Influence of the potential energy surface on the cross sections for deeply inelastic transfer reactions induced by heavy ions

Large differences are observed in the cross sections for deeply inelastic reactions involving the transfer of several charges from ⁴⁰Ca and ⁴⁰Ar projectiles to the same rare-earth targets. The cross sections for four and six charge transfers from projectile to target are enhanced for ⁴⁰Ca incident ions. These differences are qualitatively explained by considering that the drift paths in the (Z, A) plane are governed by a static potential energy surface which describes the composite system. Shell corrections have been included in the calculation of this potential energy surface.     

The reactions 2H(40Ar,n)41K and 2H(40Ar,p)40Ar and electromagnetic decays of low-lying states in 41K and 41Ar

The γ-decay of states in ⁴¹K and ⁴¹Ar populated in the reactions ²H(⁴⁰Ar, n)⁴¹K and ²H(⁴⁰Ar, p)⁴¹Ar has been investigated at a bombarding energy of 56 MeV. Using the Doppler shift attenuation method and three different stopping materials, mean lifetimes were determined for the states in ⁴¹K at 980 keV (0.5±0.2 ps), 1560 keV (0.6_?0.2^+0.3ps), 1698 keV (0.1_?0.1^+0.2ps), 2144 keV (0.8_?0.2^+0.3ps) and in ⁴¹Ar at 1354 keV (0.664_?0.08^+0.09ps). Shell-model calculations have been performed for the positive parity states in ⁴¹K using a model space of a proton hole in the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits and two neutrons in the $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbit. The resulting excitation energies and electromagnetic properties of the low-lying states are in good agreement with experiment. An empirical value for a [Y₂s]₁ contribution in the effective M1 operator is obtained.     

Isotopic effects in high-energy nuclear reactions and isospin correlations of fragmentation cross sections

The experimental study of cross sections and kinematic characteristics of H, He and Li isotopes produced in the interaction of 660 MeV protons with separated isotopes of the target nuclei B, Ni, Sn and Sm, has been performed. The two-dimensional isospin correlation of cross sections for secondary particles in the nucleon-nucleus inelastic interaction is discussed. The systematization formula for fragmentation cross sections in broad regions of fragment and target nucleus masses over a large interval of incident proton energies is given.     

Comparison of cross sections for C + O reactions in the second regime of complete fusion

Kinetic energy spectra, angular distributions, and elemental yield distributions have been measured for the ¹² C + ¹⁶ O, ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reaction products over an energy range from 2 to 7 times the Coulomb barrier energy. A careful kinematic analysis of the evaporation residues and comparisons with statistical-model calculations show that fusion proceeds with full momentum transfer followed by a statistical decay of the compound nucleus. The competition between complete fusion process and peripheral reactions in the ¹² C + ¹⁶ O system is less important than for the ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reactions. The unexpectedly high ¹² C + ¹⁶ O complete fusion cross sections are related to the possible occurrence of a superdeformation of the ²⁸ Si compound nucleus.     

Heavy-ion fusion cross sections

The absolute cross sections for heavy-ion induced reactions in the rare earth region are studied systematically as functions of projectile energy, charge and mass. Targets and projec-tiles are chosen so that the same final states are fed in erbium, holmium and dysprosium nueleides with mass numbers A = 159–162. As the low lying states in these final nucleides are well known, the cross sections for the various reaction channels can be determined from singles γ-ray spectra. By summing these cross sections, the heavy-ion fusion cross sections are determined, and compared to theoretical calculations based on the Bass model as well as to total reaction cross sections deduced from optical model fits to elastic scattering data.     

Adiabatic time-dependent Hartree-Fock calculation of fusion cross sections: Application to 40Ca-40Ca

Using the adiabatic time-dependent Hartree-Fock method we calculate the interaction and inertial mass parameter relevant for a heavy-ion collision. In this work, which extends an earlier study for lighter systems, we investigate the case of ⁴⁰Ca-⁴⁰Ca for which detailed experimental information is available. As already found for lighter colliding ions, the mass parameter exhibits a large peak for interdistances slightly smaller than the barrier radius. We use our results to evaluate the fusion cross section and we find that the structure in the inertial mass brings the theoretical cross section in close agreement with data.     

The photodisintegration of 40Ar

High resolution measurements of the (γ, n), (γ, 2n), (γ, p), (γ, np) and (γ, 2p) cross sections of ⁴⁰Ar over a photon energy range of 10 to 28 MeV are reported. From this data, the total photon absorption cross section integrated to 26 MeV is found to be 434 ± 40 MeV mb. The results of a dynamic collective model (DCM) calculation compare favourably with the photoabsorption cross section, supporting the use of the DCM in this mass region. It is confirmed that isospin plays an important role in the decay of the ⁴⁰Ar giant dipole resonance.     

Measurement of cross sections for 14 MeV neutron capture

Activation cross sections for neutron capture have been measured at an energy of 14.6 ± 0.2 MeV relative to $\text{σ(}{}^{27}\text{Al}\text{(}\text{n}\text{,α)}{}^{24}\text{Na}\text{) = 114.2}\text{mb}\text{± 1.2\%}$ for the nuclei ³⁷Cl, ¹⁴K, ⁵⁰Ti, ⁵¹V, ⁵⁵Mn, ⁷¹Ga, ⁸⁷Rb, ⁸⁹Y, ¹²⁷I, ¹³⁰Te, ¹³⁸Ba, ¹³⁹La, ¹⁴²Ce, ¹⁸⁶W, ¹⁹⁸Pt,¹⁹⁷Au. Gamma-ray spectra of the product nuclei were measured with a Ge(Li) detector. Special attention was paid to taking into account all possible sources of error, especially contributions of lower energy neutrons. It seems to be shown that consistent results can be obtained for the cross sections for 14 MeV neutron capture if one properly takes into account the influence of lower energy neutrons even in cases where the relevant correction is large. In particular results from activation measurements agree well with results obtained by the method of integrated γ-spectra.     

Photoneutron cross sections for 9Be obtained with quasi-monoenerget1c photons

Absolute (γ, xn) cross sections for ⁹Be were measured with monochromatic photons from positron annihilation in flight in the energy range from 17 to 37 MeV. No pronounced structure was found in the cross sections in contrast to recent experiments performed with bremsstrahlung sources. The results are compared with many-particle shell model calculations.     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Heavy-ion reactions induced by O, O and F ions

Excitation curves have been determined from γ-ray yield measurements for heavyion reactions induced by E_lab = 12–30 MeV ¹⁶O, ¹⁸O and ¹⁹F ions incident upon thick targets of ⁹Be, ¹⁰B, ¹¹B, ¹²C and ²³Na. The yields of radioactive decay products with half-lives greater than one second were measured; hence a large number of the outgoing reaction channels could be observed. The preponderance of heavy reaction products suggests compound-nucleus formation as the dominant reaction mechanism. Statistical-model calculations with a spin-dependent level density have been performed, in which the nuclear moment of inertia was treated as a parameter. Many of the results can be explained satisfactorily with a nuclear moment of inertia 0.55 to 0.7 of the rigid body value.     

Recoil study of multinucleon transfer reactions: Capture of six charges by Nd targets in Ar induced reactions

Multinucleon transfer reactions induced with Ar ions and involving the capture of six charges by the target have been studied. The targets were all the separated isotopes of Nd, and the observed nuclei were ^149gTb, ¹⁵⁰Dy, ¹⁵¹Dy. The experimental technique involved the measurement of the cross sections, angular distributions, and recoil range at each recoil angle, of the heavy residual nuclei. After transformation of the data into the c.m. system, the angular distributions appear to be peaked backwards, close to 180°. This observation suggests that the present reactions are of the same type as the multinucleon transfer reactions studied by other authors for which the angular distribution of the light fragment was peaked forward in the c.m. system. The energy distributions in the c.m. system were used to check the feasibility of various mechanisms which could lead to the production of the observed isotopes. Each mechanism was supposed to be a two-step process: the first step was the exchange, from the projectile to the target, of a number n of nucléons, leading to an excited intermediate nucleus, and the second step the deexcitation of the intermediate nucleus by nuclear evaporation. This analysis indicates that the most probable mechanisms correspond to n close to 12 (6 protons and 6 neutrons), and to an excitation energy of about 60 MeV for the intermediate nucleus. The distribution of cross sections versus the number of nucléons gained by the target is also in accord with this reaction model.     

Mechanism of neon-induced reactions studied between 7.5 and 20 MeV/nucleon: Inclusive cross sections

Light and projectile-like fragments as well as fission fragments have been observed from the ²⁰Ne + ¹⁹⁷Au system at 150, 220, 290 and 400 MeV beam energy. Inclusive cross sections are given, and characteristic parameters like the centroids and the widths of momentum, Z- and A-distributions were derived. For comparison, some results of measurements on the ²²Ne + ¹⁹⁷Au and ^{20, 22}Ne + ⁵⁸Ni systems are included. The qualitative behaviour of the cross sections and the derived parameters show that with increasing bombarding energy the incomplete-fusion mechanism (massive transfer) and the sequential decay of projectile transfer residues (sequential break-up) appear in addition to the complete-fusion and ordinary transfer reactions predominant at the lowest bombarding energies. Other mechanisms do not contribute significantly in the energy range up to 20 $\text{MeV}\text{nucleon}$.     

Total cross sections for some (α, n) and (α, p) reactions in medium-weight nuclei

Total cross sections have been measured for the ⁴⁵Sc(α, n), ⁴⁶Ti(α, n), ⁵⁰Cr(α, n), ⁵¹V(α, n), ⁵⁴Fe(α, n) and ⁵⁸Ni(α, p) reactions, and stellar reaction rates have been calculated from them. These have been compared to recent theoretical calculations which used compound nuclear theory. The calculated values are generally higher than the experimental values by factors ranging from 2 to 10.     

Total nuclear photon absorption cross sections for some light elements

Absolute nuclear photon absorption cross sections have been measured for the elements Li, Be, C, O, Al, Si and Ca from 10 MeV up to photon energies beyond the meson production threshold. Magnetic Compton spectrometers and a bremsstrahlung spectrum with fixed end-point energy were used. The cross sections show structure in the region of the giant resonance and fall off smoothly towards higher energies. In the giant resonance region recent 1p-1h calculations are in poor agreement with these measurements except for one calculation for carbon, which included low lying excited states of the residual mass-11 system. The cross section in the intermediate region (40 to 140 MeV) can be described by the quasideuteron model with the density of deuteron-like structures taken as 8 NZ/A. The moments of the measured cross sections are compared with sum rule predictions. The integrated cross sections from 10 MeV up to the meson production threshold (140 MeV) exceed the classical dipole sum by a factor of 1.4 to 2.     

Neutron activation cross sections at 14.7 MeV for isotopes of tungsten

Cross sections for (n, 2n), (n, p), (n, α) and [(n, n′p) + (n, pn)] reactions at 14.7 ± 0.3MeV on enriched ^{180, 182, 183, 184, 186}W isotopes have been measured by the activation technique using Ge(Li) detector γ-ray spectroscopy. Some systematic trends in the cross-section data have been analysed. The (n, 2n) reaction at this energy in this mass region is by far the most favoured reaction and accounts for > 80 % of the total inelastic cross section.     

Neutron transfer reactions with very heavy ions

We have studied neutron transfer reactions induced by ¹³²Xe on three rare-earth targets at $\text{E}\text{V}{}_{\mathrm{C}}\text{～ 1.1}$. By using particle-particle-γ coincidence techniques we were able to identify final products and states populated in the one- and two-neutron reactions.The dependence of the transfer probabilities on the distance of closest approach is discussed in terms of effective penetration factors. The results seem to indicate the importance in two-neutron transfer of intermediate states with ? 6 MeV of excitation energy. The effect of excitation energy on the enhancement of the two-neutron transfer is discussed. A qualitative interpretation of the spin dependence of the one-neutron γ-ray yields in terms of the spatial localization of the wave functions involved is given.     

Complete fusion and quasi-fission reactions induced by Kr ions on heavy targets

Cross sections for fission (complete fusion) and quasi-fission are measured at a given angle for the systems Kr + Ho, Kr + W, Kr + Bi, Kr + U in the energy range 450–525 MeV. The cross sections for complete fusion are unexpectedly low and the cross sections for quasi-fission are high. The cross section for close collisions (sum of the complete fusion and quasi-fission cross sections) is compared to the value calculated with the critical distance concept. The possibility that complete fusion does not occur for the lowest impact parameters is discussed.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

Optical phase shifts from low-energy neutron cross sections

The Lorentz-weighted average of the S-matrix introduced by G.E. Brown is used in the Feshbach theory of the generalized optical potential to show that the average many-body S-matrix for elastic scattering is exactly equal to the two-body S-matrix of an optical potential. However, the optical potential S-matrix must be evaluated at the complex energy $\text{E}\text{= E + iI,}\text{where}\text{I}$ is the half-width of the lorentzian. The resulting equation for the optical phase shifts (OPS) δ_c, exp $\text{[2iδ}{}_{\mathrm{c}}\text{(}\text{E}\text{)] = 〈S}{}_{\mathrm{cc}}\text{(E)〉}$, holds even when the level spacing D forces the use of an averaging half-width I > D which is comparable to the energy E, providing that the OPS are also evaluated at the complex $\text{E}$ instead of being approximated by their values on the real energy axis at E. An appendix discusses briefly the conditions on a potential necessary for the result obtained by Brown that $\text{〈S}{}_{\mathrm{cc}}\text{(E)〉 = S}{}_{\mathrm{cc}}\text{(}\text{E}\text{)}$ when Lorentz-weighted averaging is used.