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Analysis of Spectroscopic Factors in 11Be and 12Be in the Nilsson Strong Coupling Limit

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 Publication date 2017
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Spectroscopic factors in 10Be, 11Be and 12Be, extracted from (d,p), one neutron knockout, and (p,d) reactions are interpreted within the rotational model. Assuming that the ground state and first excited state of 11Be can be associated with the 1/2[220] and 1/2[101] Nilsson levels, the strong coupling limit gives simple expressions that relate the amplitudes of these wavefunctions (in the spherical basis) with the measured cross-sections and derived spectroscopic factors. We obtain good agreement with both the measured magnetic moment of the ground state in 11Be and the reaction data.



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Neutron-unbound resonant states of 11Be were populated in neutron knock-out reactions from 12Be and identified by 10Be-n coincidence measurements. A resonance in the decay-energy spectrum at 80(2) keV was attributed to a highly excited unbound state in 11Be at 3.949(2) MeV decaying to the 2+ excited state in 10Be. A knockout cross section of 15(3) mb was inferred for this 3.949(2) MeV state suggesting a spectroscopic factor near unity for this 0p3/2- level, consistent with the detailed shell model calculations.
We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling $G$ and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius $G_{rm sing}$ of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore $G_{rm sing}$ is not related to the critical values of the coupling $G_{rm crit}$, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points.
The bound states of 12Be have been studied through a 11Be(d,p)12Be transfer reaction experiment in inverse kinematics. A 2.8 MeV/u beam of 11Be was produced using the REX-ISOLDE facility at CERN. The outgoing protons were detected with the T-REX silicon detector array. The MINIBALL germanium array was used to detect gamma rays from the excited states in 12Be. The gamma-ray detection enabled a clear identification of the four known bound states in 12Be, and each of the states has been studied individually. Differential cross sections over a large angular range have been extracted. Spectroscopic factors for each of the states have been determined from DWBA calculations and have been compared to previous experimental and theoretical results.
Spectroscopic factors to low-lying negative-parity states in $^{11}$Be extracted from the $^{12}$B($d$,$^3$He)$^{11}$Be proton-removal reaction are interpreted within the rotational model. Earlier predictions of the $p$-wave proton removal strengths in the strong coupling limit of the Nilsson model underestimated the spectroscopic factors to the $3/2^-_1$ and $5/2^-_1$ states and suggested that deviations in the $1^+$ ground state of the odd-odd $^{12}$B due to Coriolis coupling should be further explored. In this work we use the Particle Rotor Model to take into account these effects and obtain a good description of the level scheme in $^{11}$B, with a moderate $K$-mixing of the proton Nilsson levels [110]1/2 and [101]3/2. This mixing, present in the $1^+$ bandhead of $^{12}$B, is key to explaining the proton pickup data.
We study the phase diagram of quark matter and nuclear properties based on the strong coupling expansion of lattice QCD. Both of baryon and finite coupling correction are found to have effects to extend the hadron phase to a larger mu direction relative to Tc. In a chiral RMF model with logarithmic sigma potential derived in the strong coupling limit of lattice QCD, we can avoid the chiral collapse and normal and hypernuclei properties are well described.
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