Angular-momentum or parity-dependent nonlocal optical potentials for nucleon-${}^{16}\mathrm{O}$ scattering able to fit differential cross section data over the whole angular regime are developed and applied to the description of deuteron-${}^{16}\mathrm{O}$ scattering in the framework of three-body Faddeev-type equations for transition operators. Differential cross sections and deuteron analyzing powers for elastic scattering and ${}^{16}\mathrm{O}(d,p){}^{17}\mathrm{O}$ transfer reactions are calculated using a number of local and nonlocal optical potentials and compared with experimental data. Angular-momentum or parity-dependence of the optical potential turns out to be quite irrelevant in the considered three-body reactions while nonlocality is essential for a successful description of the differential cross section data, especially in transfer reactions.
We discuss the scientific motivation, possible experiments, and beam requirements for measurements of parity violation in photonuclear reactions at an intensity upgraded HIGS facility, HIGS2.
Parity violation in the $(n,α)$ reactions on $^6$Li and $^{10}$B nuclei and in the $γ$-transition between two lowest levels of $^7$Li nucleus is discussed. It appears that the effects (neutral currents contribution in particular) are measurable due to the large values of the neutron cross sections. This holds promise for the theoretical extraction of the constants of the weak NN potential because of the relative simplicity of the investigated systems.
A precise determination of the neutron skin thickness of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (the neutron skin thickness is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on 208Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of the neutron skin thickness of 208Pb from the parity-violating asymmetry probed in the experiment. We demonstrate a high linear correlation between the parity-violatin…
The method based on microscopic theory of nuclear reactions has been applied for the analysis of parity violating effects in a few-body systems. Different parity violating and parity conserving asymmetries and their dependence on neutron energy have been estimated for $n + ^3He \rightarrow ^3H + p$ reaction. The estimated effects are in a good agreement with available exact calculations.
The saturation density of nuclear matter $ρ_0$ is a fundamental nuclear physics property that is difficult to predict from fundamental principles. The saturation density is closely related to the interior density of a heavy nucleus, such as $^{208}$Pb. We use parity violating electron scattering to determine the average interior weak charge and baryon densities in $^{208}$Pb. This requires not only measuring the weak radius $R_{\rm wk}$ but also determining the surface thickness of the weak charge density $a$. We obtain $ρ_0=0.150\pm0.010$ fm$^{-3}$, where the 7\% error has contributions form …
The anapole moment is a parity-odd and time-reversal-even electromagnetic moment. Although it was conjectured shortly after the discovery of parity nonconservation, its existence has not been confirmed until recently in heavy nuclear systems, which are known to be the suitable laboratories because of the many-body enhancement. By carefully identifying the nuclear-spin-dependent atomic parity nonconserving effect, the first clear evidence was found in cesium. In this talk, I will discuss how nuclear anapole moments are used to constrain the parity-nonconserving nuclear force, a still less well-…
Transfer reactions are an important tool in nuclear astrophysics. These reactions allow us to identify states in nuclei and to find the corresponding energies, to determine if these states can contribute to astrophysical nuclear reactions and ultimately to determine the strength of that contribution. In this paper, the basic details of how transfer reactions may be used in nuclear astrophysics are set out along with some common pitfalls to avoid.
We analyze two types of spin observables in the reaction $π\vec D\to\vecΣΘ^+$ near the threshold. One concerns the spin-transfer coefficients $K_x^x$ and $K_z^z$. The second one is the deuteron spin anisotropy. These observables are sensitive to the $Θ^+$ parity and can be used as a tool for the $Θ^+$ parity determination.
Parity violation in nuclear systems is reviewed. A few ingredients relevant to the description of the parity-violating nucleon-nucleon force in terms of meson exchanges are reminded. Effects in nuclear systems are then considered. They involve pp scattering, some complex nuclei and the deuteron system.
Nuclear physics tests of parity- and time-reversal invariance have both shaped the development of the Standard Model and provided key tests of its predictions. These studies now provide vital input in the search for physics beyond the Standard Model. We give a brief review of a few key experimental and theoretical developments in the history of this sub-field of nuclear physics as well as a short outlook, focusing on weak decays, parity-violation in electron scattering, and searches for permanent electric dipole moments of the neutron and neutral atoms.
We present an introduction to ab initio nuclear theory with a focus on nuclear reactions. After a high-level overview of ab initio approaches in nuclear physics, we give a more detailed description of the no-core shell model technique equivalent to a large extent to configuration-interaction methods applied in quantum chemistry. We then introduce the no-core shell model with continuum approach that provides a quantum many-body description of nuclear reactions. After a brief review of nuclear reactions important for astrophysics, we present examples of results of ab initio calculations of radia…
Time-dependent Hartree--Fock (TDHF) method has been applied to various low-energy nuclear reactions, such as fusion, fission, and multinucleon transfer reactions. In this Mini Review, we summarize recent attempts to bridge a microscopic nuclear reaction theory, TDHF, and a macroscopic aspect of nuclear reactions through nucleus--nucleus potentials and energy dissipation from macroscopic degrees of freedom to microscopic ones obtained from TDHF in various colliding systems from light to heavy mass regions.
We discuss the implications of a doorway state model for parity mixing in compound nuclear states. We argue that in order to explain the tendency of parity violating asymmetries measured in $^{233}$Th to have a common sign, doorways that contribute to parity mixing must be found in the same energy neighbourhood of the measured resonance. The mechanism of parity mixing in this case of nearby doorways is closely related to the intermediate structure observed in nuclear reactions in which compound states are excited. We note that in the region of interest ($^{233}$Th) nuclei exhibit octupole defo…
The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a "hedgehog" situation, which exists only if nuclear states contain some amount of parity violation.
In this brief review we discuss the basic theoretical concepts used in the experimental studies of the most common cases of direct reactions such as (a) elastic scattering, (b) inelastic scattering, (c) Coulomb excitation, (d) transfer reactions and (e) breakup reactions.
The nuclei 11Be and 11Li provide paradigmatic examples of one-and two- neutron halo systems. Because the reaction 1H(11Li,9Li)3H is dominated by successive transfer, one can use the quantitative picture emerging from a nu- clear field theory description of the structure and reaction mechanism of the above Cooper pair transfer process and of the 2H(10Be,11Be)1H and 1H(11Be,10Be)2H reactions, to shed light on the structure of 10Li. This analysis provides important support for a parity inverted scenario with a 1/2+ virtual state at about 0.2 MeV.
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
Knowledge about parity-violating effects both from theory and experiment is reviewed. Further information that could be obtained from measurements of nuclear anapole moments is discussed.
Nuclear-spin-dependent P-odd optical activity in atomic Tl, Pb and Bi is calculated. Its magnitude is expressed analytically through the main contribution to the optical rotation, which is independent of nuclear spin. The accuracy of results is discussed.
Nuclear multifragmentation is an important phenomenon, the study of which can throw light on reaction mechanism in heavy ion collisions at intermediate and high energies. Based on statistical and dynamical model studies, this thesis is concentrated mainly on, the following three aspects of nuclear multifragmentation reactions namely (i) production of exotic nuclei which are normally not available in the laboratory (ii) nuclear symmetry energy from heavy ion collisions at intermediate energies and (iii) Nuclear liquid-gas phase transition. In addition to these equivalence of statistical ensembl…
We analyze the problem of how to determine the parity of the $Θ^+$ pentaquark in the reaction $γN\to KΘ\to NK\bar{K}$, where $N=n,p$. Our model calculations indicate that the contribution of the non-resonant background of the reaction $γN\to NK\bar{K}$ cannot be neglected, and that suggestions to determine the parity based solely on the initial-stage process $γN\to KΘ$ cannot be implemented cleanly. We discuss the various mechanisms that contribute to the background, and we identify some spin observables which are sensitive.
Nuclear reaction rate ($λ$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei …
We show that the asymmetries in the nuclear resonance fluorescence processes with a circular polarized photon beam may be used as a tool for studying the parity non-conservation (PNC) in nuclei. The PNC asymmetry measurements both in exciting the parity doublet states and in exciting the discrete states near the ground states with parity mixing are discussed. We derived the formulae needed for measuring the PNC asymmetries.
Astrophysical reaction rates are sensitive to the parity distribution at low excitation energies. We combine a formula for the energy-dependent parity distribution with a microscopic-macroscopic nuclear level density. This approach describes well the transition from low excitation energies, where a single parity dominates, to high excitations where the two densities are equal.
Based on an isospin dependent transport model IBUU, effects of high density behavior of nuclear symmetry energy in the proton-rich reaction $^{22}$Si+$^{22}$Si at a beam energy of 400 MeV/nucleon are studied. It is found that the symmetry energy affects $π^{+}$ production more than $π^{-}$. More interestingly, comparing with neutron-rich reactions, for $π^{-}/π^{+}$ and dense matter's N/Z ratios, effects of symmetry energy in the proton-rich reaction both show contrary behaviors. The practical experiment by using the proton-rich reaction $^{22}$Si+$^{40}$Ca to study nuclear symmetry energy are…
The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuc…
We investigate the properties of isospin-symmetric nuclear matter and neutron stars in a chiral model approach adopting the SU(2) parity doublet formulation. This ansatz explicitly incorporates chiral symmetry restoration with the limit of degenerate masses of the nucleons and their parity partners. Instead of searching for an optimized parameter set we explore the general parameter dependence of nuclear matter and star properties in the model. We are able to get a good description of ground state nuclear matter as well as large values of mass for neutron stars in agreement with observation.
Isospin-dependent nuclear forces play a fundamental role in nuclear structure. In relativistic models of nuclear structure constructed at the quark level these isovector nuclear forces affect the u and d quarks differently, leading to non-trivial flavour dependent modifications of the nuclear parton distributions. We explore the effect of isospin dependent forces for parity-violating deep inelastic scattering on nuclear targets and demonstrate that the cross-sections for nuclei with N /= Z are sensitive to the flavour dependence of the EMC effect. Indeed, for nuclei like lead and gold we find …
The strong interaction effects of isospin- and spin-dependent nucleon-nucleon correlations observed in many-body calculations are interpreted in terms of a one-pion exchange mechanism. Including such effects in computations of nuclear parity violating effects leads to enhancements of about 10%. A larger effect arises from the one-boson exchange nature of the parity non-conserving nucleon- nucleon interaction, which depends on both weak and strong meson-nucleon coupling constants. Using values of the latter that are constrained by nucleon-nucleon phase shifts leads to enhancements of parity vio…
Parity violating electron nucleus scattering is a clean and powerful tool for measuring the spatial distributions of neutrons in nuclei with unprecedented accuracy. Parity violation arises from the interference of electromagnetic and weak neutral amplitudes, and the $Z^0$ of the Standard Model couples primarily to neutrons at low $Q^2$. Experiments are now feasible at existing facilities. We show that theoretical corrections are either small or well understood, which makes the interpretation clean. A neutron density measurement may have many implications for nuclear structure, atomic parity no…
In the last decade, the scattering of polarized neutrons on compound nucleus resonances proved to be a powerful experimental technique for probing nuclear parity violation. Longitudinal analyzing powers in neutron transmission measurements on p-wave resonances in nuclei such as $^{139}$La and $^{232}$Th were found to be as large as 10%. Here we examine the possibilities of carrying out a parallel program to measure asymmetries in the $(n,γ$) reaction on these same compound nuclear resonances. Symmetry-violating $(n,γ$) studies can also show asymmetries as large as 10%, and have the advantage o…
The collisions of large nuclei at high energies could produce metastable vacua which are odd under parity, P, charge conjugation, C, and/or CP. Using only the three-momenta of charged pions (or kaons), we show how to construct global observables which are odd under P, C, and CP, and which can be measured on an event by event basis. Model dependent estimates of the P-odd observables are on the order of 10^(-3).
I discuss in qualitative terms the implications of the recent measurement by C. S. Wood et al. of the hyperfine dependence of atomic parity violation in 133Cs. The derived anapole moment constrains the strength of hadronic parity violation.
Within spectator model we study the reaction $γd \to K^-Θ^+p \to K^-K^+np$ in the threshold energy region. We present the predictions for the exclusive and inclusive antikaon angular distributions in the laboratory system for this reaction calculated for two possible parity states of the $Θ^+$ resonance at 1.5 and 1.75 GeV beam energies with and without imposing the relevant kinematical cuts on those parts of the sampled phase space where contribution from the main background sources associated with the $ϕ(1020)$, $Λ(1520)$ production as well as with the $K^-p$--rescattering in the final state…
Parity violation in atoms: neutrino-mediated long range forces and finite nuclear size
PRISMA ++ Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität（PRISMA++卓越集群，核物理研究所，约翰内斯·古腾堡大学）；PRISMA ++ Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität（PRISMA++卓越集群，物理研究所，约翰内斯·古腾堡大学）
Microscopic calculations show a strong parity dependence of the nuclear level density at low excitation energy of a nucleus. Previously, this dependence has either been neglected or only implemented in the initial and final channels of Hauser-Feshbach calculations. We present an indirect way to account for a full parity dependence in all steps of a reaction, including the one of the compound nucleus formed in a reaction. To illustrate the impact on astrophysical reaction rates, we present rates for neutron captures in isotopic chains of Ni and Sn. Comparing with the standard assumption of equi…
We introduce a novel method to obtain level densities in large-scale shell-model calculations. Our method is a stochastic estimation of eigenvalue count based on a shifted Krylov-subspace method, which enables us to obtain level densities of huge Hamiltonian matrices. This framework leads to a successful description of both low-lying spectroscopy and the experimentally observed equilibration of $J^π=2^+$ and $2^-$ states in $^{58}$Ni in a unified manner.
The parity violating longitudinal asymmetry ${\cal A}$ is calculated for quasielastic electron scattering. We use a variety of relativistic mean field models for the response of nuclear matter and $^{12}$C at a momentum transfer of q=550 MeV/c. Relativistic effects from a reduced nucleon mass, RPA correlations and vacuum polarization can all change ${\cal A}$ by a relatively large amount. These large nuclear structure corrections could make it impossible to extract strange quark matrix elements or radiative corrections to weak axial currents.
A simple description for obtaining the parity distribution of nuclear levels in the pf + g9/2 shell as a function of excitation energy was recently derived. We implement this in a global nuclear level density model. In the framework of the statistical model, cross sections and astrophysical reaction rates are calculated in the Fe region and compared to rates obtained with the common assumption of an equal distribution of parities. We find considerable differences, especially for reactions involving particles in the exit channel.
Tensor representation (TR) for wave function (WF) of three-nucleon bound state with the total angular momentum I=1/2 is discussed. The WF in TR has 16 complex components depending on vectors of relative momenta. Constraints on the WF imposed by requirements of invariance with respect to space inversion and time reversal are studied. Both parity-even and parity-odd components of the 3N bound state are constructed using 16 scalar functions. The arguments of the functions are magnitudes of relative momenta and scalar product of the momenta. With nuclear forces being time-reversal invariant these …
It is well known that coincidence quasielastic $(\vec{e},e'N)$ reactions are not appropriate to analyze effects linked to parity violation due the presence of the fifth electromagnetic (EM) response $R^{TL'}$. Nevertheless, in this work we develop a fully relativistic approach to be applied to parity-violating (PV) quasielastic $(\vec{e},e'N)$ processes. This is of importance as a preliminary step in the subsequent study of inclusive quasielastic PV $(\vec{e},e')$ reactions. Moreover, our present analysis allows us to disentangle effects associated with the off-shell character of nucleons in n…
High precision measurements of the parity-violating asymmetry in polarized electron scattering from nuclei can be used to extract information on nuclear and nucleon structure or to determine Standard Model couplings and higher-order radiative corrections. To this end, low uncertainties are also required in the effects that inevitably arise from modeling the underlying nuclear structure. An experimental precision of a few tenths of a percent may be attainable for the asymmetry if the appropriate kinematic range is chosen, as will be discussed here for the case of $^{12}$C. And given this, the d…
A simple formula for the ratio of the number of odd- and even-parity states as a function of temperature is derived. This formula is used to calculate the ratio of level densities of opposite parities as a function of excitation energy. We test the formula with quantum Monte Carlo shell model calculations in the $(pf+g_{9/2})$-shell. The formula describes well the transition from low excitation energies where a single parity dominates to high excitations where the two densities are equal.
We propose a nuclear mechanism which can induce an atomic electric dipole moment (EDM). Parity and time reversal violating (P,T-odd) nuclear forces generate a mixed P,T-odd nuclear polarizability beta_{ik} (defined by an energy shift U = -beta_{ik} E_{i}H_{k}, E is electric field and H magnetic field). The interaction of atomic electrons with beta_{ik} produces an atomic EDM. We performed an analytical calculation of the P,T-odd nuclear polarizability and estimated the value for the induced atomic EDM. The measurements of atomic EDMs can provide information about P,T-odd nuclear forces and tes…
Photo nuclear reactions are shown to be used for studying neutrino/weak nuclear responses involved in astro-neutrino nuclear interactions and double beta decays. Charged current weak responses for ground and excited states are studied by using photo nuclear reactions through isobaric analog states of those states, while neutral current weak responses for excited states are studied by using photo nuclear reactions through the excited states. The weak interaction strengths are studied by measuring the cross sections of the photo nuclear reactions, and the spin and parity of the state are studied…
We study dense nuclear matter and the chiral phase transition in a SU(2) parity doublet model at zero temperature. The model is defined by adding the chiral partner of the nucleon, the N', to the linear sigma model, treating the mass of the N' as an unknown free parameter. The parity doublet model gives a reasonable description of the properties of cold nuclear matter, and avoids unphysical behaviour present in the standard SU(2) linear sigma model. If the N' is identified as the N'(1535), the parity doublet model shows a first order phase transition to a chirally restored phase at large densi…
The reaction $K^-p\rightarrowΛη$ at low energies is studied with a chiral quark model approach. Good descriptions of the existing experimental data are obtained. It is found that $Λ(1670)$ dominates the reaction around threshold. Furthermore, $u$- and $t$-channel backgrounds play crucial roles in this reaction as well. The contributions from the $D$-wave state $Λ(1690)$ are negligibly small for its tiny coupling to $ηΛ$. To understand the strong coupling properties of the low-lying negative parity $Λ$ resonances extracted from the $\bar{K}N$ scattering, we further study their strong decays. It…
Recently at JLab using polarised electron beam on unpolarised deuteron target measurements have been performed for the parity violating asymmetry($A_{PV}$) and there are future plans to measure this asymmetry using various nuclear targets. In this paper, we study $A_{PV}$ in nuclear targets like $^{12}C$, $^{56}Fe$ and $^{208}Pb$, in a local density approximation using spectral function which takes into account Fermi motion, binding energy correction and nucleon correlations. Furthermore, the pion and rho cloud contributions have also been taken into account. The present model has been used ea…
At finite density parity can be spontaneously broken in strong interactions with far reaching implications. In particular, a time-dependent pseudoscalar background would modify QED by adding a Chern-Simons term to the lagrangian. As a striking consequence we propose a novel explanation for the dilepton excess observed in heavy ion collisions at low invariant masses. The presence of local parity breaking due to a time-dependent pseudoscalar condensate substantially modifies the dispersion relation of photons and vector mesons propagating in such a medium, changing the $ρ$ spectral function and …
The newly discovered exotic $Θ$ baryon of mass 1540 MeV (and very small width) truly has a very low mass, if it is a pentaquark system of even parity. A schematic model in which the coherent interaction of $u\bar s$ and $d\bar s$ pairs leads to a very large residual (non-confining) attractive interaction is introduced. This collective vibrational model accounts for the mass and small decay width to the $KN$ channel, but yields a significant coupling to the virtual $K^*N$ channel. The schematic model predicts an attractive $Θ$-nucleon interaction strong enough to bind a $Θ$ particle to a nucleu…
The relevant energy ranges for stellar nuclear reactions are introduced. Low-energy compound and direct reactions are discussed. Stellar modifications of the cross sections are presented. Implications for experiments are outlined.
A generalized method to calculate the excitation-energy dependent parity ratio in the nuclear level density is presented, using the assumption of Poisson distributed independent quasi particles combined with BCS occupation numbers. It is found that it is crucial to employ a sufficiently large model space to allow excitations both from low-lying shells and to higher shells beyond a single major shell. Parity ratios are only found to equilibrate above at least 5-10 MeV of excitation energy. Furthermore, an overshooting effect close to major shells is found where the parity opposite to the ground…
Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretica…
In light of new data on neutron distributions from experiments with antiprotonic atoms [ Trzcinska {\it et al.}, Phys. Rev. Lett. 87, 082501 (2001)], we reexamine the role of nuclear-structure uncertainties in the interpretation of measurements of parity violation in atoms using chains of isotopes of the same element. With these new nuclear data, we find an improvement in the sensitivity of isotopic chain measurements to ``new physics'' beyond the standard model. We compare possible constraints on ``new physics'' with the most accurate to date single-isotope probe of parity violation in the Cs…
Effects of difference in the spin and parity distributions for the surrogate and neutron-induced reactions are investigated. Without assuming specific (schematic) spin-parity distributions, it was found that the surrogate ratio method can be employed to determine neutron fission and capture cross sections if 1) weak Weisskopf-Ewing condition (defined in this paper) is satisfied, 2) there exist two surrogate reactions whose spin-parity distributions of the decaying nuclei are almost equivalent, and 3) difference of the representative spin values between the neutron-induced and surrogate reactio…
Spin observables of a binary reaction $1+2\to 3+4$ are discussed at the threshold in general form using P-parity and angular momentum conservation. General formulae for polarization transfer, spin-spin correlation parameters in the initial and final states and induced tensor polarization are derived for arbitrary spins of participating particles. This formalism is worked out in detail for the $NN\to YΘ^+$ reaction. Assuming that the spin of the pentaquark $Θ^+$ takes the values 1/2, 3/2 and 5/2, whereas the spin of the hyperon $Y$ equals 1/2, explicite formulae are obtained for the observables…
