Second-order nucleon-nucleus optical potential

The second-order nucleon-nucleus optical potential has been calculated by using a simple second-order perturbation formalism. The results obtained by using an effective energy denominator indicate that the closure approximation is not valid for scattering.     

Calculation of the imaginary part of the nucleon-nucleus optical-model potential

The imaginary part of the optical-model potential for the scattering of nucleons by nuclei is studied in the frame of the shell-model approach to nuclear reactions. Special attention is paid to the one-hole target nuclei. The imaginary part of the optical-model potential in the second order in the nucleon-nucleus interaction is divided into two parts. The first corresponds to the average resonant scattering. The second corresponds to the inelastic scattering leading to the non-collective states of the target nuclei. A local potential equivalent to the non-local theoretical one is constructed in order to facilitate comparison with experiment. Numerical calculations concern the scattering of 14.5 MeV protons by ³⁹K. It is found that the imaginary part depends upon the angular momentum and that its radial variation is governed by strong shell effects. The predicted absorption is approximately 60% of the experimental one. The average resonant scattering contributes to the imaginary part of the optical-model potential as much as the inelastic non-collective excitations of the target.     

The optical potential for vector-polarized deuterons of 52 MeV

The vector analysing power for elastic scattering of 52 MeV polarized deuterons was measured for ¹²C, ¹⁶O, ²⁰Ne, ²⁸Si, ³²S, ⁴⁰Ar, ⁵⁸Ni, ⁹⁰Zr and ¹⁹⁷Au. The data were analysed together with previously measured differential cross sections in the framework of the optical model. Best-fit and average optical-model parameters were obtained both for surface and volume absorption. Fits with surface absorption are superior to those with volume absorption, especially for heavier nuclei. Typical parameters of the spin-orbit part of the best-fit optical potentials are found to be V_s.o. ～- 5.5 MeV, r_s.o. ～- 1.15 fm and a_s.o. ～- 0.4 fm, and there is no evidence for an imaginary component. The volume integrals and rms radii of real, imaginary and l · s potentials show a smooth mass dependence and differ insignificantly for different sets of potentials.     

Target excitations and the optical potential for protons scattering from nuclei

We calculate the contributions to the optical potential for 30 MeV protons due to inelastic excitations of the target nucleus. The scattering due to this non-local potential is calculated exactly and some of the results subjected to conventional optical model analysis. When only one excited state is included, a resonant dependence on the excitation energy is observed. Even with ten excited states, the position of a single one can strongly influence the scattering. It is possible to account for about $\text{3}\text{4}$ of the observed absorption in ⁴⁰Ca and ²⁰⁸Pb, but only by postulating unobserved states which exhaust the remainder of the experimental sum rules at somewhat unreasonably low energies. It was not possible to find simple local potentials which gave the same scattering because of the strong L-dependence of the absorption. The constructed potentials concentrate the absorption at too small radii. It is suggested that rearrangement (pick-up) processes contribute a substantial amount of absorption at larger radii, while compound formation will give rise to a volume term in the imaginary potential.     

Explicit treatment of internucleon P- and D-states in the calculation of the nucleon optical potential

Usual calculations of the nucleon optical potential using the Brueckner t-matrix treat the internucleon P- and D-states in a nuclear matter approximation. We use the method of Kisslinger to obtain the potential when P- and D-states are treated more precisely. We show phenomenologically that the effect of an explicit treatment of P-states is small, consistent with calculations indicating that the total P-state contribution to the t-matrix is small. This result provides additional verification that the Brueckner method is reasonably satisfactory. The potential obtained from an explicit treatment of the D-states is such that, although large, it can be reduced approximately to the form usually used. We show that the error in this approximation is not large though non-negligible when comparing calculated cross sections with experimental data. We also show that the P- and D-states corrections do not substantially affect phenomenological fits to experimental data.     

On the self-consistency requirement in the low density expansion of the optical potential in nuclear matter

We critically discuss the choice of the auxiliary potential U which is introduced in the low density expansion of the mass operator M(k, w). This choice is related to the analytical properties of M(k, w) in the complex w-plane and we take due account of momentum conservation in the intermediate states appearing in the diagrams associated with M(k, w). We also provide a computation of the one-hole line, rearrangement and renormalization contributions to the optical potential, of the hole state spectral function and of the momentum distribution in nuclear matter. We use a real auxiliary potential which is self-consistent up to the order considered here, i.e. which takes into account the rearrangement and the renormalization corrections. Rearrangement is treated rigorously. The dependence of the obtained results on the choice of the nucleon-nucleon interaction, namely the Hamman-Ho Kim one in our calculation, is discussed.     

Two-nucleon transfer reactions analysis using a coupled-channel formalism for the isospin-dependent optical potentials

A coupled-channel treatment of isospin-dependent optical potentials (ISOCCBA) has been developed to study two-nucleon transfer reactions. This formalism has been applied to the analysis of reactions populating isobaric multiplets in the region 40 ≦ A ≦ 56. A comparison is made of this calculation with the isospin-defined and charge-defined distorted-wave approximations.     

Near threshold production of neutral pions by complex particles

Cross sections for the inclusive neutral pion production cross section have been measured for near threshold energy ³He particles on complex nuclei. The results of these measurements are of order 10^?36 cm²/sr · MeV. The neutral pion cross section for 710 MeV ⁴He on ¹²C has been found to be comparable to the production cross section for nucleons, 10^?30 cm²/sr · MeV. Comparisons are made with a naive model relating complex particle production to nucleon production of pions.     

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from ¹⁹⁷Au, ²⁰⁸Pb and ²⁰⁹Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V_R and W_SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V_Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.     

One-dimensional integral equations for a system of three identical particles in the boundary condition model and the possibility of changing the off-shell behaviour of the two-particle T-matrix

It is shown that in the framework of the boundary condition model (BCM) for the two-particle interaction the Schrödinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle (-matrix and therefore to simulate three-particle effects.     

Emission of light charged particles in the reactions of 120 MeV 20Ne with 27Al

The emission of H and He isotopes in the reactions of 120 MeV ²⁰Ne with ²⁷A1 has been studied using light particle-heavy ion coincidence measurements. The energy spectra and angular correlations of the light particles emitted in coincidence with products of $\text{Z ≧ 14}$ agree well with the predictions of the statistical model applied to the decay of the compound nucleus ⁴⁷V. Results on α-particle emission associated with deep inelastic reactions leading to carbon and oxygen products are also reported.     

Elastic scattering of 217 MeV 3He particles

Differential cross sections have been measured for the elastic scattering of 217 MeV ³He particles from ⁶Li, ⁹Be, ¹²C, ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ⁸⁹Y, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸pb. The data have been analysed with an optical potential. The ambiguities found at lower energies (discrete families of real potential well depths) disappear. An optical potential is also calculated with an effective ³He-N interaction and a matter distribution. The agreement with experiment is good. Some comparisons are made with 166 MeV α-particle elastic scattering data.     

The elastic scattering of 33 MeV He particles from Ni,Cu and Zn

Differential cross sections have been measured for the elastic scattering of 33 MeV ³He particles from targets of ^58,60,62,64Ni,^63,65Cu and ^64,66,68Zn over the angular range 5° to 175°. The data have been analysed with the optical model, with particular emphasis on the investigation of the ambiguities in the real potential, the form of the imaginary potential and the use of a spin-orbit term.     

The imaginary part of the nucleon-nucleus optical potential in semiclassical approximation

We calculate in a novel Thomas-Fermi theory for multiparticle-multihole states the contributions of the correlation and polarization graphs to the imaginary part of the nucleon-nucleus optical potential $\text{W(ω,}\text{R}\text{,}\text{P}\text{)}$ depending on energy, radius and momentum. The present theory generalizes the older Fermi-gas and local-density approximations to this problem in the sense that we can assess precisely the validity of our approach. We show that it yields results which coincide with the average part of a corresponding quantal calculation. We use a gaussian finite-range effective interaction derived from the Gogny force and phenomenological mean-field potentials of the Woods-Saxon or harmonic-oscillator type. With these ingredients and no further adjustable parameters our results for the depth and volume integrals are in good agreement with the average trend of the elastic scattering data. Further, the resulting momentum dependence of W is strong, especially for small P. The influence of the Pauli principle is studied in detail.     

Energy spectra of single neutrons and charged particles emitted following the absorption of stopped negative pions in 4He

Energy spectra have been measured of single neutrons, protons and deuterons emitted following the capture at rest of negative pions in ⁴He. The neutron energy spectrum has been measured with an energy resolution of 4% at 90 MeV. The absolute number of stopped pions has been measured.     

Linear momentum transfer in the reaction 232Th(14N,light particles) AT 208 MeV

The longitudinal momentum transferred to a target nucleus (ΔP) has been studied for light-particle emission in the ¹⁴N-induced reaction on ²³²Th at 208 MeV. The transferred momentum was deduced by measuring folding angles between two fission fragments resulting from the sequential decay of the target-like nucleus. It was found that the fraction $\text{?}{}_2\text{=}\text{(〈ΔP〉 + P}{}_{\mathrm{<mtext>out</mtext>}}{}^{\mathrm{\parallel }}\text{)}\text{P}{}_{\mathrm{<mtext>beam</mtext>}}$ averaged over light-particle energy was about 0.68, almost independent of light-particle species and detection angle, where P_beam is the initial momentum of the beam particle and P_out^∥, the momentum component parallel to the beam carried away by the observed light particle. A possible mechanism for describing the phenomena is discussed.     

Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (II). Application to N-4He scattering

A “Coulomb-modified” dispersion relation is applied to low-energy p-⁴He forward elastic scattering. To check the validity of the modification, the results are compared with those deduced from n-⁴He elastic scattering. Completely analogous information is obtained for the two processes. The exchange of three bound nucleons is found to contribute strongly to N-⁴He forward scattering. The corresponding ⁴He-³H-p and ⁴He-³He-n coupling constants are evaluated as R_p = 3.8±0.3 and R_n = 3.0±0.3, respectively. These constants are related to the strength of the asymptotic wave function of nucleons in ⁴He and thus to the tail of the nucleon distribution. A comparison of R_p with the empirical proton distribution in ⁴He as deduced from e-⁴He elastic scattering shows excellent agreement. From R_p and R_n the effective ranges of the singlet ³H-p and ³He-n interactions in the ground state of ⁴He are determined to be equal, in accordance with charge symmetry, and to have a value of r_eff = 1.072±0.006 fm.     

Search for γ-rays emitted in the formation of a fission isomer

A search for γ-rays preceding isomeric fission in the reaction²³⁸U(α, 2n)^240mPu yielded negative results. Upper limits are given for the number of unconverted photons per isomer formed.     

Cross sections for the n+d breakup reaction

The n+d breakup cross section has been measured between 8 and 22 MeV by integrating the energy distributions of breakup protons and recoil deuterons observed in a deuterated scintillator. The results obtained deviate from the trend suggested by recent measurements of the cross section for proton-induced breakup and favour predictions based on a local N-N potential having a hard core in the singlet state.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.