Two-nucleon Data Research Articles

One-boson-exchange potential and structure of finite nuclei in the local-density approximation

Closed shell nuclei ranging from 16O to 208Pb are calculated using a density-dependent Hartree-Fock (DDHF) method. The effective interactions applied in these calculations have been derived from one-boson-exchange potentials, which describe the two-nucleon data correctly. The derivation has been made by means of nuclear matter Brueckner theory. The results of the DDHF calculations 3re compared with those obtained by using the Reid soft-core potential and with the experimental data.

One-boson-exchange potential and the ground state of 16O

Two one-boson-exchange potentials (OBEP), which fit two-nucleon data and give reasonable results in nuclear matter, are tested in 16O. Ground state properties are calculated in the framework of the Brueckner-Hartree-Fock approach. The density dependence of the reaction matrix elements stemming from the Pauli operator and starting energy are carefully taken into account.

Meson exchange effects on the deuteron magnetic moment

Meson exchange correction to the deuteron magnetic moment is investigated by dividing it into the long range and the short range parts. The former is related to the pion-photo-production amplitude for which the ϱ-meson exchange model is used, but its reliable estimation is difficult at present. The latter is calculated within the framework of the one-boson-exchange model which describes two-nucleon data quite well. It is found that the short range part is sufficient to explain the observed value of the deuteron magnetic moment.

Relativistic one-boson-exchange potential and two-nucleon data

A one-boson-exchange potential (OBEP) represented in momentum space and a helicity state basis is used to calculate the nuclear phase shifts up to 330 MeV, the deuteron and two-nucleon low-energy data. It satisfies the requirement of minimal relativity and contains off-energy-shell behaviour based upon covariant perturbation theory as well as relativistic features like energy dependence. In addition to the scalar σ 0( T = 0) and δ( T = 1) resonances the well-established π-, η,- θ-, ω- and φ-mesons have been exchanged. The good fit to the empirical Livermore data is represented by a least-squares value of 2.6 for 103 pieces of data. The fitted meson coupling constants essentially agree with those known from other sources. The results are compared with those owing to a former OBEP given in the configuration space.

Neutron-Deuteron Elastic Scattering Above the Breakup Threshold

Amplitudes for elastic $s$-wave neutron-deuteron scattering above the breakup threshold are calculated by the method of complex coordinates. The nucleon-nucleon interaction is represented by a local spin-and parity-dependent central Yukawa potential, with parameters chosen to fit low-energy two-nucleon data. Results for inelastic parameters indicate possible errors in a previous phase-shift analysis. Results for the quartet phase shift and quartet and doublet inelastic parameters are consistent with separable potential calculations, but the doublet phase shifts from the two models differ significantly.

Ambiguity in the Nucleon-Nucleon Phase Parameters near 330 MeV

The two-nucleon data in the energy range 290-350 MeV are found to contain an additional solution to the one recently reported by MacGregor et al. Potential models are much closer to this additional solution. Experiments are proposed for deciding between the two solutions.

Reliability of Shell Model Calculations using the Dispersion Relation Approach

Two techniques for deriving the Born approximation from the two-nucleon phase shift data in states having l ≤ 4 are employed to study the influence of the high energy form of the phase shifts in deducing two-body matrix elements and shell model spectra. A comparison is made with results obtained by other approaches.

Generalization of the Independent Pair Model to degenerate nuclear states

The equations of the Independent Pair Model for finite nuclei are generalized to nuclear states non describable by a single shell model configuration. As an application of these generalized equations to excited states, the energy of the excitedT=0,J π=0+ -state of4He has been calculated by an approximate solution. Using a spin-averaged square well potential with hard core and Serber exchange character, with all parameters beeing determined from two-nucleon data, the calculation yields an excitation energy of 21.58 MeV compared to the experimental value of about 20.1 MeV.

Convenient Expansion for Local Potentials

We introduce a new separable expansion for local potentials. The expansion, called the unitary pole expansion, has real, energy-independent form factors, and satisfies the requirements of two-particle unitarity in all orders. The convergence of the expansion is investigated by comparing expanded and exact $T$ matrices for negative energies, and by performing three-body bound-state calculations. In the latter case, a one-term approximation gives energies accurate to within 2% for potentials containing repulsion of the magnitude indicated by two-nucleon data.

The soft core potential matrix elements in a basis of harmonic oscillator wave functions

The paper presents methods of calculation of the soft core potential matrix elements in the space of the harmonic oscillator wave functions and their values for several frequencies of the oscillator. The realistic soft core potential is used. It is a superposition of the Yukawa type potentials and fits to the two-nucleon data.

Ground-State Energy of Neutron Gas

In the calculation of the energy per neutron in the zeroth cluster and first perturbative order at different neutron densities, a complete set of correlated basic functions has been used to represent the ground-state wave function for a system of neutron gas. Three potentials, all fitting two-nucleon data, were used. They are the Hamada-Johnston (HJ), Breit, and Brueckner-Gammel-Thaler (BGT) potentials. The results show that the energy decreases monotonically, as neutron density decreases and that the energy values at low densities are nearly the same for all three potentials. But at high densities, the BGT result departs quite markedly from those for HJ and Breit potentials. The results also indicate that a bound state due to the nuclear $n\ensuremath{-}n$ force alone does not exist for a system of neutron gas.

Independent-pair wave functions for the three- and four-body nuclei

A method which was described previously for generating independent-pair wave functions for three-nucleon systems is generalized so that the S′ state with mixed symmetry can be included in three-body calculations and so that the method can be used to generate independent pair wave functions for the alpha particle. This procedure is used to find approximate ground-state functions for several three- and four-body Hamiltonians. The functions so obtained are used to calculate an upper and, in some cases, a lower bound to the ground-state energy and to calculate the charge form factors for these three- and four-body systems. When the interactions are chosen so that both low- and high-energy two-nucleon data are correctly predicted, then the calculated binding energies are slightly too large, the ratio of the form factors for 3H to that of 3He is consistent with the experimental ratio, and the form factors for all three nuclei are too large at large momentum transfers. By increasing the radius of the hard core, the calculated form factor functions are decreased closer to the experimental ones.

Odd-parity states of 16O with a realistic nucleon-nucleon interaction

The effective interaction between nucleons on the Fermi surface of light nuclei is calculated with a realistic two-nucleon force having a hard core and tensor component. The relative S-state part of the effective force which corresponds to the Brueckner-Gammel-Thaler potential is shown to be very similar to the one obtained earlier for a simpler exponential S-state force, which however, fits the low-energy two-nucleon data. This effective force is used to calculate the properties of the odd-parity states of 16O. It is found that the energies of O − states are particularly sensitive to the tensor part of the effective force. In general, the agreement with experiment is satisfactory.

Nuclear matter binding energy and the two-nucleon potential

The Moszkowski-Scott approximation to the Brueckner theory is used to compare the nuclear matter binding energy predictions of two different two-nucleon potential models. Although the Hamada-Johnston potential has been found to be a much better fit to the two-nucleon data than is the Brueckner-Gammel-Thaler potential, the latter is found to be in much better agreement with the semi-empirical value of the nuclear matter binding energy. The discrepancy is found to be attributable mostly to the singlet odd potential, which has been only poorly defined by the available two nucleon data.

VELOCITY-DEPENDENT NUCLEON–NUCLEON POTENTIALS AND SATURATION IN NUCLEAR MATTER

Recently, nonsingular velocity-dependent potentials have been constructed which fit the the two-nucleon data, but do not give saturation in nuclear matter at reasonable densities. In this paper, we have asked what features a potential should have in order to give saturation, and we have found that the short-range wave-function distortion (defined in the text) is important. Reasons are given for the failure of the earlier potentials to saturate, and a new velocity-dependent potential is proposed which gives results similar to the standard hard-core potential model. We speculate on the usefulness of such potentials for future calculations of nuclear properties.

A potential model representation of two-nucleon data below 315 MeV

An energy independent nucleon-nucleon potential model is described. The model represents the two-nucleon data below 315 MeV more faithfully than any other potential model known to date. The data include the effective range expansion parameters and the deuteron properties as well as the scattering data at higher energies. It is of special significance that the n-p data have been represented by the energy independent potential model in a satisfactory manner for the first time. For this purpose a quadratic LS potential was found essential in the T = 0 state. The T = 1 potential differs little from those previously proposed by several authors. The phase shifts predicted by the model are in fair agreement with the solutions YLAM ( T = 1) and YLAN3M ( T = 0) recently found by the Yale group.

One-pion exchange and the optical model

Starting with the two-body scattering amplitude, an optical model potential for nucleon-nucleus scattering has been calculated (1) using the one-pion exchange interaction alone, (2) modifying the s-wave part of this by using effective range theory, and (3) using the modified phase shift analysis for p-p scattering supplemented by charge independence and the Gammel-Thaler potential for the n-p scattering information. Part (1) works sufficiently well to suggest that the one-pion exchange force contributes more importantly to the nucleon-nucleus interaction than to the basic two-nucleon scattering process. Part (2) produces an indifferent improvement on part (1). Part (3) represents the optical potential inferred from the most accurate two-nucleon data presently available. This last evaluation of the optical potential is considered the most reliable to date since it includes, in a good approximation, an infinite number of the high angular momentum states of the two-nucleon amplitude, which play a very essential part in the optical potential. A systematic derivation of the optical model equations is included with special emphasis on the needs of the present calculation; in addition, criteria for the validity of the model are discussed. Allowance has been made for the nuclear volume not being strictly proportional to the mass number (nuclear size effect) and for the inequality of the numbers of neutrons and protons in the nucleus (effect of neutron excess). For heavy nuclei, these effects influence the results up to 25%.

THE ROLE OF REPULSIVE CORES IN THE PHOTONUCLEAR EFFECT

The dipole sum rule is used to investigate the effect of nuclear forces on the integrated photonuclear cross section σint of a large nucleus, for a Serber potential containing a hard core. A Jastrow wave function is assumed to describe the nuclear ground state, and the first term in the cluster expansion of the resultant expression for σint evaluated under two different sets of assumptions for the potential and correlation function, corresponding to two different studies of the nuclear matter problem. The presence of a repulsive core in the potential is found to enhance considerably the calculated σint, compared with the result for a potential without a core which fits the same (low-energy) two-nucleon data.

A Semi-phenomenological Neutron-Proton Potential

A T=O two-nucleon potential is found which, when combined with the T= 1 potential reported previously, can reproduce all experimental neutron-proton data below 300 Mev. The triplet even parity potential is not strictly energy independent. The required energy depend­ ence is, however, very small and confined in the core region. In the triplet even parity state, it is found that both linear and quadratic LS potentials are required. The linear LS potential is weak and repulsive. The quadratic LS potential is here stronger than that required in the T=1 state and it is attractive. The singlet odd parity potential is slightly more repul­ sive than that of the one-pion-exchange potential. We conclude that all two-nucleon data up to 300 Mev can be understood in terms of a potential picture which is consistent with the current implications of the pion theory of nuclear forces.

JjCoupling Model in Odd-Odd Nuclei

An analysis has been made, using the $\mathrm{jj}$ coupling model, of the spins of 76 low-lying levels of odd-odd nuclei with $20<A<120$. Levels have been excluded from the analysis if any ambiguity exists in the assignment of a configuration. Excluding particle-hole configurations we find Nordheim's "strong" rule obeyed in the 22 cases in which it is applicable. Nordheim's "weak" rule is replaced by a rule predicting a ground state of the highest or lowest allowable spin. This revised rule is obeyed in 38 out of 41 cases. This competition between two levels of greatly differing spin results in the frequent occurrence of isomerism. For particle-hole configurations the state of the highest spin minus one is the ground state in 6 out of 13 cases. This agreement with experiment is obtained using proton and neutron configurations which, in 66 of the 76 cases, are found as ground states in the neighboring odd-even nuclei. The three revised coupling rules are predicted by the calculations of Schwartz, in which the residual proton-neutron interaction has a delta-function radial dependence, if the singlet-to-triplet strength is taken as 0.6, independent of mass number. This value is the same as that required to fit the free two-nucleon data. Exceptions to the empirical coupling rules and this theory will be discussed.