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We present neutron elastic scattering amplitude for arbitrary polarized target in irreducible spherical tensor representation. Here, the general approach for the description of neutron spin dynamics for the propagation trough the medium with an arbitrary polarization is discussed in a relation to the search for time reversal invariance violation in neutron scattering.
Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: R -matrix theory is used as the primary tool to interoperate among the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon + 12 C, nucleon + 16 O, and nucleon + 26 Al are presented. A new approach to multilevel mirror symmetry is derived and applied to the first three 2 + states of 18 O and 18 Ne. Conclusions: In this work, the relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second 2 + state in 18 Ne deduced from the mirror state in 18 O is significantly larger than found in previous work. This finding has the effect of increasing the 17 F($\textit{p,γ}$) 18 Ne reaction rate in novae.
The neutron skin thickness Δr np in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy E sym (ρ) around $\frac{2}{3}$ of the saturation density ρ 0 of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for 208 Pb and 48 Ca from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter L of the nuclear symmetry energy at ρ 0 from imagined Δr np ( 208 Pb)=0.15, 0.20, and 0.30 fm with a 1σ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as Δr np ( 48 Ca)=0.12, 0.15, and 0.25 fm, with different 1σ error bar of 0.01 and 0.02 fm, respectively. The results are compared with the PDFs of L inferred using the same approach from the available Δr np data for 116, 118, 120, 122, 124, 130, 132 Sn from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives L = 45.5 $^{+ 26.5}_{-21.6}$ MeV surrounding its mean value or L = 53 . 4 $^{+ 18.6}_{ -29.5}$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the L = 66 $^{+ 12}_{-20}$ MeV from the neutron star data within their 68% confidence intervals. We found that Δr np = 0.17 –0.18 fm in 208 Pb with an error bar of about 0.02 fm leads to a PDF of L compatible with that from analyzing the Sn data. To provide additionally useful information on L extracted from the Δr np of Sn isotopes, the experimental error bar of Δr np in 208 Pb should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the Δr np ( 48 Ca) needs to be larger than 0.15 fm but smaller than 0.25 fm to be compatible with the Sn and/or neutron star results. To further improve our current knowledge about L and distinguish its PDFs in the examples considered, even higher precisions leading to significantly less than ±20 MeV error bars for L at 68% confidence level are necessary.
We investigate the effects of prehydrodynamic evolution on final-state observables in heavy-ion collisions using state-of-the art event simulations coupled to different prehydrodynamic scenarios, which include the recently developed effective kinetic transport theory evolution model KøMPøST. Differential flow observables are found to be mostly insensitive to the details of prehydrodynamic evolution. The main effect we observe is in the p T spectra, particularly the mean transverse momentum. However, at least part of this effect is a consequence of the underlying conformal invariance assumption currently present in such approaches, which is known to be violated in the temperature regime probed in heavy-ion collisions. This assumption of early time conformal invariance leads to an artificially large out-of-equilibrium bulk pressure when switching from (conformal) prehydrodynamic evolution to hydrodynamics (using the nonconformal QCD equation of state), which in turn increases the transverse momentum. Our study indicates that a consistent treatment of prehydrodynamic evolution in heavy-ion collisions requires the use of nonconformal models of early time dynamics.
We report that nuclear state densities are important inputs to statistical models of compound-nucleus reactions. State densities are often calculated with self-consistent mean-field approximations that do not include important correlations and must be augmented with empirical collective enhancement factors. Here, we benchmark the static-path plus random-phase approximation (SPA + RPA) to the state density in a chain of samarium isotopes 148–155 Sm against exact results (up to statistical errors) obtained with the shell-model Monte Carlo (SMMC) method. The SPA + RPA method incorporates all static fluctuations beyond the mean field together with small-amplitude quantal fluctuations around each static fluctuation. Using a pairing plus quadrupole interaction, we show that the SPA + RPA state densities agree well with the exact SMMC densities for both the even- and odd-mass isotopes. For the even-mass isotopes, we also compare our results with mean-field state densities calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation. We find that the SPA + RPA repairs the deficiencies of the mean-field approximation associated with broken rotational symmetry in deformed nuclei and with the violation of particle-number conservation in the pairing condensate. In particular, in deformed nuclei the SPA + RPA reproduces the rotational enhancement of the state density relative to the mean-field state density.
The neutron distribution of neutron-rich nuclei provides critical information on the structure of finite nuclei and neutron stars. Parity violating experiments—such as PREX and CREX—provide a clean and largely model-independent determination of neutron densities. Such experiments, however, are challenging and expensive, which is why sound statistical arguments are required to maximize the information gained. We introduce a new framework, the “transfer function formalism,” aimed at uncertainty quantification, model selection, and experimental design in the context of neutron densities. The transfer functions (TFs) are built analytically by expressing the linear response of the objective function (e.g., χ2) to small perturbations of the data. Using the TF formalism, we are able to analyze the expected overall uncertainty—quantified in terms of bias and variance—of the mean square radius and interior density of 48 Ca and 208 Pb. Using relativistic mean field models as a proxy for the weak-charge density—and assuming that a total of five measurements could be performed on the weak form factor of 48 Ca and 208 Pb—we identify the optimal models and experimental locations that minimize the uncertainty in the extraction of the radius and interior density. We also explore the use of the TF formalism to understand the influence of prior distributions for the model parameters, as well as the optimization of model hyperparameters not constrained by the data. Here,we establish how the choice of experimental locations and the model that is used can have a significant impact on the final uncertainties of the extracted quantities of interest. For challenging experiments such as CREX and PREX, a proper quantification of such uncertainties is critical. We have demonstrated how the TF formalism provides several advantages for this type of analysis.
Background: The recent announcement by the PREX collaboration of an unanticipated thick neutron skin in 208 Pb ($R^{208}_{skin}$) has challenged the understanding of neutron-rich matter in the vicinity of nuclear saturation density. Whereas earlier constraints indicate that the symmetry energy is relatively soft, the PREX-2 result seems to suggest the opposite. Purpose: To confront constraints on the symmetry energy obtained from measurements of the electric dipole polarizability against those informed by the PREX-2 measurement of $R^{208}_{skin}$ and by the correlations that it entails. Methods: Here, covariant energy density functionals informed by the properties of finite nuclei are used to compute the electric dipole response of 48 Ca, 68 Ni, 132 Sn, and 208 Pb. The set of functionals used in this work are consistent with experimental data, yet are flexible enough in that they span a wide range of values of $R^{208}_{skin}$ Results: It is found that theoretical predictions of the electric dipole polarizability that are consistent with the PREX-2 measurement systematically overestimate the corresponding values extracted from the direct measurements of the distribution of electric dipole strength. Conclusions: The neutron skin thickness of 208 Pb extracted from parity violating electron scattering and the electric dipole polarizability measured in photoabsorption experiments are two of the cleanest experimental tools used to constrain the symmetry energy around nuclear saturation density. However, the recent value of $R^{208}_{skin}$ that suggests a fairly stiff symmetry energy stands in stark contrast to the conclusions derived from the electric dipole polarizability. At present, I offer no solution to this dilemma.
The isobaric multiplet mass equation (IMME) is known to break down in the first T=2,A=32 isospin quintet. In this work we combine high-resolution experimental data with state-of-the-art shell-model calculations to investigate isospin mixing as a possible cause for this violation. The experimental data are used to validate isospin-mixing matrix elements calculated with newly developed shell-model Hamiltonians. Our analysis shows that isospin mixing with nonanalog T=1 states contributes to the IMME breakdown, making the requirement of an anomalous cubic term inevitable for the multiplet.
The chiral magnetic effect (CME) is predicted to occur as a consequence of a local violation of P and CP symmetries of the strong interaction amidst a strong electro-magnetic field generated in relativistic heavy-ion collisions. Experimental manifestation of the CME involves a separation of positively and negatively charged hadrons along the direction of the magnetic field. Previous measurements of the CME-sensitive charge-separation observables remain inconclusive because of large background contributions. In order to better control the influence of signal and backgrounds, the STAR Collaboration performed a blind analysis of a large data sample of approximately 3.8 billion isobar collisions of $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr at $\sqrt{s_{NN}}$ = 200 GeV. Prior to the blind analysis, the CME signatures are predefined as a significant excess of the CME-sensitive observables in Ru + Ru collisions over those in Zr + Zr collisions, owing to a larger magnetic field in the former. Here, a precision down to 0.4% is achieved, as anticipated, in the relative magnitudes of the pertinent observables between the two isobar systems. Observed differences in the multiplicity and flow harmonics at the matching centrality indicate that the magnitude of the CME background is different between the two species. No CME signature that satisfies the predefined criteria has been observed in isobar collisions in this blind analysis.
It has been proposed that strong electromagnetic fields produced in the early stages of heavy-ion collisions can lead to splitting of the rapidity-odd directed flow of positive and negative hadrons. For light hadrons, the interpretation of such measurements is complicated by the low magnitude of directed flow as well as by ambiguities arising from transported quarks. To overcome these complications, we propose measurements using only hadrons carrying produced quarks (u¯, d¯, s s¯ ). Here, we discuss how to identify the kinematics where such hadrons are produced via the coalescence mechanism and therefore their flow is the sum of the flow of their constituent quarks. With this sum rule verified for certain combinations of hadrons, the expected systematic violation of this rule with increasing electric charge can be measured, which could be a consequence of the electromagnetic fields produced in the collisions. Our approach can be tested with the high statistics data from Phase II of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.
Heavy charged particles after nuclear muon capture are an important nuclear physics background to the muon-to-electron conversion experiments Mu2e and COMET, which will search for charged lepton flavor violation at an unprecedented level of sensitivity. Here, the AlCap experiment aimed to measure the yield and energy spectra of protons, deuterons, tritons, and α particles emitted after the nuclear capture of muons stopped in Al, Si, and Ti in the low-energy range relevant for the muon-to-electron conversion experiments. Individual charged particle types were identified in layered silicon detector packages and their initial energy distributions were unfolded from the observed energy spectra.
This paper presents an analysis of neutron skins based on fully microscopic equations of state, including chiral two- and three-nucleon forces consistently at N 3 LO. Other theoretical predictions and recent constraints are also addressed, such as those from the PREX II experiment and the latest parity-violating electron scattering measurement of the 27 Al neutron skin.
Here, we report measurements of forward jets produced in Cu + Au collisions at $\sqrt{s{NN}}$=200 GeV at the Relativistic Heavy Ion Collider. The jet-energy distributions extend to energies much larger than expected by Feynman scaling. This constitutes the first clear evidence for Feynman-scaling violations in heavy-ion collisions. Such high-energy particle production has been in models via QCD string interactions, but so far is untested by experiment. One such model calls this a hadronic accelerator. Studies with a particular heavy-ion event generator ( HIJING ) show that photons and mesons exhibit such very high-energy production in a heavy-ion collision, so a QCD accelerator appropriately captures the physics associated with such QCD string interactions. All models other than HIJING used for hadronic interactions in the study of extensive air showers from cosmic rays either do not include these QCD string interactions or have smaller effects from the QCD accelerator.
A data-driven idea is presented to test if light nuclei and hypernuclei obey the coalescence-inspired sum rule, i.e., to test if the flow of a light nucleus or hypernucleus is the summed flow of each of its constituents. Here, the mass difference and charge difference among the constituents of light nuclei and hypernuclei are treated appropriately. The idea is applied to the available data for $\sqrt{^sNN}$ = 3 GeV fixed-target Au + Au collisions at the Relativistic Heavy Ion Collider (RHIC), published by the STAR Collaboration. It is found that the sum rule for light nuclei is approximately valid near midrapidity (-0.3 < $\mathcal{y}$ < 0), but there is a clear violation of the sum rule at large rapidity ($\mathcal{y}$ < -0.3). Further, the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, generates a similar pattern as obtained from the experimental data. In the present approach, the rapidity dependence of directed flow of the hypernuclei $^3_Λ$H and $^4_Λ$H is predicted in a model-independent way for $\sqrt{^sNN}$ = 3 GeV Au + Au collisions, which will be explored by ongoing and future measurements from STAR.
Global polarizations (P) of Λ (Λ¯) hyperons have been observed in non-central heavy-ion collisions. The strong magnetic field primarily created by the spectator protons in such collisions would split the Λ and Λ¯ global polarizations (ΔP=P Λ –P Λ ¯<0). Additionally, quantum chromodynamics (QCD) predicts topological charge fluctuations in vacuum, resulting in a chirality imbalance or parity violation in a local domain. This would give rise to an imbalance (Δn = N L –N R /< N L +N R > ≠0) between left- and right-handed Λ (Λ¯) as well as a charge separation along the magnetic field, referred to as the chiral magnetic effect (CME). This charge separation can be characterized by the parity-even azimuthal correlator (Δγ) and parity-odd azimuthal harmonic observable (Δa 1 ). Measurements of ΔP, Δγ, and Δa 1 have not led to definitive conclusions concerning the CME or the magnetic field, and Δn has not been measured previously. Correlations among these observables may reveal new insights. Furthermore, this paper reports measurements of correlation between Δn and Δa 1 , which is sensitive to chirality fluctuations, and correlation between ΔP and Δγ sensitive to magnetic field in Au+Au collisions at 27 GeV. For both measurements, no correlations have been observed beyond statistical fluctuations.
The Gamow-Teller and Fermi matrix elements, 〈 GT 〉 and 〈 F 〉 , respectively, for tritium β decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb interactions and isospin violation giving the leading order predictions 〈 GT 〉 0 = 0.9807 and 〈 F 〉 0 = 1 . Using an experimentally determined value for the tritium β decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding L 1 , A = 6.01 ± 2.08 fm 3 at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. The impact of L 1 , A on proton-proton fusion is also discussed. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element. Published by the American Physical Society 2024
187 Ta (Z = 73, N = 114) is located in the neutron-rich A ≈ 190 region where a prolate-to-oblate shape transition via triaxial softness is predicted to take place. A preceding work on the K π = (25/2 - ) isomer and a rotational band to which the isomer decays carried out by the same collaboration revealed that axial symmetry is slightly violated in this nucleus. Here, this paper focuses on a higher-lying isomer, which was previously identified at 2933(14) keV by mass measurements with the Experimental Storage Ring at GSI. The isomer of interest has been populated by a multinucleon transfer reaction with a 136 Xe primary beam incident on a natural tungsten target, using the KEK Isotope Separation System at RIKEN. New experimental findings obtained in the present paper include the internal and external β-decay branches from the high-spin isomer and a revised half-life of 136(24) s. The evaluated hindrances for K-forbidden transitions put constraints on the spin-parity assignment, which can be interpreted as being ascribed to a prolate shape with a five-quasiparticle configuration by model calculations.
The chiral magnetic effect (CME) in heavy-ion collisions reflects the local violation of P and CP symmetries in strong interactions and manifests as electric charge separation along the direction of the magnetic field created by the wounded nuclei. The experimental observables for the CME, such as the γ 112 correlator, the R Ψ$_2$ (ΔS) correlator, and the signed balance functions, however, are also subject to non-CME backgrounds, including those from resonance decays. A previous study showed that the CME observables are affected by the diagonal component of the spin density matrix, the ρ 00 for vector mesons. Here, in this work, we study the contributions from the other elements of the spin density matrix using a toy model and a multiphase transport model. We find that the real part of the ρ 1-1 component, Re ρ 1-1 , affects the CME observables in a manner opposite to that of the ρ 00 . All three aforementioned CME observables show a linear dependence on Re ρ 1-1 in the model calculations, supporting our analytical derivations. The rest elements of the spin density matrix do not contribute to the CME observables. The off-diagonal terms in the spin density matrix indicate spin coherence and may be nonzero in heavy-ion collisions due to local spin polarization or spin-spin correlations. Thus, Re ρ 1-1 , along with ρ 00 , could play a significant role in interpreting measurements in search of the CME.