Session CA: Correlations in Structure Up To and Beyond Bound Limits

Ab initio calculations of $^{12}$C and neutron drops

Ab initio calculations of nuclei, which treat a nucleus as a system of $A$ nucleons interacting by realistic two- and three-nucleon forces, have made tremendous progress in the last 15 years. This is a result of better Hamiltonians, rapidly increasing computer power, and new or improved many-body methods. Three methods are principally being used: Green's function Monte Carlo (GFMC), no-core shell model, and coupled cluster. In the limit of large computer resources, all three methods produce exact eigenvalues of a given nuclear Hamiltonian. With DOE SciDAC and INCITE support, all three methods are using the largest computers available today. Under the UNEDF SciDAC grant, the Argonne GFMC program was modified to efficiently use more than 2000 processors. E. Lusk (Argonne), R.M. Butler (Middle Tennessee State U.) and I have developed an Asynchronous Dynamic Load-Balancing (ADLB) library. In addition all the cores in a node are used via OpenMP as one ADLB/MPI client. In this way we obtain very good scalability up to 30,000 processors on Argonne's IBM Blue Gene/P. Two systems of particular interest that require this computer power are $^{12}$C and neutron drops. V.R. Pandharipande (UIUC, deceased), J. Carlson (LANL), R.B. Wiringa (Argonne), and I have developed new trial wave functions that explicitly contain the three-alpha particle structure of $^{12}$C. These are being used with the Argonne V18 and Illinois-7 potentials which reproduce the energies of 51 states in 3$\leq A\leq$12 nuclei with an rms error of 600\,keV. Neutron drops are collections of neutrons confined in an artificial external well and interacting with realistic $NN$ and $NNN$ potentials. Their properties can be used as ``experimental data'' for developing energy-density functionals.   

Nuclear Halo and Shell Evolution along the Neutron Drip Line

Nuclear halo is a weakly-bound exotic state of nuclear matter where one or two valence neutrons extend far beyond the nuclear potential well. We present recent experimental results on halo nuclei, using Coulomb and nuclear breakup. In the first part, we show experimental results on Coulomb breakup of $^{11}$Li, where observed three-body energy spectrum allows us to discuss the di-neutron correlation of this nucleus. In the second part, we show the results of nuclear breakup of $^{14}$Be where its Borromean constituent $^{13}$Be structure is revealed. We discuss the shell melting of this unbound nucleus. In the third part, we show the most recent results on the inclusive breakup reactions of $^{22}$C and $^{31}$Ne at 230MeV/nucleon using the newly commissioned RI-beam facility RIBF (RIKEN RI-Beam Factory) at RIKEN. These nuclei are candidates of halo nuclei, located heavier than the known halo nuclei. We have observed enhancement of the Coulomb and nuclear breakup cross sections of these two nuclei, suggesting that these nuclei have halo structures. The detailed comparison of the observed cross sections and calculation shows that $^{31}$Ne has a halo property as well as shell vanishing in nature.   

In-beam $\gamma$-ray spectroscopy towards the nucleon driplines

The often surprising properties of neutron-rich nuclei have prompted extensive experimental and theoretical studies aimed at identifying the driving forces behind the dramatic changes encountered in the exotic regime. In-beam nuclear spectroscopy with fast beams and thick reaction targets - where $\gamma$-ray spectroscopy is used to tag the final state - provides information on the single-particle structure as well as on collective degrees of freedom in nuclei that are accessible for experiments at beam rates of only a few ions/s. Recent results from nuclear spectroscopy experiments that utilize the interplay of nuclear-structure effects and reaction mechanisms performed at the National Superconducting Cyclotron Laboratory at Michigan State University will be presented.   

Exotic clusters in an unbound region of light neutron-rich systems

In light neutron-rich systems, many kinds of molecular structures are discussed from the view point of the clustering phenomena.In particular, much attention has been concentrated on Be isotopes. The molecular orbital (MO), such as $\pi^-$ and $\sigma^+$ associated with the covalent binding of atomic molecules, have been shown to give a good description for the low-lying states of these isotopes. In their highly-excited states, furthermore, recent experiments revealed the existence of the interesting resonant states which dominantly decay to the $^{6,8}$He fragments. In this report, we show the unified study of the exotic structures of $^{12}$Be=$\alpha$+$\alpha$+4$N$ in an unbound region and the $\alpha$+$^{6,8}$He resonant scattering. We applied the generalized two-center cluster model in which the covalent MO and the atomic orbital (AO) configurations with $^x$He+$^y$He could be described in a unified manner. First, we calculated the energy spectra below an $\alpha$ decay-threshold. The ($\pi_{3\slash2}^-$)$^2 $($\sigma_{1\slash2}^+$)$^2$ configuration corresponding to $\nu$(0p)$^4$(sd)$^2$ becomes the ground state, while ($\pi_{3 \slash2}^-$)$^2$($\pi_{1\slash2}^-$)$^2$ having a large overlap with $\nu$(0p)$^6$ appears as the first excited state. The rotational band of the ground state reaches to the maximum spin of J$^\pi$ = 8$^+$. This result means that the magicity of $N$=8 is broken in $^{12}$Be due to the formation of ($\pi_{3 \slash2}^-$)$^2$($\sigma_{1\slash2}^+$)$^2$. Next, we solved the scattering problem of $\alpha$+$^8$He and identified the several resonance poles. In the continuum region, we found the rotational bands having the AO configurations of $\alpha$+$^8$He, $^6$He+$^6$He, and $^5$He+$^7 $He. Furthermore, a much more exotic band appears in the same energy region. In this band, two valence neutrons are localized at individual $\alpha$-cores (the $^5$He+$^5$He cluster), while the other two neutrons form the covalent $\sigma^+$- bonding between two $^5$He clusters; hence, it has a ``hybrid structure'' between the MO configuration and the AO one. In the J$^\pi$=0$^+$ state, it is strongly excited by the two-neutron transfer reaction, $\alpha$+$^8$He$\rightarrow$$^6$He+$^6$He. We also calculated the matrix elements of isoscalar monopole transition (MTR), $|<0_f^+|\sum_i^{12}r_i^2| 0_1^+>|^2$. The MTR matrix element going to the AO state of $\alpha$+$^8$He is the largest in all the excited states, although an certain enhancement also occur in the transition to the first excited 0 $^+$, which seems to be consistent to the observed electric MTR. Therefore, this result strongly suggests that the monopole transition is enhanced when the final state have a developed cluster (AO) structure. In order to analyze the enhancement of MTR in the realistic reaction process, we also performed the calculation of the continuum discretized coupled-channels (CDCC) for the monopole breakup of $^{10}$Be into $\alpha$+$^6$He by a $^{12}$C target. This breakup reaction is mainly induced by a nuclear interaction from the $^{12}$C target, and the multi-step of the continuum-continuum coupling is quite strong. We confirmed the strong enhancement in the transition of 0$_1^+$ $\rightarrow$ 0 $_3^+$, which have an AO configuration of $\alpha$+$^6$He(2 $_1^+$). Therefore, the cluster state is strongly excited in the nuclear breakup reaction, which is consistent to the result in the analysis of MTR for $^{12}$Be. Similar studies of even Be isotopes and future perspectives will also be presented.