Spectroscopy of Neutron-Rich Nuclei: the Current Status

High spin spectroscopy in neutron-rich nuclei represents a formidable experimental challenge. The fusion evaporation reactions which are commonly used to populate high-spin states give rise to evaporation residua which are proton-rich. Therefore, even stable nuclei are not accessible using the standard in-beam techniques. Consequently, a number of methods have been applied to obtain spectroscopic information on neutron-rich systems [2,3].

One way of carrying out spectroscopic studies in the neutron-rich systems is to analyze the prompt gamma rays from nascent fission fragments (produced either in spontaneous fission or in heavy-ion-induced fission). In such measurements it is possible to approach spectroscopically relatively neutron-rich nuclei [4,5,6,7,8,9,10]. Rotational structures in neutron-rich nuclei have also been studied using transfer reactions [11,12], incomplete fusion [13], neutron-induced fission [14,15], and deep inelastic reactions [16,17]. The technique of Coulomb excitation at intermediate energies (employing in-flight isotopic separation of projectile fission fragments) has been used to study the lowest excited states in very neutron-rich light and medium-mass nuclei [3,18,19,20]. Very recently, it was possible, for the first time, to perform spectroscopic measurements with accelerated radioactive neutron-rich beams using coulex and fusion-evaporation reactions [21]. This new development offers a number of exciting opportunities for nuclear structure studies on the neutron-rich side.

However, in spite of many experimental efforts, detailed information on high-spin properties of neutron-rich nuclei still remains scarce. This is most unfortunate, since - in many cases - even by adding as few as 2-3 neutrons to the last known isotope, one enters a region where new phenomena occur. A classic example is the region of the neutron-rich Ba-Ce nuclei which exhibit strong octupole correlations, and even octupole deformations, manifesting themselves in the presence of alternating-parity bands [22]. These nuclei are spontaneous fission products; hence some spectroscopic information, mainly at medium spins, already exists. One of the most interesting regions on the neutron-rich side of the stability valley are the nuclei around ¹⁰²Zr, also produced in spontaneous fission, where a variety of deformation effects and shape changes due to quasi-particle alignment are expected as a function of angular momentum [23]. From the theoretical point of view, probably the most attractive nuclei in this mass region are the systems near ¹⁰⁴Mo and ¹⁰⁸Ru, which are predicted to have stable collective triaxial shapes ($\gamma$$\approx$-30$^\circ$). Although the question of whether they are $\gamma$-soft or $\gamma$-deformed at low spins has not yet been settled, these nuclei seem to be ideal for testing theoretical models of nuclear triaxiality. In particular, at higher spins, where the triaxial minima are predicted to be deeper, the shape with $\gamma$$\approx$-30$^\circ$ can give rise to interesting selection rules associated with the effective C₄ symmetry of the Hamiltonian [24]. The presence of static triaxial deformations is prerequisite for the existence of chiral bands[25] and wobbling bands[26] - new collective modes of the rotating nucleus. Figure 1 shows the total Routhian surfaces for ¹⁰⁸Ru calculated within the cranked shell correction approach with the Woods-Saxon average potential and monopole pairing. This heavy ruthenium isotope is triaxial in its ground state, and the corresponding collective triaxial minimum with $\beta_2$$\approx$0.28 and $\gamma$$\approx$-30$^\circ$ is yrast in a wide range of rotational frequencies. The alignment of h_11/2 neutrons, g_9/2 protons, followed by the second h_11/2 neutron alignment, produces triaxial shapes with $\beta_2$$\approx$0.2, $\gamma$$\approx$-45$^\circ$. (For recent experimental data on high-spin behavior of ¹⁰⁸Ru, see Ref. [8].) At high spins, transition to superdeformed shapes is predicted. According to calculations [23], the most favorable candidates for superdeformation in this mass region are ¹⁰⁰Mo and ^108-112Ru.

  

Figure 1: Total Routhian surfaces in the ( $\beta_2, \gamma$)-plane for the ($\pi$=+, r=1) quasi-particle vacuum configuration of ¹⁰⁸Ru at four values of rotational frequency: $\hbar\omega$=0.3, 0.6, 0.9, and 1.2MeV. At each ($\beta_2$, $\gamma$) point the total Routhian has been minimized with respect to hexadecapole deformation $\beta_4$. The distance between thick contour lines is 1MeV, while between the thin contour line it is 250keV. The angular momentum values at local minima are indicated. (From Ref. [23].)

It is only in light nuclei that it has been possible to approach the neutron drip line experimentally and to obtain some spectroscopic information on nuclei with an extreme neutron excess. The neutron-rich nuclei with N$\approx$20 are spectacular examples of coexistence between spherical and deformed configurations in the sd shell (8 $\le$ Z,N $\le$ 20). A classic example is the ``semi-magic'' nucleus <sup>32</sup><sub>12</sub>Mg<sub>20</sub>, which has a very low-lying 2<sup>+</sup> state at 886 keV [27] and an anomalously high value of the two-neutron separation energy S<sub>2n</sub>. Deformed shapes in this mass region have been inferred from the intermediate-energy Coulomb excitation studies [28,19,20] which provided information on position and collectivity of the lowest 2<sup>+</sup> and 4<sup>+</sup> states in <sup>32,34</sup>Mg. Many calculations based on the mean-field theory have predicted deformed ground states in nuclei from the <sup>32</sup>Mg region (sometimes dubbed as an ``island of inversion").

  

Figure 2: Single-neutron levels in ³⁴Mg as a function of the proton charge quadrupole moment Q₂₀ (Q₂₂=0) calculated in the HF+SLy4 model. The crossing between the [330]1/2 intruder level and the [201]3/2 extruder level is indicated. (From Ref. [29].)

The origin of the shape coexistence effects around ³²Mg can be traced back to the crossing between the prolate-driving [330]1/2 intruder level, originating from the 1f_7/2 shell, and the oblate-driving [201]3/2 extruder level; see Fig. 2 and Ref. [30] for more discussion. Another, recently discovered, island of inversion are the neutron-rich nuclei from the pf shell centered around ⁴⁴₁₆S₂₈ [31,18,32]. According to the mean-field calculations [30,33,34], deformation effects around ⁴⁴S can be attributed to the appreciable breaking of the N=28 core. In the shell-model language, islands of inversion have their roots in the monopole effect caused by the proton-neutron residual interaction [35,36].