On the rms radius of the deuteron

We use the world data on electron-deuteron elastic scattering to determine the deuteron structure functions and the charge rms radius. Coulomb distortion is included using second-Born approximation. We find a radius of 2.130 ± 0.003 ± 0.009 fm (±stat., ±syst.), which agrees with the information obtained from nucleon-nucleon scattering and from optical isotope shifts.     

Determination of the deuteron mean square radius

Three new methods are applied to the problem of extracting the deuteron rms matter radius from the experimental ratio of (e, d) to (e, p) scattering. A new value r_Ed = 1.953 (3) fm is obtained. The asymptotic method also yields 〈r⁴〉 = 54.5 ± 0.3 fm⁴ and 〈r⁶〉 = 1914 ± 20 fm⁶. Potential models of the deuteron are apparently unable to explain this r_Ed simultaneously with the low energy effective-range parameters of the neutron-proton system.     

On the determination of the proton RMS-radius from electron scattering data

It is shown that the proton rms radius should be determined from fitting a polynomial of second order to the low-q ² form factors. The commonly used polynomial of first order yields radius values which are too small. The proton rms radius has been redetermined from an analysis of the electron scattering data measured at three laboratories. The best fit value is 〈r _E ² 〉^1/2=0.87±0.02 fm.     

Measurement of the rms radius of12C by elastic electron scattering at 53 MeV

Elastic electron scattering cross sections for carbon were measured relative to hydrogen. An analysis of the data with phase shift calculations and a static charge distribution yields a model-independent rms radius of (2.42±0.04) fm for the natural isotopic mixture of carbon.     

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.     

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     

Determination of the root-mean-square radius of the deuteron from present-day experimental data on neutron-proton scattering

The correlation between the root-mean-square matter radius of the deuteron, r _m , and its effective radius, ρ, is investigated. A parabolic relationship between these two quantities makes it possible to determine the root-mean-square radius r _m to within 0.01% if the effective radius ρ is known. The matter (r _m ), structural (r _d ), and charge (r _ch) radii of the deuteron are found with the aid of modern experimental results for phase shifts from the SAID nucleon-nucleon database, and their values are fully consistent with their counterparts deduced by using the experimental value of the effective deuteron radius due to Borbély and his coauthors. The charge-radius value of 2.124(6) fm, which was obtained with the aid of the SAID nucleon-nucleon database, and the charge-radius value of 2.126(12) fm, which was obtained with the aid of the experimental value of the effective radius ρ, are in very good agreement with the present-day chargeradius value of 2.128(11) fm, which was deduced by Sick and Trautmann by processing world-average experimental data on elastic electron scattering by deuterons with allowance for Coulomb distortions.     

Nuclear charge radii of Al and Si from elastic electron scattering between 25 and 60 MeV

Elastic electron scattering cross sections of²⁷Al and Si (natural isotopic mixture) have been measured relative to carbon. The rms charge radiiR _m , deduced with partial wave calculations, are (3.01±0.05) fm for²⁷Al and (3.06±0.05) fm for Si, in good agreement with results from muonic X-ray energies. The values given are those for a Fermi charge distribution with skin thickness 2.5 fm; harmonic oscillator shell model distributions yield radii smaller by 0.03 fm. The ratioR _m (²⁷Al)/R_m(Si) is 0.984±0.016.     

On the disintegration energies of174Lu isomers

The cross section of⁴He for elastic electron scattering has been measured relative to that of the proton using a gas target with helium, hydrogen or a mixture of both gases. Scattering angles were between 56° and 130°, and the energy varied from 30 to 59 MeV. A model independent rms charge radius of (1.63 ± 0.04) fm has been evaluated for the α-particle.     

Electron scattering from 70Ge and 72Ge

Cross sections have been measured for the elastic and inelastic scattering of electrons from ⁷⁰Ge and ⁷²Ge for momentum transfers from 0.65 to 1.14 fm^?1. Values for the parameters of a Fermi type ground-state charge distribution were obtained from a phase shift analysis of the elastic cross sections. The rms charge radius corresponding to these parameters is 4.07±0.02 fm for ⁷⁰Ge and 4.05±0.03 fm for ⁷²Ge. Using DWBA analysis the reduced transition probabilities for the electroexcitation of the 2₁⁺ and 3₁^? states were found to be: B(E2, ω)↑ = 19.7±1.2, 26.8±2.0 W.u.; B(E3, ω)↑ = 36±5, 37±7 W.u. for ⁷⁰Ge and ⁷²Ge respectively. The J^π = 3^? assignments for the state at 2.562 MeV in ⁷⁰Ge and 2.515 MeV in ⁷²Ge are confirmed.     

Solution of the four-nucleon Schrödinger equation

We present a solution of the Schrödinger equation for the case of four nucleons interacting via the Malfliet-Tjon potential. The Schrodinger equation is integrated by means of the Green function Monte Carlo method. The adaption of this method to treat finite systems is given. For the four-nucleon case, the ground-state eigenvalue is found to be ?31.3 ± 0.2 MeV and the rms point mass radius 1.36 ± 0.01 fm. The point mass distribution is given and does not exhibit a central depression. The method is also applied to the problem of four helium atoms interacting via the Lennard-Jones potential.     

Nuclear matter distributions for 16,17,18O from a microscopic analysis of elastic proton scattering

An analysis of 65 MeV elastic proton scattering by ^16,17,18O has been made in terms of a reformulated optical model. Matter distributions for ¹⁷O and ¹⁸O have been obtained relative to ¹⁶O. The results for the rms matter radii are R₁₇?R₁₆ = 0.04±0.03 fm and R₁₈?R₁₆ = 0.35± 0.07 fm.     

Bose-Einstein correlations in e+e− annihilation in the γ(1S) and continuum

Bose-Einstein correlations in direct γ(1S) decays and continuum in the energy region √s=7.2?10.3 GeV have been studied using data taken with the MD-1 detector at VEPP-4 storage ring. Assuming gaussian density of the pion source the data indicate the radius of the sourceπ=0.73±0.10±0.04 fm for direct γ (1S) decays andπ=0.83±0.22±0.05 fm for the continuum. The correlation strengthsλ for both data samples also are similar. Thus Bose-Einstein correlations do not reveal a noticeable difference between quark and gluon fragmentation.     

Interactions of slow neutrons with the chromium isotopes

Neutron transmission experiments and determinations of coherent scattering lengths were performed on natural chromium and enriched samples of⁵⁰Cr,⁵²Cr,⁵³Cr and⁵⁴Cr. By means of the Christiansen-filter-technique we obtained new values for the scattering lengths of the bound atoms:b(^natCr)=3.635±0.007 fm,b(⁵⁰Cr)=?4.50±0.05 fm,b(⁵²Cr)=4.914±0.015 fm,b(53Cr)=?4.20±0.03 fm, andb(⁵⁴Cr)=4.55±0.10 fm. The transmission experiments with neutrons of 510 ΜeV, 1.26 eV and 5.19 eV energy resulted in data for the absorption cross sectionσ _a (^natCr) =3.05±0.08 b and for the scattering cross section at “zero energy”:σ ₀ (^natCr)=3.381±0.010 b. Data for incoherent and spin-state scattering and for the potential-scattering radius of the nuclei could be deduced from these results.     

Pionic x-rays and the neutron radius of 44Ca

Differences between strong interaction level shifts and widths for 2p states in pionic atoms of ^44,40Ca have been measured. Analysis in terms of an effective pion-nucleus potential leads to a difference in neutron rms radii of r_n(44)?r_n(40) = 0.05 ± 0.05 fm.     

Cross-sections of high energy nuclear reactions

Cross-sections of high-energy hadron-nucleus reactions σ _h (A) are investigated using ther optical model. A closed formula is drived for σ _h (A); itsA-dependence agrees with the rms radius of the Fermi distribution of nuclear matter. The properties of the radius parameter and the absorption mean free pathλ _h are investigated using Serpukhov data forp, π^α,K ^± , and \(\bar p\) . It is foundλ _p =1.44 ± 0.23 fm ～-1/m _π andλ _π =2.14 ± 0.21 fm forp and π-reactions, respectively; withλ _π /λ _p ?3/2 as expected from quark-counting. The approach extended to heavyion (HI) reactions leads to a formula of Bradt-Peters type, with an overlapping parameter decreasing withA. Analyses of HI data of LBL and ISR with this formula are presented.     

New methods for interferometric neutron scattering lengths measurements

A skew symmetric neutron interferometer has been used for tests of a nondispersive and phase contrast variation measuring technique of scattering lengths and for the measurement of anomalous scattering lengths of strongly absorbing substances. The following bound coherent scattering lengths have been obtained: b_c(Pt)=9.60 ± 0.01 fm, b_c(Te) =5.6 ± 0.1 fm and as real parts of anomalous scattering lengths at λ=l.86Å: b_c(Sm) =0.7 ± 0.2 fm, b_c(Eu)=5.3 ± 0.3fm, b_c(Gd)=5.1 ±0.4 fm, b_c(Dy)=16.9 ± 0.3 fm.     

Nuclear radii of 17,19B and 14Be

The interaction cross sections (σ_I) of light radioactive nuclei close to the neutron drip line (^17,19B, ¹⁴Be) have been measured at around 800A MeV. The effective root-mean-square (r.m.s.) matter radii of these nuclei have been deduced from σ_I by two different methods, a Glauber-type calculation based on the optical limit approximation and a few-body reaction model. The deduced radii from both approaches agree with each other within experimental uncertainty. The r.m.s. radii of ¹⁷B (2.99±0.09 fm) and of ¹⁴Be (3.10±0.15 fm) in this work are consistent with the previously determined values, and have a higher accuracy. The r.m.s. radius of ¹⁹B (3.11±0.13 fm) was newly determined. Assuming a “core plus 2n” structure in ¹⁷B and ¹⁴Be, the mixing of ν(2s_1/2) and ν(1d_5/2) was studied and the s-wave spectroscopic factor is found to be 36±19% and 47±25%, respectively. A valence radius analysis suggests a “core plus 4n” structure in ¹⁹B.     

The (7Li, 8Li) reaction to the (h92)−1 state in 207Pb

Relative differential cross sections for the reaction ²⁰⁸ P(⁷Li, ⁸Li) leading to the predominantly single-hole states in ²⁰⁷Pb have been analysed using the DWBA to determine the rms radius of the 1h_{$\text{9}\text{2}$} neutron orbital in ²⁰⁸Pb by comparison with known sizes of the 3p_{$\text{1}\text{2}$} and 2f_{$\text{7}\text{2}$} orbits. The experiment was performed at a beam energy of 52 MeV. The insensitivity of the technique to unknown input parameters to the DWBA analysis is demonstrated and a value of 5.94±0.11 fm for the rms radius of the 1h_{$\text{9}\text{2}$} orbit obtained assuming 70% of the hole strength is concentrated on the $\text{9}\text{2}{}^{\mathrm{?}}$, 3.41 MeV state in ²⁰⁷Pb. Effects due to fragmentation of the different hole strengths are examined and a value of 6.00 ± 0.11 fm is extracted as the best value for the rms radius of the neutron excess in ²⁰⁸Pb. The relevance of these data to mean-field calculations of nuclei is discussed.     

Proton-proton correlations in central collisions of Ni+Ni at 1.93 A·GeV and the space-time extent of the emission source

Small-angle correlations of proton pairs produced in central Ni+Ni collisions at a beam energy of 1.93 A·GeV are investigated with the FOPI detector system at GSI Darmstadt. Simultaneous comparison of longitudinal and transverse correlation functions with the predictions of the Koonin model allows to unravel the space-time ambiguity of the source extension. The determination of the source rest frame is found essential for the identification of this effect. For the present system, the selection of central events comprising about 8 % of the total cross section allows for the isolation of a compact source in momentum space which is centered around the c.m. velocity of the colliding nuclei. Taking into account the strong collective expansion of the participant zone, which introduces a reduction of the extracted source radius of more than 30 %, r.m.s. radius and emission time parameters of R _rms = (4.2 ± 1.2) fm and t _trms = (11 _? ⁺⁷ ) fm/c are extracted, respectively. In contrast, the analysis of the angle-integrated correlation function mixes the spatial and temporal size of the source and gives an upper limit R _trms = (7.0 ± 0.8) fm of the source radius.