Neutron Distributions In Nuclei Research Articles

Nuclear structure uncertainties in coherent elastic neutrino-nucleus scattering

The effects of the nuclear structure uncertainties on the description of processes induced by coherent scattering of neutrinos on nuclei are investigated. A reference calculation based on a specific nuclear model is defined and the cross sections and also the expected number of events produced by neutrinos generated by the explosion of a supernova in our galaxy, and by a spallation neutron source are evaluated. By changing the input parameters of the reference calculation their relevance on cross sections and on the number of the detected events is estimated. Seven spherical nuclei with different proton to neutron ratios are considered as possible targets of the neutrinos in the detector, the lightest being 12C and the heaviest 208Pb. The effects generated by the uncertainties of the nuclear model are much smaller than those due to the supernova neutrino flux models. This makes the coherent elastic neutrino-nucleus scattering a reliable tool to investigate the details of the neutrino sources, the neutrino-nucleus interaction, and, eventually, also to extract information about neutron distributions in nuclei.

Effect of nuclear quadrupole moments on parity nonconservation in atoms

Nuclei with spin $I \ge 1$ have a weak quadrupole moment which leads to tensor contribution to the parity non-conserving interaction between nuclei and electrons. We calculate this contribution for Yb$^+$, Fr and Ra$^+$ and found it to be small. In contrast, in many lanthanides (e.g., Nd, Gd, Dy, Ho, Er, Pr, Sm) and Ra close levels of opposite parity lead to strong enhancement of the effect making it sufficiently large to be measured. Another possibility is to measure the PNC transitions between the hyperfine components of the ground state of Bi. Since nuclear weak charge is dominated by neutrons this opens a way of measuring quadrupole moments of neutron distribution in nuclei.

Investigation of the structure of light exotic nuclei by proton elastic scattering in inverse kinematics

In order to study the spatial structure of exotic nuclei, it was proposed at the Petersburg Nuclear Physics Institute (PNPI) to measure the differential cross section for small-angle proton elastic scattering in inverse kinematics. Several experiments in beams of 0.7-GeV/nucleon exotic nuclei were performed at the heavy-ion accelerator facility of GSI (Gesellschaft fur Schwerionenforschung, Darmstadt, Germany) by using the IKAR ionization spectrometer developed at PNPI. The IKAR ionization chamber filled with hydrogen at a pressure of 10 bar served simultaneously as a target and as a recoil-proton detector, which measured the recoil-proton energy. The beam-particle scattering angle was also measured. The results obtained for the cross sections in question were analyzed on the basis of the Glauber-Sitenko theory using phenomenological nuclear-density distributions with two free parameters. Nuclear-matter distributions and root-mean-square radii were found for the nuclei under investigation. The size of the halo in the 6He, 8He, 11Li, and 14Be nuclei was determined among other things. Information about neutron distributions in nuclei was deduced by combining the data obtained here with the known values of the radii of proton distributions. A sizable neutron skin was revealed in the 8Li, 9Li, and 12Be nuclei.

Atomic probes of electromagnetic and weak interactions with trapped radioactive atoms

The alkali element francium has a simple electronic structure, and copious amounts of a wide range of isotopes can be produced in present and future rare isotope facilities. The atomic parity violating weak interaction in Fr is 18 times larger than in Cs, which makes it one of the best candidates to search for the effects of the weak interaction and its isotopic dependence. Atomic trapping methods now offer new ways to study these atoms with precision, and we will discuss some of our recent measurements with trapped Fr atoms. Future measurements of the spin-independent weak interaction can be used to test the standard model, but advances in atomic theory and improved understanding of the neutron distribution in nuclei are needed to make progress. We have made precise hyperfine-anomaly measurements in Fr and have shown that they are sensitive to the radial distribution of the neutron magnetization. Measurements of this type can help to constrain the neutron distributions. Future measurements of the spin-dependent weak interaction should allow extraction of the nuclear anapole moments for a sequence of isotopes, and allow separation of the neutron and proton weak interactions between hadrons.

Sensitivity of parity-violating A( [formula omitted], e′) A scattering and atomic parity nonconservation to neutron distributions in nuclei

Sensitivity of parity-violating A( [formula omitted], e′) A scattering and atomic parity nonconservation to neutron distributions in nuclei

Neutron distributions from pionic atoms

Abstract The radii of neutron distributions in nuclei are extracted from experimental shifts and widths of pionic atoms. A best fit to pionic-atom data is carried out by varying simultaneously the neutron radii and the parameter of a pion-nucleus optical potential. We have used three different potentials: one of them theoretical plus a small phenomenological part, another one semiphenomenological, with the linear terms in the density obtained from experimental πN amplitudes and the quadratic terms fitted to the pionic-atom data, and a third one purely phenomenological, obtained from a direct fit to pionic-atom data. The radii obtained with all of them are remarkably close and also close to the Hartree-Fock values. The combined statistical and systematic errors of the neutron mean-root-square radii are smaller than 0.2 fm for light and medium nuclei and smaller than 0.1 fm for heavy nuclei.

Parity-violating electron scattering

Parity-violating responses, occurring as interferences between electromagnetic and weak neutral currents in studies of inclusive scattering of longitudinally polarized electrons, are discussed. Three specific aspects of such studies are highlighted: (1) The role played by isospin-mixing in elastic scattering from 0 + N = Z nuclei; (2) The possibility of having a clean probe of ground-state neutron distributions in nuclei; (3) The sensitivity found in particular experimentally accessible observables to sizes of various form factors of the nucleon itself, including dependences on G E n and on form factors which arise from s s configurations in the nucleon.

Isospin dependences in parity-violating electron scattering

The role of the isospin structure of nuclear states in parity-violating single-arm electron scattering from nuclei is examined. Specific examples of elastic scattering from even-even N = Z (0 +, M T = 0, nominally T = 0) nuclei, which are supposed to be ideally suited for studying the electroweak interaction, are considered in detail. The aim is to find when nuclear structure effects due to isospin impurities significantly enter into the parity-violating asymmetry, and hence to determine the level of precision at which one can hope to extract the underlying weak neutral current couplings in a relatively model-independent way. The formalism is then extended to the general case of J > 0 states and even-even N ≠ Z nuclei. Finally, it is shown that measurement of the parity-violating asymmetry may provide a determination of the neutron distribution in nuclei.

Are the low-lying isovector 1 + states scissor vibrations?

In 1984 Richter and coworkers detected in deformed nuclei in electron scattering low-lying isovector 1 + states. In the same year Dennis Hamilton and coworkers from the University of Sussex found in (n,γ)-reactions low-lying 2 + isovector states in spherical nuclei. Such states have been predicted in several theoretical models. The first prediction was work of the author in 1966 where he extended the Bohr-Mottelson-model to include independent collective motions of the proton and the neutron distributions in nuclei. Both motions are coupled by the symmetry energy which dislikes demixing of the protons and neutrons. Thus one obtains the usual low-lying isoscalar quadrupole vibrations and rotations, but in addition also isovector states in spherical and deformed nuclei. In these states protons and neutrons move out of phase. The 1 + states found by Richter and coworkers in deformed nuclei can then be interpreted as vibrations of the deformed proton and neutron shapes in a scissor like way. In spherical nuclei the data of Dennis Hamilton and coworkers can be explained as harmonic quadrupole vibrations of protons and neutrons out of phase around the spherical equilibrium. We show here that this collective interpretation can very nicely reproduce the energies of the isovector 1 + states in deformed nuclei and of the isovector 2 + states in spherical nuclei. If the parameters are fixed to the low-lying isoscalar quadrupole rotations or vibrations the energies of the isovector states can be predicted without adjusting an additional parameter. Although the energies are reproduced very nicely one finds in deformed nuclei that the B( M1;0 +→1 +)-transition probability is too collective by a factor 5. In this collective description the M1-strength is concentrated in one state. In reality this isovector 1 + state contains only part of the Oπω-two-quasi-particle exitations. The rest of the strength is shifted to higher energies. A microscopic description using the quasi-particle random phase approximation or MONSTER can reproduce the exitation energies and transition probabilities correctly. It turns out to be important that in deformed nuclei the spurious state connected with the rotation of the whole system has to be put to zero energy by adjusting the parameter of the scalar part of the nucleon-nucleon interaction. In addition, one has to take care that the low-lying isovector 1 +-state is orthogonal to the spurious state |S>. If we request that the Hamiltonian is rotational invariant, that means that it commutes with the angular momentum operator, we can determine the nucleon-nucleon interaction from the given one-body part. For the one-body Hamiltonian we use the kinetic energies of the single nucleons, a deformed Saxon-Woods potential with spin-orbit coupling and slightly different shapes for protons and neutrons. By the quasi-particle transformation we include also a pairing interaction into the one-body piece. With the requirement that the Hamiltonian should commute with the total angular momentum, one can determine the many-body Hamiltonian parameter free if the Saxon-Woods potential and the pairing force are given. This symmetry restoring interaction is very nicely reproducing the energies and the magnetic transition probabilities from the ground state to these low-lying isovector 1 + states in the rare earth nuclei. We furthermore apply this formalism to the Ti-isotopes. There we get also similar satisfactory results using MONSTER and VAMPIR. The theoretical results indicate that the low-lying isovector 1 + states in deformed nuclei are in average half of orbital and half of spin character. A comparison of the excitation of these states with electron scattering and with proton scattering suggest that they are of more purer orbital character. A closer analysis of these measurements shows that they are not contradicting to a spin and an orbital character of these states which is roughly half and half. For the MONSTER we compare also M1-form factors with the data and find excellent agreement.

Different deformations of proton and neutron distributions in nuclei

Different collective deformation coordinates for neutrons and protons are introduced to allow for both stretching and $\ensuremath{\gamma}$ transitions consistent with experiments. The rotational actinide nuclei $^{234\ensuremath{-}238}\mathrm{U}$ and $^{232}\mathrm{Th}$ are successfully analyzed in this model.NUCLEAR STRUCTURE $^{232}\mathrm{Th}$, $^{234\ensuremath{-}238}\mathrm{U}$ calculated $B$ ($E2$) values, collective model.

On radii of neutron distributions in nuclei

Abstract We consider the analyses of the differences between rms radii (Δ = rn − rp) of neutron and proton distributions in a wide variety of nuclei. We note that apart from its own intrinsic interest, the quantity Δ is of importance for isotope shifts, core polarization contributions to the Coulomb energy differences of mirror pairs (Nolen-Schiffer anomaly) and the renormalization of the effective interaction. For example, if Δ were very small in 48Ca then the Nolen-Schiffer anomaly could be explained by a core polarization mechanism. We consider critically the various methods of determining Δ and conclude that at present probably the most reliable method is high energy (≈ 1 GeV) proton-nucleus scattering. The different theoretical analyses based upon, e.g., the multiple diffraction theory (where Glauber amplitude is the leading term) or the optical potential (KMT) formalisms appear to be converging to essentially the same answer when analyzing the same data. High energy α-particles and medium energy pions can also become useful sources of information if higher order optical potentials are treated with care. We find that Δ is rather large in 48Ca, i.e. there is a neutron skin, so that the Nolen-Schiffer anomaly cannot be explained by a core polarization mechanism. The results of high energy proton-nucleus scattering are in excellent agreement with current density dependent Hartree-Fock calculations.

Pionic atoms and the neutron distribution in nuclei

We calculate the widths and shifts of the atomic levels due to the strong pion-nucleus interaction. A formula with two phenomenological parameters is presented. These are determined from pionic data on 28Si, 32S and 40Ca. The data on the 2p levels are used to predict the r.m.s. radii of the neutron distributions in some nuclei.

The nucleon optical potential

We use the impulse approximation, the Tabakin internucleon potential and a Fermi gas model for the nucleus to calculate the low energy nucleon-nucleus optical potential. The real and imaginary parts are calculated simultaneously but it is found to be an extremely good approximation to calculate them separately as is usually done. The main features of the real part of the isospin independent potential are reproduced by our calculation. We also estimate the size and shape of the asymmetry term in the real part of the potential. The size is in agreement with empirical analyses and the predicted shape may be useful as a guide when fitting data. Our calculations for the imaginary part are much less satisfactory. In particular we cannot reproduce the large surface peaking of the empirical potentials perhaps reflecting our neglect of collective states. We find that the observed difference between the imaginary parts for protons and neutrons cannot be explained as a consequence of a reasonable difference between the proton and neutron distributions in nuclei.

The neutron distribution in nuclei from bremsstrahlung-weighted cross-sections

Bremsstrahlung-weighted cross-section (bwcs) measurements may be a decisive step to obtain information about the difference between neutron and proton radii. A model-independent relation is discussed between the total bwcs, the relative intensity of the bwcs of the upper ( T >) fragment of the dipole excitation and the neutron and proton radii.

π±Absorption and the Distribution of Neutrons in Nuclei

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>Absorption and the Distribution of Neutrons in Nuclei

The distribution of neutrons in nuclei

Considerations are presented which indicate that procedures now exist which make it possible to obtain accurate information on the distribution of neutrons in nuclei. However, these procedures make considerable simplifications in their approach to the many-body problem and hence verification of their predictions through direct high energy experiments is urgently required.