Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Pairing correlation and quasi-particle resonances in neutron drip-linenuclei
Y. Kobayashi∗1 and M. Matsuo∗2
In neutron drip-line nuclei, which have an extremely
shallow Fermi surface, the pairing correlation is expected to inﬂuence low-energy scattering and resonances of a neutron. An interesting phenomenon
predicted in the theory of superﬂuid nuclei is quasiparticle resonance.1–3) A scattering neutron can couple to a hole state by creating a Cooper pair and thusresulting in a narrow resonance. The quasi-particle
resonance has also been studied for neutron drip-line
nuclei.4–6) As neutron drip-line nuclei are expected toprovide better opportunities for observation of quasiparticle resonance, we study these drip-line nuclei toclarify the properties of quasi-particle resonance. In
the present study, we focus on the inﬂuence of the pairing on the resonance width.
We use the coordinate space Hartree-Fock-Bogoliubov(cHFB) equation7) to describe the scattering wave
function of a neutron under the pairing eﬀect. We
solve the cHFB equation such that the quasi-particle
wave function satisﬁes the scattering boundary condition:())(cos δlj jl (k1 r) − sin δlj nl (k1 r)
ulj (r),(1)→(1)
vlj (r)Dhl (κ2 r)√√
where k1 = 2m(λ + E)/h̄, κ2 = −2m(λ − E)/h̄.
Here, m, λ and E are the mass of neutron, Fermi energy and quasi-particle energy, respectively. Next, we
calculate the phase shift δlj and the elastic cross section.
We consider the (46 Si+n) system. According to several HFB calculations, 46 Si is a neutron drip-line nucleus of Si isotopes. We assume that this nucleus has aspherical shape. Note that 46 Si has a weakly bound 2porbit. We use the Woods-Saxon potential as the nuclear potential, and the pair potential is also assumed
to have the Woods-Saxon shape. The averaged pairing¯ is a strength of the pair potential.
gap ∆Fig.1 shows the calculated partial cross section. Narrow low-lying peaks seen in p1/2 and p3/2 are thequasi-particle resonances. These peaks disappear if
we switch oﬀ the pairing as they are originally weakly
bound 2p1/2 and 2p3/2 orbits in the Woods-Saxon potential. In order to analyze the eﬀect of pairing on theresonance width, we calculate the width of the p1/2 res¯ We extract theonance for various pairing strengths ∆.
resonance width and resonance energy from the phaseshift using a ﬁtting method. The green line in Fig.2∗1∗2

Graduate School of Science and Technology, Niigata University
Department of Physics, Faculty of Science, Niigata University- 56 -shows the relation between the resonance width and¯ As thethe resonance energy for various values of ∆.
pairing strength increases, both the resonance width
and the resonance energy increase. For comparison,
we plot the width vs. energy relation for the singleparticle potential resonance of the 2p1/2 state (red linein Fig.2), which is obtained by varying the depth of
the Woods-Saxon potential V0 . If we compare these
two results at the same resonance energy, we ﬁnd thatthe width of quasi-particle resonance is narrower than
the width of single-particle potential resonance. We
conclude that the pairing has an eﬀect of reducing theresonance width¯ = 1.0MeV.
Fig. 1. Partial cross section with ∆Fig. 2. Comparison of results of resonance width.

References
1) S. T. Belyaev et al.: Sov. J. Nucl. Phys. 45, 783 (1987).
2) A. Bulgac: nucl-th/9907088.
3) J. Dobaczewski et al.: Phys. Rev. C 53, 2809 (1996)
4) M. Grasso et al.: Phys. Rev. C 64, 064321 (2000).
5) I. Hamamoto et al.: Phys. Rev. C 68, 034312 (2003).
6) J. C. Pei et al.: Phys. Rev. C 84, 024311 (2011).
7) J. Dobaczewski et al.: Nucl. Phys. A 422, 103 (1984).