and weak transitions between these levels. A previously developed unified analysis of semi-leptonic weak and electromagnetic interactions in nuclei which determines one-body transition densities, including their spin and spatial dependences, through electron scattering provides nuclear transitions to serve as known analyzers in testing the structure of this part of the weak interaction. Examples are given using Weinberg's model of the weak neutral currents. Feinberg's result for elastic scattering from spin-0 nuclei is rederived and two new examples using previously determined one-body densities are discussed : the 1 +0 → 0 +1 (3.56 MeV) transition in 6Li and the 0 +0 → 1 + 1(15.1 MeV) transition in 12C.

Interpretation of ortho–para hydrogen conversion

The interpretation of statistics of the nuclear spin states in the ortho–para hydrogen conversion by hydrogen atoms is considered. It is shown that the observable rate coefficient (which is the sum of the forward and reverse rate coefficients for ortho→para conversion) equals the distinguishable-atom rate coefficient in the classical limit. In addition to spin-1/2 nuclei, we also consider spin-1 nuclei and spin-0 nuclei.

Recoil corrections to elastic electron scattering in the Breit approximation

Recoil corrections to the cross sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and second-Born approximation is investigated in detail using time-dependent perturbation theory, and it is found that the center-of-mass (CM) frame is particularly convenient to work in. Transformation equations relating the lab and CM frames are developed. Those parts of the second-Born amplitude which correspond to the Breit amplitude are isolated, and the Breit equation with the electromagnetic Breit interaction is investigated in detail. Corrections to the scattering cross sections which are inversely proportional to the nucleus mass (recoil corrections) are calculated. Numerical results are presented for the particular case of 16O.

Polarized Nucleons

An elementary description of polarization phenomena involving spin-1/2particles is given. With the aid of schematic diagrams, the relation between analyzing power and polarization is obtained. Single and double scattering by spin-0 nuclei and depolarization effects in the scattering by nuclei with spin are discussed. A brief treatment of polarization phenomena in reactions is presented.