Neutron density distributions deduced from antiprotonic atoms

The differences between neutron and proton density distributions at large nuclear radii in stable nuclei were determined. Two experimental methods were applied: nuclear spectroscopy analysis of the antiproton annihilation residues one mass unit lighter than the target mass and the measurements of strong-interaction effects on antiprotonic x rays. Assuming the validity of two-parameter Fermi neutron and proton distributions at these large radii, the conclusions are that the two experiments are consistent with each other and that for neutron rich nuclei it is mostly the neutron diffuseness which increases and not the half-density radius. The obtained neutron and proton rms radii differences are in agreement with previous results.     

Nuclear charge radii from X-ray transitions in muonic atoms of carbon,nitrogen and oxygen

Energies of muonic X-rays of the K-series of carbon, nitrogen and oxygen have been measured with an accuracy of about 15 eV. Root mean square radii of the nuclear charge distributions were deduced. The results 2.49±0.05 fm for carbon, 2.55±0.03 fm for nitrogen and 2.71 ±0.02 fm for oxygen are in good agreement at comparable accuracy with recent electron scattering data.     

Neutron and proton densities in nuclei

A simple expression for nuclear densities which incorporates the correct asymptotic and central behaviour, gives quite accurate values for rms radii and surface thicknesses. It also brings out some important nuclear properties, (i) global constancy of neutron densities, (ii) equality of half-density radiiR for neutrons and protons, (iii) near constancy ofRN ^?1/3, (iv) larger surface thickness and rms radius for neutrons (v) shell effects on charge density.     

Some characteristics of nuclear densities

We propose a simple expression for nuclear densities, which brings out the following important nuclear properties: (i) shell effects in proton and neutron central densities, (ii) approximate global constancy of neutron central densities, (iii) approximate constancy ofRN ^?1/3 and R_pZ^?1/3 whereR is the nuclear half-density radius andR _p is the rms radius of the proton density, (iv) larger surface thickness and rms radius for neutron density as compared to those for proton density.     

Determination of the proton and neutron densities at the nuclear periphery with antiprotonic X-rays and \overline p -nucleus reactions

The nucleon density at the nuclear periphery has been investigated with two different methods. The first one is the measurement of the energy shift and the width of antiprotonic X-ray lines. Besides various other nuclides the X-rays from the isotopes ¹⁷²Yb and ¹⁷⁶Yb have been measured very extensively. From these data the absorption widths of six antiprotonic levels and the shifts of the lowest visible transitions could be determined. The comparison of the experimental intensities of the transitions with results from calculations of the antiprotonic cascade showed a good agreement. The second method is the determination of the yield of the annihilation products from the reaction of the antiprotons with nuclei. From this the neutron-to-proton density ratio at a distance of about 3 fm outside the half-density radius can be determined. This method was extended to short-lived residual nuclei with a half-life down to 5 s. The experiment confirmed the previously found negative correlation between the size of the neutron skin and the binding energy of the last neutron. The results have been compared with calculations. For many nuclei a good agreement was found between experiment and calculation, however for some nuclei measured and calculated values are at variance. This revised version was published online in August 2006 with corrections to the Cover Date.     

Elastic electron deuteron scattering

Measurements of the ratio of the deuteron to proton electric form factors were made for low q. The rms radius of the deuteron structure factor was found to be 1.9635 ± 0.0045 fm, yielding an rms charge radius of 2.095 ± 0.006 fm.     

Nuclear charge radii of 9,11Li: the influence of halo neutrons

The nuclear charge radius of 11Li has been determined for the first time by high-precision laser spectroscopy. On-line measurements at TRIUMF-ISAC yielded a 7Li-11Li isotope shift (IS) of 25 101.23(13) MHz for the Doppler-free [FORMULA: SEE TEXT]transition. IS accuracy for all other bound Li isotopes was also improved. Differences from calculated mass-based IS yield values for change in charge radius along the isotope chain. The charge radius decreases monotonically from 6Li to 9Li, and then increases from 2.217(35) to 2.467(37) fm for 11Li. This is compared to various models, and it is found that a combination of halo neutron correlation and intrinsic core excitation best reproduces the experimental results.     

Nuclear Rms charge radii from relative electron scattering measurements at low energies

The nuclear rms charge radii measured by low energy electron scattering at Darmstadt are summarized. Improvements in the experimental equipment and method permitted a redetermination of the¹²C radius which yieldedR _m (¹²C)=2.462 ± 0.022fm. This value has been used to recalibrate the radii measured relative to¹²C.     

Nuclear charge radius of 12Be

The nuclear charge radius of (12)Be was precisely determined using the technique of collinear laser spectroscopy on the 2s(1/2)→2p(1/2,3/2) transition in the Be(+) ion. The mean square charge radius increases from (10)Be to (12)Be by δ(10,12)=0.69(5) fm(2) compared to δ(10,11)=0.49(5) fm(2) for the one-neutron halo isotope ^{11}Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of ^{12}Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.     

Nuclear charge radius of 8He

The root-mean-square (rms) nuclear charge radius of 8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of 6He was measured to be 2.068(11) fm, in excellent agreement with a previous result. The significant reduction in charge radius from 6He to 8He is an indication of the change in the correlations of the excess neutrons and is consistent with the 8He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations.     

Garvey-Kelson relations for nuclear charge radii

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this paper we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation of 0.01fm between the GK predictions and the experimental values. Predictions are provided for 116 nuclei whose charge radius is presently unknown.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.     

Elastische Elektronenstreuung an14N,15N,16O und18O bei kleiner Impulsübertragung

Elastic electron scattering cross sections of¹⁴N and¹⁶O have been measured relative to the proton and of¹⁵N and¹⁸O relative to the lighter isotope (¹⁴N,¹⁶O resp.) using gas targets. The momentum transfer ranged from 0.22 to 0.48 fm^?1. The data were analyzed by phase shift calculations assuming harmonic oscillator shell model charge distributions. The following rms charge radii have been deduced: R_m(¹⁴N)=2.540±0.020 fm R_m(¹⁵N)=2.580±0.026 fm R_m(¹⁶O)=2.718±0.021 fm R_m(¹⁸O)=2.789±0.027 fm. The errors include statistical and systematic uncertainties and an estimate of effects due to the choice of the model. The radius differences of the isotopes are smaller than the values predicted by anA ^1/3 relation     

On the Present Status of the Problem of Charge Dependence and Charge Asymmetry of the Nucleon-Nucleon Force

The charge dependence of the nucleon-nucleon force can be derived from the low-energy scattering parameters. The p-p and n-p parameters were measured in direct scattering experiments. The n-n parameters a_nn = (-16.70 ± 0.38) fm and r_nn = (2.78 ± 0.13) fm have been determined from few particle reactions. The difference of the scattering lengths (a_nn - a_nn) ≈ 7 fm demonstrates the violation of the charge independence. Information on the charge symmetry is still doubtful due to the inaccuracy of the charge correction for the p-p parameters. Whereas the n-n and the charge corrected p-p parameters known at present yield a weaker n-n force than the p-p force, the opposite result follows from the binding energy difference for ³He and ³H and the meson theory of the nuclear forces.     

Nuclear charge distribution of41Ca

The mean square nuclear charge radius of⁴¹Ca equals the one of double magic⁴⁰Ca within 0.006 fm.     

DIFFUSENESS AND DEFORMATION EFFECT IN NUCLEAR CHARGE RADIUS

On the basis of Yukawa folded density distribution, a new formula of nuclear charge radius is proposed to include the effect of both spheroidal and tetroidal deformation. With the values of only two constants, the resulting root-mean-square error in calculated nuclear radii of 148 nuclides is 0.034 fm, which is near to that of Droplet model. It can be used to explain the nuclear radii of some isotopic sequences where the Z^1/3 law has difficulties. Taking the fluctuation of diffuseness width into account, the peculiar behaviors of some isotopic sequences can be well explained. The dependence of all the fluctuation on the neutron shell structure is also discussed.     

Extended analysis of the Ar VII spectrum in the vacuum ultraviolet region

The current status of the determination of corrections to the hyperfine splitting of the ground state in hydrogen is considered. Improved calculations are provided taking into account the most recent value for the proton charge radius. Comparing experimental data with predictions for the hyperfine splitting, the Zemach radius of the proton is deduced to be 1.045(16) fm. Employing exponential parametrizations for the electromagnetic form factors we determine the magnetic radius of the proton to be 0.778(29) fm. Both values are compared with the corresponding ones derived from the data obtained in electron-proton scattering experiments and the data extracted from a rescaled difference between the hyperfine splittings in hydrogen and muonium.     

The Lamb-shift experiment in Muonic helium

We propose to measure several transition frequencies between the 2S and the 2P states (Lamb shift) in muonic helium ions (μ ⁴He^?+? and μ ³He^?+?) by means of laser spectroscopy, in order to determine the alpha-particle and helion root-mean-square (rms) charge radius. In addition, the fine and hyperfine structure components will be revealed, and the magnetic moment distribution radius will be determined. The contribution of the finite size effect to the Lamb shift (2S???2P energy difference) in μHe^?+? is as high as 20 %. Therefore a measurement of the transition frequencies with a moderate (for laser spectroscopy) precision of 50 ppm (corresponding to 1/20 of the linewidth) will lead to a determination of the nuclear rms charge radii with a relative accuracy of 3 ×10^???4 (equivalent to 0.0005 fm). The limiting factor for the extraction of the radii from the Lamb shift measurements is given by the uncertainty of the nuclear polarizability contribution. Combined with an ongoing experiment at MPQ aiming to measure the 1S???2S transition frequency in the helium ion, the Lamb shift measurement in μHe^?+? will lead to a sensitive test of problematic and challenging bound-state QED terms. This measurement will also help to clarify the discrepancy found in our previous μ _p experiment. Additionally, a precise knowledge of the absolute nuclear radii of the He isotopes and the hyperfine splitting of μ ³He^?+? provide a relevant test of few-nucleon theories.     

Precision measurement of the 2p-1s transition in muonic C: Search for new muon-nucleon interactions or accurate determination of the rms nuclear charge radius

The wavelength of the 2p3/2-ls1/2 transition in muonic ¹²C was measured with a crystal spectrometer as 16.473765 (88) pm. With an improved model-independent analysis we deduce an rms charge radius for ¹²C of 2.4829 (19) fm. A 2.4 standard deviation difference between our rms charge radius and that deduced from recent elastic electron-scattering experiments is tentatively attributed to a short-range additional interaction between muon and nucleons. A comparison is made with other experiments yielding information on such interactions.