Neutron pick-up pion transfer reactions for the formation of deeply bound pionic atoms in 208Pb

We study (n, d) and (d, ³He) reactions on ²⁰⁸Pb leading to deeply bound pionic atoms with one neutron hole being left. We develop a theoretical model to calculate cross sections of deeply bound pionic atoms and quasi-elastic pion production. The results are compared with data which have been obtained so far. We show that the theoretical model describes the data of both reactions well.     

Pionic atom spectroscopy in the (d,<Superscript>3</Superscript> He) reaction at finite angles

We study the formation of deeply bound pionic atoms in the (d, ³He) reactions theoretically and show the energy spectra of the emitted ³He at finite angles, which are expected to be observed experimentally. We find that the different combinations of the pion-bound and neutron-hole states dominate the spectra at different scattering angles because of the matching condition of the reaction. We conclude that the observation of the (d, ³He) reaction at finite angles will provide the systematic information of the pionic bound states in each nucleus and will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.     

Spectrum of the high spin neutron hole states of205Pb

The high resolution (³He,α) reaction on²⁰⁶Pb shows the distribution of the 2f _7/2, 1h _9/2 and 1i _{1 3/2} neutron states of²⁰⁵Pb within the 6 MeV excitation energy of²⁰⁵Pb. The spectrum of these three-hole states is obtained within the hole-core vibrational coupling scheme. The shell model energies of the neutron hole states arising from the core-polarization effect are compared with the Bansal-French energy weighted sum rule. The possible implication of the present neutron hole energies has been discussed in the light of the deduced shell model wave functions of the collective states of²⁰⁶Pb.     

Study of giant pairing vibrations with neutron-rich nuclei

We investigate the possible signature of the presence of giant pairing states at an excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly bound projectiles. Performingparticle-particle RPA calculations on ²⁰⁸Pb and BCS + RPA calculations on ¹¹⁶Sn, we obtain the pairing strength distribution for two-particle addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the macroscopic model. The weak-binding nature of the projectile kinematically favors transitions to high-lying states. In the case of the (⁶He, ⁴He) reaction, we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.     

Nucleon transfer reactions to rotational states induced by206, 208Pb projectiles

In a systematic study of nucleon transfer reactions accompanied by Coulomb excitation we have bombarded¹⁵²Sm,¹⁶⁰Gd and²³²Th with^{206, 208}pb beams at incident energies close to the Coulomb barrier. Particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and in nucleon transfer reactions. One-neutron stripping and pick-up reactions on¹⁵²Sm were observed leading to known states of the rotation alignedi _13/2-bands in¹⁵³Sm and¹⁵¹Sm. In the¹⁶⁰Gd+^{206, 208}Pb systems no significant population of low lying states of product nuclei was found in the nucleon-transfer channels. Large cross sections were observed for one- and two-neutron pick-up from²³²Th at an incident energy of 6.4 MeV/u. Around the grazing angle they are of the same order of magnitude as the cross section measured for inelastic scattering. The results are analyzed in the framework of semiclassical models.     

Chiral symmetry probed with pionic atoms

Study of pionic atom has been revisited by a recent discovery of deeply bound pionic states in the context of possible sensitivity to the partial chiral restoration in the nuclear medium. Precisely measured binding energies and widths of the deeply bound π^? Is states in ^115,119,123Sn in ^116,120,124Sn(d,³He) reactions at recoil-free conditions are used to deduce the medium-modified isovector scattering amplitude as b₁ = 0.115 ± 0.007m _π ^?1. The observed enhancement of b ₁ over the free πN value infers 34% reduction of $\left\langle {\bar qq} \right\rangle $ at the normal nuclear density, ρ = 0.17 fm^?3.     

Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of ²⁰⁸Pb and ⁴⁰Ca by a ²⁰⁸Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for ²⁰⁸Pb and 20% for ⁴⁰Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.     

Discovery of deeply bound π− states in the208Pb(d,3He) reaction

Narrow lines were observed around 133 MeV excitation energy in the²⁰⁸Pb(d,³He) reaction atT _d=300 MeV/u using the Fragment Separator System at GSI. They are assigned to the deeply boundπ ^??²⁰⁷Pb states with configurations of $\left( {2p} \right)_{\pi ^ - } $ (3p_1/2, 3p_3/2) _n ^?1 .     

Formation of Deeply Bound Pionic Atoms in Sn Isotopes

We study the formation of deeply bound pionic atoms in the (d,³He) reaction theoretically. At different scattering angles, we find that the different subcomponents dominate the formation spectra because of the matching condition of the reaction. We also find that the pionic 1s state which is free from the residual interaction effects appears clearly in ¹¹⁷Sn(d, ³He) spectra. We conclude that the observation of the (d,³He) reaction for these new cases will provide more systematic and accurate information on the pionic bound states, and it will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.     

Study on the 208Pb(α, 6He)206Pb reaction at Eα = 109 MeV

The ²⁰⁸Pb(α, ⁶He)²⁰⁶Pb reaction induced by 109 MeV α particles has been studied with 70 keV energy resolution. Twenty-five transitions up to 6.2 MeV in excitation energy have been analyzed. The shapes of the angular distributions are reproduced well by the zero-range distorted-wave Born approximation (DWBA) calculations. The spin and parity of the level at 6.10 MeV are proposed to be 9⁻. It is interpreted as a weakly-coupled state of the collective 3⁻ state and the two-hole 6⁺ shell-model state.The energy dependence of the total cross sections of the (α, ⁶He) and (p, t) reactions has been studied systematically by using our present data and other data from the literatures. It reveals that there exists an empirical rule which allows one to compare quantitatively the ratios of the transition strengths of both reactions. The transition strength of the (α,⁶He) reaction is found to be about 35 times smaller than that of the (p, t) reaction for the transitions to the natural parity states, while it is about 15 times smaller for the transition to the unnatural parity 3⁺ state. These small transition strengths are explained by the fact that this reaction occurs at the surface region of the nucleus.     

Low- and medium-spin states in theN=124 isotones208Po and209At

Excited levels in²⁰⁸Po and²⁰⁹At were populated in the reactions (p, 2n) and (³He, 3n), and²⁰⁸Po also in the EC-decay of the²⁰⁸At ground state, which was produced in the²⁰⁹Bi(³He, 4n) reaction. The experimental procedures comprised gamma-ray excitation functions,γ- γ coincidences, as well as gamma-ray angular distribution and conversionelectron measurements, both on- and off-line. The properties of about twenty-five levels in each nuclide were studied. In²⁰⁸Po the energy of the 8⁺→6⁺ transition could be determined to be 4.0±0.2keV and the 8⁺ state thus has an excitation energy of 1,528 keV. The effective quadrupole charge of theh _9/2 proton can be derived ase _eff(τ h _9/2)=1.69(15)e. For the previously reported isomeric half-lives more accurate values are obtained, the systematics of electricL=1, 2 and 3 transition rates are discussed, and their microscopic structure is elucidated. Shell model considerations are used to support the configuration assignments, as are the logft values for the strongest²⁰⁸At(EC)²⁰⁸Po decay branches. The effect of core polarixation on the excitation energies of yrast states is studied in both²⁰⁸Po and²⁰⁹At. Many of the states populated in the²⁰⁸At EC decay are shown to be of core-excited character.     

Low-energy fusion cross sections of D + D and D + 3He reactions

The D(d, n)³He and D(d, p)T reactions have been investigated at E_c.m = 2.98 to 162.5 keV and the ³He(d, p)⁴He reaction at E_c.m. = 6.95 to 141.8 keV. The studies involved high-current accelerators with well-known beam characteristics and windowless gas target systems of the extended and quasi-point supersonic jet type. The measurement of absolute cross sections, angular distributions and excitation functions is reported. The data extend into the thermal energy region of future fusion reactors. The results for the D(d, n)³He and D(d, p)T reactions are in good agreement with previous work, while substantial differences are found for ³He(d, p)⁴He.     

Observation of the ABC effect and final-state isospin

Despite the number of inclusive measurements of the pionic fusion reactions, the nature of the ABC effect discovered in 1960 was not completely established. Exclusive measurements of the doublepion-production reactions leading to either fused d, ³He and ⁴He nuclear final states or pp pairs are analyzed. A significant ABC effect—enhancement in the region of low ππ mass—is found only in the isoscalar ππ channel while in the isovector channels it is small or absent. For the reaction with isovector pp final state an ABC effect was not observed even at the special kinematic conditions to reproduce a quasi-bound two-proton state. The total cross sections for the d and 4He fusion reactions show similar resonance-like energy dependence.     

Enhanced excitation of giant pairing vibrations in heavy-ion reactions induced by weakly bound projectiles

The use of radioactive ion beams is shown to offer the possibility to study collective pairing states at high excitation energy, which are not usually accessible with stable projectiles because of large energy mismatch. In the case of two-neutron stripping reactions induced by ⁶He, we predict a population of the giant pairing vibration in ²⁰⁸Pb or ¹¹⁶Sn with cross-sections of the order of a millibarn, dominating over the mismatched transition to the ground state. Received: 30 November 2001 / Accepted: 25 February 2002     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.     

Core polarisation effect on the 3p 1/2, 3p 3/2, 2f 5/2, 2f 7/2 and 1i 13/2 proton states of209Bi

The weak fragments of the 3p_1/2, 3p_3/2, 2f_5/2, 2f_7/2 and 1i_13/2 proton states of²⁰⁹Bi as seen in the²⁰⁸Pb (³He,d) reaction can be explained with the coupling of the renormalised proton states and the vibrational states of²⁰⁸Pb. The energies of the zerothorder proton shell-model states as well as the collective admixtures of the weak fragmented proton states of²⁰⁹Bi have been deduced from the core-particle coupling model.     

Study of the 2n-evaporation channel in the He + Pb reactions

Excitation functions of the reaction products were measured for the reactions induced by ^4,6He projectiles on ^208,206Pb targets, leading to the same compound nucleus. This was accomplished by using the stacked-foil activation technique. The identification of the reaction products (accumulated in the Pb targets) was done by their radioactive α-decays. The excitation functions for the various products were obtained at energies including the sub-Coulomb barrier region. A large value of the fusion cross section was observed in the case of the reaction induced by the weakly bound ⁶He projectile.     

Single-particle proton admixtures in core-excited states of Bi

At least 18 states up to 3.5 MeV of excitation have been observed in the ²⁰⁶Pb(³He, d)²⁰⁷Bi reaction at 35 MeV. The experimental spectrum and spectroscopic factors are in fair agreement with the predictions of the weak-coupling model up to an excitation energy of 2.5 MeV.     

Gross structure in excitation functions for207Pb(p,p′)207Pb in the region of overlapping isobaric analogue resonances

Prominent resonances in the reaction²⁰⁷Pb(p, p′)²⁰⁷Pb leading to the low-lying states in²⁰⁷Pb(1/2^? g.s., 5/2^? 0.57 MeV, 3/2^? 0.89 MeV, 7/2^? 2.33 MeV) are observed betweenE _p =16 and 18 MeV. The structures in the excitation functions are interpreted as being due to analogues of states in²⁰⁸Pb which are mixtures of neutron particle-hole configurations.