Spin-dependence and coherent summations in two-nucleon transfer reactions

The differential cross sections of the ¹⁹F(p, ³He)¹⁷O and ¹⁹F(p, t)¹⁷F reactions leading to the ground and first three excited states have been measured at an incident energy of 42.4 MeV. The polarization analysing powers of two of the (p, ³He) reactions have been measured at a higher energy of 49.5 MeV with a polarized incident beam. The experimental results have been analysed in terms of conventional DWBA theory, and the importance of interference terms arising from the proper coherent summations contained in the definition of the differential cross section and analysing power, have been investigated. It is found that the interference term arising from the coherent summation over the transferred spin S is significant and should not normally be neglected.     

(n,t) and (n, α) reactions on 9Be

A metallic ⁹Be target was bombarded with 13.99 MeV neutrons; α-particles, tritons and ⁶He recoil nuclei were detected and identified with a telescope consisting of two proportional counters and a solid state detector. Absolute differential cross sections were measured for the (n, t) reactions leading to the ground state and first excited state of ⁷Li and for the (n, α) reactions leading to the ground state and first excited state of ⁶He. No evidence for higher excited states in ⁶He has been found. An attempt has been made to interpret the observed (n, α) angular distributions in terms of the direct reaction model.     

Study of the <Superscript>12</Superscript>C (<Superscript>8</Superscript>B, <Superscript>7</Superscript>Be)<Emphasis Type="Italic">X</Emphasis> knockout reaction at intermediate energies

The breakup reactions of ⁸B on a ¹²C target at 142, 285, 790, and 936MeV/nucleon have been studied. One-proton-removal cross sections, leading to the production of ⁷Be fragments in the ground and first excited states (at 0.429MeV), and the longitudinal momentum distributions of the ⁷Be fragments are obtained in the Eikonal approximation of the Glauber Model. The results of the calculations including the contribution of the ⁷Be to the ground and first excited states of ⁸B are compared with the available experimental data. One-proton-removal cross section for the ¹²C(⁸B, ⁷Be)X knockout reaction at 142, 285, 790, and 936 MeV/nucleon energy has been calculated. ⁸B and ⁷Be cross sections and momentum distribution are in a good agreement with available data.     

Polarisation und differentieller Wirkungsquerschnitt der Neutronen aus der Reaktion9Be(α,n)12C

The differential cross section and the angular distribution of the polarization of neutrons from the reaction⁹Be(α, n) leading to the ground state of¹²C have been determined at 1.75 and 1.96 MeV energy of theα-particles. The polarization was measured by left-right asymmetry induced by elastic scattering from⁴He. From Blatt, Biedenharn and Simon, Welton theory analysis a set of spectroscopic data has been obtained for five states of the compound nucleus¹³C.     

Nuclear field theory predictions for 11Li and 12Be: Shedding light on the origin of pairing in nuclei

Recent data resulting from studies of two-nucleon transfer reaction on ¹¹Li, analyzed through a unified nuclear-structure-direct-reaction theory have provided strong direct as well as indirect confirmation, through the population of the first excited state of ⁹Li and of the observation of a strongly quenched ground state transition, of the prediction that phonon-mediated pairing interaction is the main mechanism binding the neutron halo of the 8.5-ms-lived ¹¹Li nucleus. In other words, the ground state of ¹¹Li can be viewed as a neutron Cooper pair bound to the ⁹Li core, mainly through the exchange of collective vibration of the core and of the pigmy resonance arizing from the sloshing back and forth of the neutron halo against the protons of the core, the mean field leading to unbound two-particle states, a situation essentially not altered by the bare nucleon-nucleon interaction acting between the halo neutrons. Two-neutron pick-up data, together with (t, p) data on ⁷Li, suggest the existence of a pairing vibrational band based on ⁹Li, whose members can be excited with the help of inverse kinematic experiments as was done in the case of ¹¹Li(p, t)⁹Li reaction. The deviation from harmonicity can provide insight into the workings of medium polarization effects on Cooper-pair nuclear pairing, let alone specific information concering the “rigidity” of the N = 6 shell closure. Further information concerning these questions is provided by the predicted absolute differential cross sections σ _abs associated with the reactions ¹²Be(p, t)¹⁰Be(g.s.) and ¹²Be(p, t)¹⁰Be(pv) (≈¹⁰Be(p, t)⁸Be(g.s.)). In particular, concerning this last reaction, predictions of σ _abs can change by an order of magnitude depending on whether the halo properties associated with the d _5/2 orbital are treated selfconsistently in calculating the ground state correlations of the (pair removal) mode, or not.     

An experimental study of He elastic,inelastic and charge-exchange scattering from Li

A target of ⁶Li was bombarded with the ³He beam from the University of Illinois cyclotron. Differential cross sections for the elastic scattering, the inelastic scattering to the first two excited states of ⁶Li, and the (³He, t) charge-exchange reaction to the ground state of ⁶Be were determined over angular ranges of approximately 20° to 115° (c.m.) at ³He energies of 24.6 MeV and 27.0 MeV. (The weak inelastic transition to the 3.56 MeV state of ⁶Li, ordinarily obscured by a background of three-body break-up, was observed by requiring a coincidence at most angles between the scattered ³He and the ⁶Li recoil.) The ratio of the integrated charge-exchange cross section between 55° and 115° to the integrated inelastic cross section for this transition (both with ΔT = 1) is somewhat less than expected from isospin considerations (i.e., about 1.6 instead of 2.0).     

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.     

Determination of the nuclear vertex constants for the 7Be ↔ 3He4He vertex using theN/D equations and calculation of the astrophysical S factor for the 4He(3He, γ)7Be reaction

N/D equations taking into account the Coulomb interaction effects are used to consider the phase analysis data on ³He⁴He scattering and determine the nuclear vertex constants for the ⁷Be ? ³He⁴He vertex, where the beryllium nucleus is in the ground (3/2^?) or first excited (1/2^?) states. Information about the asymptotic normalization coefficients of the wave functions of the ⁷Be nucleus in the noted states is derived. The data obtained are used to calculate the astrophysical S factor for the ⁴He(³He, γ)⁷Be reaction.     

Study of the 3He(α, γ)7Be radiative-capture reaction with resonating-group wave functions

A fully microscopic calculation of the electric-dipole capture reaction of ³He + α to the ground and first excited states of ⁷Be is performed by using the wave functions obtained from a coupled-channel resonating-group calculation. The result for the cross-section factor at zero energy is 0.598 keV · b, which agrees with the values deduced from activation measurements of the capture cross section, but is somewhat higher than the values obtained from direct measurements. The fact that the calculated value for this quantity is rather large indicates that the solar-neutrino puzzle cannot be resolved by only examining the nuclear-physics aspect of this problem.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Investigation of the mechanism of the reaction 10B(d, pγ)11B at E d = 15.3 MeV by the method of angular pγ correlations

The results are presented that were obtained by measuring the differential cross sections for the reaction ¹⁰B(d, p)¹¹B occurring at E _d = 15.3 MeV and leading to the production of a ¹¹B nucleus in the ground state (3/2^?) and in the lowest two excited states (the 1/2^? state at 2.125 MeV and the 5/2^? state at 4.445 MeV). The energy dependence of the differential cross section for this reaction was measured for several proton emission angles in the energy range E _d = 12–15.3 MeV. The double-differential cross sections for the reaction ¹⁰B(d, pγ)¹¹B were measured for the 5/2^? state of the ¹¹B nucleus at 4.445 MeV, and the angular dependences of the even spin-tensor components of the density matrix were reconstructed on the basis of these data. The angular dependences of the populations of magnetic sublevels are also given. The experimental results in question are compared with their theoretical counterparts obtained under the assumption of various reaction mechanisms (neutron stripping, heavy-particle stripping, and a two-step mechanism that takes into account the delay of interaction). On the basis of this comparison, the deformation parameters of the boron nuclei were found to be β ₂(¹⁰B) = ?0.55 and β ₂(¹¹B) = 0.4.     

Direct reactions involving exotic nuclei 8He and 5H

The angular distribution of 26 MeV/n ⁸He ions elastically scattered from a gaseous helium target was measured in a wide CM angular range. Results are discussed in terms of the potential scattering and neutron transfer. The angular distributions of elastic scattering as well as 1n and 2n transfer reactions of these ions on protons are presented. Finite-range DWBA calculations made for the 2n transfer reaction leading to the ground (0⁺) and excited (2⁺) states of ⁶He underestimate the cross section for 2n transfer to ⁶He(0⁺). Analysis of data for this reaction channel suggests the importance of a direct ⁵H-cluster exchange process. A resonance state of ⁵H with an energy of 2 MeV above the decay threshold n+n+ ³H was obtained for the first time by making use of the reaction p(⁶He,²He)⁵H.     

The He scattering and reactions on C and cluster states of C

The ⁶He+¹²C elastic and inelastic scattering and the ⁶He+¹²C→α+¹⁴C reaction have been measured using a 18.0 MeV ⁶He beam. Experimental results for the elastic scattering are in fair agreement with optical model predictions, using the potentials found in the analysis of ⁶Li scattering on ¹²C at similar energies. In triple coincidences, the ⁶He+¹²C→¹⁰Be+2α reactions were clearly seen, with the ¹⁰Be nucleus left in ground and several excited states. The dominant mechanism of this reaction is sequential decay through cluster states of ¹⁴C.     

Elastic and inelastic scattering of 17.5 and 40.0 MeV 3He particles from 11B

The ³He scattering cross sections have been measured at 17.5 and 40.0 MeV from the ground state and first four excited levels of ¹¹B. The results are analysed with the SCA assuming ¹¹B to be a symmetric rotator and including the K-band mixing introduced by the Coriolis force. A systematic attempt is made to deduce the hexadecapole moment and the sign of the quadrupole deformation of ¹¹B.     

Single-Proton Pickup Reaction of the Halo Nucleus ^6He on a ^9Be Target at 25 MeV/nucleon

The inclusive differential cross sections of the ^7 Li nucleus in a reaction induced by ^6He on a ^9Be target are measured at an incident energy of 25 MeV/nucleon. Finite-range distorted-wave Born approximation calculations suggest that these ^7 Li particles are formed in a direct single-proton pickup reaction ^9Be（^6He,^7 Li）^8Li. The experimental data can be well reproduced by taking into account of the contributions of both the ground states and the first excited states of ^7Li and ^8Li.     

Polarization of protons from the Be(d,p)Be reaction at Ed = 12.0 MeV

The polarization of protons from the ⁹Be(d,p)¹⁰Be reaction at E_d = 12.0 MeV was measured for the ground state and first excited state transitions. The results obtained are compared with the predictions of DWBA theory. It was found that better fits to the experimental data can be obtained using volume absorption in the distorting potential of the deuteron elastic channel. A comparison of the present polarization data with the vector analysing power for the same reaction and the same incident deuteron energy has also been made.     

Optical model analysis of the elastic scattering of 45 MeV 3He particles on 1p shell nuclei

Angular distributions of elastically scattered ³He particles from the 1p shell nuclei ⁶Li, ⁷Li, ⁹Be, ¹⁰B, ¹¹B, ¹²C and ¹⁶O were measured by using a 45 MeV ³He beam. The absolute differential cross section data obtained were analysed in terms of the standard optical model. Using the fact that the rms radius of the 1p shell nuclei is nearly constant a simple folding model allows finding an optical potential family whose real potential depth varies linearly with the target mass. The best fits exhibit a normalized volume integral of about 400 MeV · fm³ for the real potential. From the best-fit parameters a mean parameter set is deduced which varies smoothly with the target mass A_T. The average parameter set compares well with the systematics found for heavier nuclei.     

The (nth, α) reaction on 147Sm, 151, 153Eu and Yb isotopes

The (n, α) reaction has been studied using the highly pure thermal neutron beam from the 87m curved neutron guide at the Grenoble high flux reactor. The ¹⁴⁷Sm(n, α)¹⁴⁴Nd reaction showed up five lines corresponding to the ground and the first four excited states of the final nucleus. It is shown that ≈53 % of the 581 μb (n, α) cross section comes from the neutron capture by a bound level of the ¹⁴⁸Sm compound nucleus. The 8.7 ± 3 μb cross section of ¹⁵¹Eu(n, α)¹⁴⁸Pm seems to consist principally of at least two lines corresponding to the ground and the second excited states of ¹⁴⁸Pm. The ¹⁵³Eu(n, α)¹⁴⁹Pm cross section for thermal neutrons is ≦ 1 μb. The lower limits of (n, α) thermal neutron cross section values on ytterbium isotopes are ≈ 20 to 40 times lower than the published data.     

Nuclear vertex constants for the virtual decay <Superscript>7</Superscript>Be → <Superscript>3</Superscript>He + <Superscript>4</Superscript>He of the 7Be bound states from a phase-shift analysis in the effective-range theory

The phase-shift-analysis data for the ³He⁴He scattering are analyzed using the effective-range theory, with the Coulomb interaction taken into account. We find both the renormalized nuclear vertex constants for the vertex ⁷Be → ³He + ⁴He in the ground (3/2⁻) and in the first excited (1/2⁻) bound states of ⁷Be, and the corresponding asymptotic normalization constants of the radial wave functions in these states. The results obtained can be used in an astrophysical S-factor calculation for radiative capture reaction ⁴He(³He, γ)⁷Be     

Coulomb dissociation of 8B and solar neutrino problem

We measured the cross section for Coulomb dissociation of ⁸B using a radioactive ⁸B beam of 46.5 MeV/u energy with a ²⁰⁸Pb target. The corss section for the ⁷Be(p,γ)⁸B capture reaction was deduced at E_cm = 0.6 – 1.7 MeV. The extracted astrophysical S₁₇ factors were consistent with the values measured by Vaughn et al. and Filippone et al. Possible corrections due to ⁷Be excited state population, E1 and M2 contribution, nuclear contribution and post acceleration effects are considered.