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Register a new userInvestigation of contributions of the $2_2^+$ resonance in $^6$He via analysis of $^6$He($p$, $p$)
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We investigate the contribution of the $2^{+}_{2}$ resonance in $^6$He to observables via analysis of the $^6$He($p,p$) reaction by using the continuum-discretized coupled channels method combined with the complex-scaling method. In this study, we obtain the $2^{+}_{2}$ state with the resonant energy 2.25 MeV and the decay width 3.75 MeV and analyse contributions of resonances and nonresonant continuum states to the cross section separately. It is found that the $2^{+}_{2}$ state plays an important role in the energy spectrum. Furthermore, contributions of nonresonant continuum states are also important to clarify the properties of the $2^{+}_{2}$ state.
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We apply the cluster-folding (CF) model for $vec{p}+^{6}$He scattering at 200 MeV, where the potential between $vec{p}$ and $^{4}$He is fitted to data on $vec{p}+^{4}$He scattering at 200 MeV. For $vec{p}+^{6}$He scattering at 200 MeV, the CF model reproduces measured differential cross section with no free parameter, We then predict the analyzing power $A_y(q)$ with the CF model, where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin construct a theory for one-neutron halo scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yield a simple relationship between the elastic scattering of a halo nucleus and of its core under certain conditions. We improve their theory with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when approximation (1)--(3) are good. Among the three approximations, approximation (2) is most essential. The CF model shows that approximation (2) is good in $0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He is the same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict $A_y(q)$ for $vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for $vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with the model-dependent and the model-independent prescription. The ratio of differential cross sections measured for $^{6}$He to that for $^{4}$He is related to the wave function of $^{6}$He. We then determine the radius between $^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radius is 5.77 fm.
The new data of the elastic scattering of $^{6}$He+$^{12}$C at about 40 MeV/nucleon are analyzed in the eikonal approximation. The $^{6}$He+$^{12}$C phase-shift function is evaluated completely without any {it ad hoc} assumption by a Monte Carlo integration, which makes it possible to use a realistic 6-nucleon wave function for a halo nucleus $^{6}$He. The effect of the breakup of $^6$He on the elastic differential cross sections as well as the optical potential is studied at different energies from 40 to 800 MeV/nucleon. PACS number(s): 24.10.-i; 21.60.Ka; 25.60.Bx; 25.10.+s Keywords: Eikonal; Glauber; Monte Carlo; Halo; Breakup
Cross sections for the ^{3}He(e,epn)p reaction were measured for the first time at energy transfers of 220 and 270 MeV for several momentum transfers ranging from 300 to 450 MeV/c. Cross sections are presented as a function of the momentum of the recoil proton and the momentum transfer. Continuum Faddeev calculations using the Argonne V18 and Bonn-B nucleon-nucleon potentials overestimate the measured cross sections by a factor 5 at low recoil proton momentum with the discrepancy becoming much smaller at higher recoil momentum.
Decay mode of the $2_1^+$ resonant state of $^6$He populated by the $^6$He breakup reaction by $^{12}$C at 240 MeV/nucleon is investigated. The continuum-discretized coupled-channels method is adopted to describe the formation of the $2_1^+$ state, whereas its decay is described by the complex-scaled solutions of the Lippmann-Schwinger equation. From analysis of invariant mass spectra with respect to the $alpha$-$n$ and $n$-$n$ subsystems, coexistence of two decay modes is found. One is the simultaneous decay of two neutrons correlating with each other and the other is the emission of two neutrons to the opposite directions. The latter is found to be free from the final state interaction and suggests existence of a di-neutron in the $2_1^+$ state of $^6$He.
Multi-step effects between bound, resonant, and non-resonant states have been investigated by the continuum-discretized coupled-channels method (CDCC). In the CDCC, a resonant state is treated as multiple states fragmented in a resonance energy region, although it is described as a single state in usual coupled-channel calculations. For such the fragmented resonant states, one-step and multi-step contributions to the cross sections should be carefully discussed because the cross sections obtained by the one-step calculation depend on the number of those states, which corresponds to the size of the model space. To clarify the role of the multi-step effects, we propose the one-step calculation without model-space dependence for the fragmented resonant states. Furthermore, we also discuss the multi-step effects between the ground, $2^{+}_{1}$ resonant, and non-resonant states in $^6$He for proton inelastic scattering.
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