Introduction

A possibility to find signatures of the T=0 neutron-proton (n-p) pairing correlations in N$\sim$Z nuclei is recently a subject of a significant fraction of experimental and theoretical studies in nuclear structure physics. At low spins, such correlations allow for a consistent description of ground states and low-T excitations in even-even and odd-odd N=Z nuclei[1]. This type of correlations may also be, in principle, visible through changes in structure of rotational nuclear bands. For example, the significance of the so-called delayed alignments in N=Z nuclei is at present intensely investigated, both experimentally[2,3] and theoretically, e.g., see recent Refs.[4,5,6,7,8] and references cited therein.

In the present study we address another experimental fact which may constitute such a signature, namely, an anomalous behavior of the second moment of inertia ${\cal J}^{(2)}$ in the superdeformed (SD) band of ⁶⁰Zn, as compared to its neighbors. The peak of ${\cal J}^{(2)}$ observed at low spins in ⁶⁰Zn has been in the original experimental paper [9] tentatively interpreted as the simultaneous alignment of the T=1 pairs of g_9/2 protons and neutrons, although no calculation supporting such a hypothesis was presented. Together with the discovery of the analogous SD band in ⁶¹Zn[10], where only a small bump of ${\cal J}^{(2)}$ was observed, the T=0 paired band crossing was proposed as an underlying structure of the ⁶⁰Zn band. Indeed, in a simple scenario such a crossing would be entirely blocked in ⁶¹Zn, while for the T=1 pairing only the neutron crossing would be blocked, leaving half of the peak intact. The T=0 paired-band structure was further corroborated by the lack of the analogous peak in the SD band in ⁵⁹Cu[11].

On the other hand, the T=1 pairing calculations performed in Ref.[12] indeed resulted in a strong rise of ${\cal J}^{(2)}$ with decreasing angular frequency of the ⁶⁰Zn SD band. However, at lower frequencies solutions could not have been obtained, and hence the complete peak of ${\cal J}^{(2)}$ was not reproduced. Neither the blocked calculations in neighboring odd and odd-odd nuclei were performed to support the possibility of reproducing smooth SD bands there within the T=1 pairing scenario. It was only argued that deformation effects can be important for the complete understanding of the physical picture.

In this study we present the first set of consistent calculations of the SD bands in ⁵⁸Cu, ⁵⁹Cu, ⁶⁰Zn, and ⁶¹Zn, performed within the T=1 pairing hypothesis. We show that the simple scenario of blocking either the neutron or proton T=1 pair indeed does not hold, and a more complicated picture is obtained. However, a gradual disappearance of the T=1 pairing correlations with increasing rotational frequency always creates too large values of ${\cal J}^{(2)}$ at high frequencies, in disagreement with data. In fact at high frequencies the values of ${\cal J}^{(2)}$, as well as the values of relative alignments, are perfectly well described by calculations that altogether neglect the T=1 pairing correlations. Therefore, it seems that the only effect that the no-pairing theory cannot describe is the peak of ${\cal J}^{(2)}$ in ⁶⁰Zn. Therefore, we attempt to describe this structure by a simple T=0 n-p pairing configuration mixing of unpaired solutions.

The superdeformed (SD) bands in the A$\simeq$60 nuclei have already been studied theoretically within various approaches[13,14,15,16,17,18,,20,21]. In the present paper we use two methods: (i) the cranked Hartree-Fock (HF) method, solved by using the HFODD (v1.75r) computer code [22], with the Skyrme SLy4 [23] effective interaction and no pairing (see Ref.[21] for details), and (ii) the cranked Strutinsky total routhian surface (TRS) calculations based on a deformed Woods-Saxon (WS) potential[24], with the T=1 pairing correlations treated within the approximate particle number projection by means of the Lipkin-Nogami (LN) method (see Refs.[25,26,27] for details). Results of these calculations are presented in Secs. 2 and 3, respectively, while in Sec. 4 we present the T=0 n-p pairing configuration-mixing calculations based on the HF results.