Δ(3, 3) excitations and effective three-nucleon forces in finite nuclei

Contributions from three-body terms with intermediate Δ(3,3) isobar excitations to the ground state energies of nuclei are investigated. These terms can either be understood as three-body clusters in a many-body theory including isobar excitations explicitly or as contributions to an effective three-nucleon force. For the example ¹⁶O the resulting contribution is attractive and its value is typically about ?0.5 MeV per nucleon. This is smaller than the typical values of 1 MeV per nucleon repulsion obtained from the modifications of the effective two-body nucleon-nucleon interaction in nuclei due to intermediate Δ(3, 3) configurations. The gain in energy from the three-body terms including Δ(3,3) configurations, however, is of the same importance as the contribution from three-body terms including nucleons only.     

Origin of projectile-like fragments from40Ar +68Zn collisions between 15 and 35 MeV/nucleon: Direct transfer of nucleons and projectile fragmentation

The projectile-like fragments emitted in the⁴⁰Ar +⁶⁸Zn reaction performed at 14.6, 19.6, 27.6 and 35 MeV/nucleon are studied. Their energy spectra and angular distributions have been measured. Velocities, widths of the linear momentum distributions and cross sections have been deduced. The results are discussedi) in terms of transfer of a few nucleons and analysed with a diffractional model. They are consistent, for stripping reactions, with a direct transfer of nucleons and a target excitation yielding multiparticlemultihole configurations,ii) In terms of projectile fragmentation-like process with a modified abrasion model taking into account the energy separation of the participant nucleons. The projectile fragmentation-like process appears above 20 MeV/nucleon and strongly competes with transfer of nucleons at 35 MeV/nucleon. The evolution of the mechanisms with incident energy is discussed on the basis of the reduced widths of the linear momentum distributions and on those of velocities and cross sections.     

Emission of intermediate-mass fragments in the interaction of 16O with 59Co, 93Nb and 197Au

In this paper we study the emission of ⁸Be_gs, B and N fragments in the interaction of ¹⁶O ions with ⁵⁹Co, ⁹³Nb and ¹⁹⁷Au at incident energies varying from 6 to 25 MeV/nucleon. The spectra of these fragments, as well as those of C fragments studied in a previous paper, are dominated at forward angles by a component originating from break-up of ¹⁶O. At the higher incident energies break-up occurs after quite a sizeable projectile energy loss. Another mechanism which dominates at large emission angles, favours the emission of low-energy fragments and is attributed to the coalescence of nucleons during the cascade of nucleon-nucleon interactions by means of which the excited nuclei produced in the primary two-ion interaction thermalize. Received: 21 January 2003 / Accepted: 27 March 2003 / Published online: 5 June 2003     

Two-nucleon stripping reactions induced by O in Fe and Ni at 80 MeV

Both the (¹⁶O, ¹⁴N) and (¹⁶O, ¹⁴C) reactions have been investigated on ⁵⁴Fe and ⁵⁸Ni target nuclei at 80 MeV incident energy. Both reactions are selective. The kinematical conditions have been found to act in two ways: (i) the high-spin states are enhanced and (ii) the states involving nucleons in the f- or p-shells are favoured. Three groups of T = 1 analog states have been located in ⁵⁶Ni and ⁶⁰Zn from a comparison of the two transfer reactions on the same target, and configuration assignments are attempted.     

Studies of multi-nucleon transfer reactions in <Superscript>90</Superscript>Zr(<Superscript>18</Superscript>O,X) and <Superscript>90</Superscript>Zr(<Superscript>16</Superscript>O,X)

Multi-nucleon transfer reactions in ¹⁸O + ⁹⁰Zr and ¹⁶O + ⁹⁰Zr have been studied at an incident energy of 90 MeV. The energy spectra and angular distributions are measured. The data have been analyzed to obtain cross-section dependence on the number of nucleons transferred and on the ground-state Q-values. In the ⁹⁰Zr(¹⁸O, X); X = ¹⁶O, ^17,16,15,14N, ^14,13,12C, ^12,11,10B, ^10,9,7Be and ^7,6Li reactions, 2n and 2n-correlated transfer cross-sections are observed to be enhanced as compared to the ¹⁶O + ⁹⁰Zr reaction. A detailed comparison in the multi-particle stripping and elastic-scattering cross-section between these two systems are made in order to investigate the possible influence of the two valence neutrons in ¹⁸O nucleus. Diffractional model DWBA calculations, based on the direct surface transfer model, have been performed to understand the reaction mechanism of multi-nucleon transfer to continuum.Received: 12 September 2002, Revised: 24 September 2003, Published online: 27 January 2004PACS: 25.70.Hi Transfer reactions - 25.70.Bc Elastic and quasielastic scattering     

Inclusive neutron,proton and deuteron energy spectra from stopped π− absorption in 6Li, 9Be, 16O and 27Al

Inclusive energy spectra (E ⩾ 20MeV) of neutrons, protons, and deuterons emitted after stopped π⁻ absorption in ⁶Li, ⁹Be, ¹⁶O and ²⁷Al (neutrons only) were measured. Single-neutron emission rates of the order of 10⁻² and 10⁻³ per stopped pion were obtained for ⁶Li, ⁹Be, ¹⁶O and for ²⁷Al respectively. The experimental data indicate a predominant contribution of two-nucleon absorption mechanism to the neutron and proton spectra for all the studied nuclei, and presence of direct deuterons from cluster-absorption for ⁶Li. Values of R_np are deduced, which are consistent with predictions based on the absorption mechanism by a correlated pair of nucleons with pion rescattering.     

Analysis of deep inelastic collisions between16O and27Al

Deep inelastic collisions in light systems formed with¹²C,¹⁴N and¹⁶O projectiles and different target nuclei have been studied at incident energies between 5 and 7 MeV/u. A detailed analysis is presented for the results of the¹⁶O+²⁷Al reaction at 80.6 MeV incident energy which is based on trajectory calculations and the transport theory. The questions of angular distributions and the interaction time, the energy dissipation and the fragment deformation as well as the element-distribution and the effect of the nuclear structure are discussed.     

Nuclear spectral energy functions beyond the shell model

We predictl=0 nucleons in¹²C to have a negative (binding) energy centered around –22 MeV with a full width at half-maximum of 5.3 MeV. Thel=1 (P _3/2 nucleons) are predicted to have a much narrower spectral energy function centered around –10.6 MeV. A strongly correlated translational invariant wave function was used to describe the ground state nucleus. A central two-nucleon potential was utilized in the hyperspherical harmonic method to approximately solve the Schrödinger equation for the ground state wave function. Both confirmation and failings of the independent particle shell model are exposed.     

Effects of non-orthogonality and virtual excitations in direct reactions (III)

Formulae are presented concerning the effects of virtual Coulomb excitation on the transfer of nucleons between heavy ions at energies below the Coulomb barrier. These formulae are applied towards calculation for the ²⁰⁸Pb(¹⁶O, ¹⁷O)²⁰⁷Pb reaction at 69.1 MeV. Generally, the effect is found to be of the order of 10% but it is not discernable owing to the small reaction cross sections. Suggestions are presented for extending the analysis to higher energies where the situation is more favourable.     

The absorption of π− at rest on complex nuclei

The energy, width and intensity of prompt nuclear γ-rays following capture of π^? at rest by ⁹Be, ¹⁰B, ¹⁶O, ¹⁹F, ³¹P, Ca and ⁹³Nb were measured with a Ge(Li) detector. In most cases it was possible to identify the final nucleus from the energy of the observed γ-ray. Using the measured Doppler broadening of γ-rays from short-lived states, the vector sum momentum distribution of the emitted nucleons was calculated. From the measured γ-ray intensities, isotopic yields were deduced corresponding to the removal of from 1 to 12 nucleons. The average number of removed nucleons changes from 3.0 to 5.5 as the target varies from ¹⁶O to ⁴⁰Ca. A comparison was made with data from both spallation reactions and multi-nucleon pickup reactions.     

Microscopic calculation of pre-equilibrium emission

Previous TDHF calculations have shown that a pre-equilibrium emission of nucleons should be seen for asymmetric collisions of nuclei. Recent calculations indicate that the added effect of two-body collisions is to enhance this pre-equilibrium emission, it being seen also for symmetric collisions. More detailed calculations of this phenomenon are presenied here. The two-body collisions are treated by the time-relaxation method. This method is reviewed, and a revised formula for the relaxation time is introduced.Calculations are made in a slab geometry. For real nuclei, as much as 6% of all nucleons are estimated to be emitted at a beam energy of E_c.m. = 20 MeV/A. The energy distribution of the emitted nucleons relates to a temperature of 13 MeV at this energy. At 5 MeV/A, the emission is reduced to about 1 %.     

Investigation of the reaction <Superscript>4</Superscript>Нe(γ, <Emphasis Type="Italic">pn</Emphasis>)<Emphasis Type="Italic">d</Emphasis> at energies below the meson-production threshold

Themomentum distributions of deuterons and nucleons from the reaction ⁴Не(γ, pn)d induced by bremsstrahlung photons whose spectrum extends up to the endpoint energy of 150 MeV weremeasured by means of a diffusion chamber placed in a magnetic field. These measurements were performed in four photon-energy intervals for deuterons and in the energy range between 100 and 150 MeV for nucleons. Angular and energy correlations of nucleons were measured at photon energies in the interval between 50 and 70 MeV. The results obtained in this way were analyzed on the basis of the quasideuteron model. The probability for final-state nucleon–deuteron interaction was estimated.     

The 12C(7Li, α)15N triton transfer reaction

The ¹²C(⁷Li, α) reaction was studied up to 16 MeV excitation energy in ¹⁵N. Excitation functions for eight α-groups were measured in the 28–38 MeV incident energy range. A high resolution angular distribution was taken at E_7Li = 35 MeV with the aid of a multi-gap magnetic spectrograph. The contribution of the compound nucleus channel to the α-intensities was estimated. A finite range DWBA calculation in which the three transferred nucleons enter the sd shell was attempted. Results of the above-mentioned studies and the strong selectivity of the reaction indicate a predominant direct reaction mechanism at the present relatively high bombarding energy. Comparison between the experimental results and calculations based on the weak coupling model of Lie and Engeland, exhibit reasonable correlation between the strongly excited states in the present study and the 3p-4h model states for which the contribution of the core excitation is small, and this gives a possible interpretation of the high selectivity of the reaction.     

Low-energy antiproton annihilation in nuclei

The annihilation of 100 MeV antiprotons in atomic nuclei is studied in the frame of an intranuclear cascade model. It is found that the antiproton is annihilated about 1 fm inside the nucleus on the average. The energy released by the annihilation is carried by an average of 5 pions, which cascade throughout the nucleus. About 5% (10%) of the primordial pions are absorbed by the ⁴⁰Ca (¹⁰⁸Ag) target. The pions transfer around 5&#x0303;50 MeV (7&#x0303;00 MeV) to the nucleons and eject about one-fifth of the nucleons. The pion and proton cross sections are calculated. In particular, the relative transparency of the nucleus to high-energy pions (and not to pions in the Δ-resonance region) gives rise to a peculiar pion emission pattern. The time evolution of the baryon density and of the spectrum of the participant nucleons is investigated. It turns out that the cascade does not generate high energy density.     

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in ¹²⁰Sn and ²⁰⁸Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for ¹²⁰Sn and 40 MeV/nucleon for ²⁰⁸Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in ²⁰⁸Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.     

Nuclear electromagnetic bremsstrahlung: A new tool for studying heavy-ion reactions

The classical theory of bremsstrahlung is applied to heavy-ion reactions. The two interacting nuclei are treated as collections of individual nucleons. It is shown that the electromagnetic radiation produced during the interaction may be separated into two components. A coherent component is related to the ordered motion of the nucleons in the entrance channel. The amount of collectivity is directly and simply related to the wavelength of the radiation, longest wavelengths corresponding to larger collectivity. The coherent component yields results on the timescale of the initial part of the reaction. An incoherent component reflects the disordered part of the motion of the nucleons. This component gives information on the total number of nucleon-nucleon collisions which take place during the reaction. A comparison is made with existing experimental data and points for a characteristic stopping time of 3 × 10^?23 s for a ¹²C projectile impinging upon a ¹⁹⁷Au target at 84 MeV/nucleon. The low-energy part of the experimental γ-spectrum is attributed to the heated compound system with a temperature of 6 MeV. The average number of collisions per nucleon would then be of order 30. We show that bremsstrahlung γ-emission may be expected even in low-energy heavy-ion collisions at the μb/MeV · sr level for γ-ray energies larger than 20 to 30 MeV.     

Energy dependence of one- and two-particle transfer reactions in the system16O+90Zr

The energy dependence of the one- and two-particle transfer reactions⁹⁰Zr(¹⁶O,¹⁷O)⁸⁹Zr,⁹⁰Zr(¹⁶O,¹⁵N)⁹¹Nb and⁹⁰Zr(¹⁶O,¹⁴C)⁹²Mo was studied at bombarding energies of 80MeV, 138.2 MeV and 194.4 MeV. A comparison with one-step DWBA calculations shows good agreement for the one-particle transfers over the whole energy range. For the two-proton transfer reaction (¹⁶O,¹⁴C) the discrepancies between experiment and theory are large with an exponential decrease towards higher energies. Current theories are unable to describe this behavior.     

Heavy ion collisions in three dimensions by the relaxation-time method

A quantum transport equation with two-body collisions included via a relaxation-time method, earlier applied to two-dimensional (slab) collisions, is now extended to three-dimensional calculations A density matrix is constructed from self-consistent field wave functions and is time-evolved in cartesian coordinates. This dynamical model of the nucleus is applicable at all nonrelativistic energies. The semiclassical limit is discussed. Results are shown for ¹⁶O-¹⁶O collisions between 40 and 200 MeV/A lab energies. Hot spots and conditions for fragmentation are discussed. The threshold for breakup of the compound system formed in a head-on collision lies between 40 and 60 MeV/A lab energies. At these energies, the maximum density-averaged thermal excitation energy is 7 and 10 MeV/A (average temperatures 8 and 11 MeV), respectively, compared with a binding energy of 8 MeV/A. The system does not thermalize completely, and the distribution in momentum space is not quite isotropic when breaking up.