T. Udagawa

Δ Excitations in Nuclei

It has been known for sometime that the peak position of the Δ (1232) -resonance spectra observed in the (p,n)-1, (3He,t)-2, and (\(\vec d\),2p)-3charge-exchange reactions at intermediate energies is systematically shifted downward for a target with A ≥ 12 as compared to the peak position for a proton target. In contrast to this, in the case of γ-absorption4 and inelastic electron scattering experiments,5 the Δ-peak does not show such a pronounced displacement. The electromagnetic probes excite the Δ transversely, i.e., by the transition operator \(\vec S \times \vec q\vec T\) (\(\vec S\) and \(\vec T\) are the spin and isospin transition operators, respectively.), while the hadronic probes measure both the transverse (TR) and the longitudinal (LO) spin-isospin response. It has thus been speculated that the shift of the Δ-peak would be due to a nuclear medium effect in the isovector spin LO(\(\vec S \cdot \vec q\vec T\))channel.6,7 That is, if the delta particle-nucleon hole (ΔN -1) interaction becomes strongly attractive at large momentum transfers \(\left| {\vec q} \right| \approx 1 - 2\) fm-1 in this channel, then this attraction might lead to a lowering of the Δ mass produced in the target. Along this line of reasoning, no shift of the Δ-peak position is to be observed with the electromagnetic probes. Recently, we have made some realistic calculations of the spectra of the 12C(p,n) and (3He,t) reactions at the Δ-excitation region, and succeeded to show that the LO response is indeed shifted downwards in energy and that this shift is caused by the energy-dependent π-exchange interaction.8

Absolute magnitude of heavy-ion induced two-nucleon transfer reactions☆

Abstract It is shown that the long standing difficulty of too small theoretical cross sections for heavy-ion induced two-nucleon transfer reaction has been solved for several cases with two-neutron transfer, and that for some others, including a few two-proton transfer cases, the situation has been improved significantly though the problem has not yet been solved completely there. It was found that this is achieved chiefly by using sufficiently sophisticated wave functions for the nuclear states involved, and by including both the simultaneous and successive transfer amplitudes in the calculation. A somewhat detailed formulation for these amplitudes is given, presenting in particular the coupled-reaction-channel equation in a form suited for exact finite-range calculations. In the course of the calculation, a surprising similarity was found between the behaviors of the successive and simultaneous amplitudes, and an explanation for this similarity is given.

Multi-step-direct-reaction analysis of continuum spectra of (p, α) reaction

Abstract Application of multi-step direct reaction theory to transfer reactions is demonstrated by successfully fitting continuous spectra of the 53 Fe(p, α) 51 Mn reaction taken as an example.

Coherent pion production in intermediate energy charge-exchange reactions

Abstract The coherent pion production in the charge exchange reaction 12 C (p,nπ + ) 12 C ( g . s .) is used to study the isovector spin- longitudinal ( S·q T ) response of nuclei in the Δ resonance region. It is shown that the pion production cross section provides unique signature of the nuclear pionic mode. The coherent pions have a peak energy of Eπ=250 MeV and a strongly forward peaked angular distribution.

Exact finite range calculations of light-ion induced two-neutron transfer reactions

Abstract Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.

Analysis of 76Ge(16O, 14C)78Se reaction in terms of exact-finite-range coupled-channel born approximation

Abstract It is shown that an exact finite-range CCBA calculation is feasible and does fit the data of 76 Se ( 16 O , 14 C ) 78 Se very well, while an exact finite-range DWBA calculation does so rather poorly.

Exact-finite-range DWBA calculations of massive transfer reactions treated as breakup-fusion reactions

Abstract Distorted-wave-Born-approximation calculations, with the exact-finite-range method, were performed, and good fits were obtained to data of the α singles cross sections in the 181 Ta ( 14 N , α) reaction, taken as an example. It is shown that the breakup-fusion is not a simple peripheral process, but takes place in a region which is about 2 fm deeper than is the usual peripheral region.

Continuous distribution of αt relative kinetic energies in 7Li breakup reactions

Abstract A newly developed technique has been used to probe a previously inaccessible region of the continuum in the at channels of 7 Li breakup reactions. This was used to investigate reactions of 63 MeV 7 Li with 58 Ni, 120 Sn, 144 Sm, and 208 Pb targets. Breakup pairs of α-particles and tritons emitted within a finite opening angle were analyzed according to their magnetic rigidity using a K = 150 Enge split-pole spectrograph. The αt coincidences were taken with two single-wire proportional counters mounted at different positions along the focal plane of the spectrograph. The large energy acceptance ( E max / E min ≈ 8) of the spectrograph is crucial to the present coincidence measurements involving two particles with different q / m values. Very small relative energy components were studied without any detection threshold. A pronounced bump was observed immediately above the αt particle threshold. No strong indication of the post Coulomb acceleration was observed. The excitation of the continuum states as well as the 7 − 2 state in 7 Li is discussed in terms of the distorted-wave Born approximation. The astrophysical implications of the data are also discussed regarding the Coulomb excitation of the continuum. The present technique offers the promise of very high sensitivity at small relative energies if it were applied in conjunction with ray-tracing, a thin target, and a dispersion-matched beam.

Simultaneous optical model analyses of elastic scattering, breakup, and fusion cross-section data for the He-6 + Bi-209 system at near Coulomb barrier energies

Based on an approach recently proposed by us, simultaneous

Observation of α-t continuum states with relative energies of 0–2 MeV in7Li breakup reactions

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