H.M. Hofmann

Consistent cluster model description of the electromagnetic properties of lithium and beryllium nuclei

Abstract We calculate the electromagnetic properties of lithium and beryllium nuclei within a resonating group model using bare charges and g-factors. For 6Li we give results for reduced transition strengths and explain the tiny quadrupole moment. For 7Li and 7Be we compute electromagnetic moments and transitions between bound states. Furthermore we reproduce the existing data on the radiative captures 3He(α, γ)7Be and 3H(α, γ)7Li. In the 7Li case the calculations indicate an increase of the astrophysical S- factor for decreasing energy which might have astrophysical consequences. We show that closed channels do not influence results on the astrophysical S-factor at low energy. Finally we demonstrate that the polarisability of 7Li originates from the virtual break-up at low energies. In this case, the 6Li + n channels contribute appreciably.

Hauser-Feshbach calculations in the presence of weakly absorbing channels with special reference to the elastic enhancement factor and the factorization assumption

In an extension of previous work on the theory of statistical cross sections model calculations have been performed in the presence of weakly absorbing channels, a case which is of particular interest in applied work involving neutron capture or neutron scattering at low energies. Improved formulas for calculating the elastic enhancement factor and compound nucleus cross sections are presented. In our model calculations we find that the factorization condition for cross sections is not satisfied in cases where a few strongly and many weakly absorbing channels are mixed. However, even in these extreme cases, the formulas provide a good description of the computer-generated cross sections involving at least one strong channel. In addition, the structure of the formula for the elastic enhancement factor has been chosen so as to reproduce all known limiting values and to describe cases where many weakly absorbing channels contribute.

Microscopic calculation of the 4He system

Abstract We report on a consistent, microscopic calculation of the bound and scattering states in the 4He system employing a realistic nucleon-nucleon potential in the framework of the resonating group model (RGM). We present for comparison with these microscopic RGM calculations the results from a charge-independent, Coulomb-corrected R-matrix analysis of all types of data for reactions in the A = 4 system. Comparisons are made between the phase shifts, and with a selection of measurements from each reaction, as well as between the resonance spectra obtained from both calculations. In general, the comparisons are favorable, but distinct differences are observed between the RGM calculations and some of the polarisation data. The partial-wave decomposition of the experimental data produced by the R-matrix analysis shows that these differences can be attributed to just a few S-matrix elements, for which inadequate tensor-force strength in the N - N interaction used appears to be responsible.

Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

Abstract.The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of 3H and 4He , and for the singlet S -wave 3He -neutron scattering length a0(3He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of 3H of (1.6±0.2) fm, for the 4He binding energy of (28±2.5) MeV, and for Re{a0(3He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.

An International Evaluation of the Neutron Cross Section Standards

Work is reported here on the process and present results of an international evaluation of the neutron cross section standards. The evaluations include the H(n,n), 3He(n,p), 6Li(n,t), 10B(n,α), 10B(n,α1γ), 197Au(n,γ), 235U(n,f), and 238U(n,f) standard reactions as well as the 238U(n,γ) and 239Pu(n,f) reactions. This evaluation was performed to include new experiments on the standards that have been made since the ENDF/B-VI evaluation was completed and to improve the evaluation process. Evaluations have been completed for the 6Li(n,t), 197Au(n,γ) and 238U(n,γ) cross sections. Also below 20 MeV the H(n,n), 235U(n,f), 238U(n,f) and 239Pu(n,f) cross sections are completed. Many of the cross sections being evaluated are used in neutron dosimetry for fluence determination. The general trend observed for the evaluations is an increase in the cross sections for most of the reactions from fractions of a percent to several percent compared with the ENDF/B-VI results.

Effects of Pion-Absorption in Pion-Helium Scattering

In the region of the (3, 3) resonance pion scattering data can be well described by models, which however, still require phenomenological input to achieve quantitative agreement with the experimental data. A fully microscopic treatment has been applied to the case of4He. It turns out that in this model the pion scattering can be reproduced satisfactorily without additional phenomenological input.

Resonating group calculations in light nuclear systems

Already in the e a r l y t imes of nuc lear physics Wheeler /WH 37/ invented the Resonating Group Method (RGM). In c lose analogy to the mo lecu la r binding he s tud ied nuc lear few body system. His idea becom~ most t r ans Parent by cons ider ing the H~-ion (neg lec t i ng f o r the momentum sp indegrees of freedom and the i d e n t i t y of p a r t i c l e s ) : The b ind ing of t h i s three body system can then be understood as the strong b ind ing of the e lec t ron to one of the protons forming a group of 2 p a r t i c l e s and the Weak b ind ing of the remaining proton by p o l a r i z i n g the neu t ra l atom. Since no proton is d i s t i n g u i s h e d , we could also s t a r t our cons iderat ions wi th the second proton forming a s t r ong l y bound group c o n s i s t i n g of the e lec t ron and the second proton and the weakly bound f i r s t proton. In Prac t i ce the e lec t ron w i l l be considered as jumping resonan t l y from One c o n f i g u r a t i o n to the o ther so tha t a v a r i a t i o n a l ansatz f o r the to ta l wave func t i on w i l l cons i s t of a l i n e a r combinat ion of the two Con f igu ra t i on . As i n t e r a c t i o n s serve the basic two body p o t e n t i a l s .

He-4 can experiments serve as a database for determining the three-nucleon force?

We report on microscopic calculations for the {sup 4}He compound system in the framework of the resonating group model employing realistic nucleon-nucleon and three-nucleon forces. The resulting scattering phase shifts are compared with those of a comprehensive R-matrix analysis of all data in this system, which are available in numerical form. The agreement between calculation and analysis is very good in most cases. Adding three-nucleon forces yields large effects in many cases. For a few cases, the new agreement is striking. We relate some differences between calculation and analysis to specific data and discuss experiments necessary to clarify the situation. From the results, we conclude that the data of the {sup 4}He system might be well suited to determining the structure of the three-nucleon force.

The nuclear systems 7Li and 7Be in a resonating group model

Abstract Refined resonating group calculations on the basis of a multi-structure and multi-channel approach are presented for the A = 7 nuclear systems 7Li and 7Be. Calculated differential cross sections and vector polarizations are compared with experimental data. Calculated phase shifts explain the bound states and resonant structures derived from experimental analyses and give predictions for the existence of additional resonant states with Jπ values of 1 2 − , 3 2 − , 5 2 − , and an indication for the appearance of a broad 7 2 + structure in the energy spectra below 12 MeV excitation energy.

Interaction of light hadrons in a constituent quark model

Abstract We describe the nucleon-nucleon interaction in a quark cluster model based on the resonating group method. Extending the model consistently to antiquark degrees of freedom, meson-meson, meson-nucleon and nucleon-antinucleon scattering become accessible. Within this extended model both the nucleon-nucleon phase shifts and the nonresonant phase shifts in the pion-pion and pion-nucleon scattering are reproduced reasonably well. Finally, we demonstrate how scattering and annihilation of the pp-system can be described consistently in a coupled channel approach.