Quadrupole collectivity in neutron-rich Cd isotopes

The proximity to the closed shells at Z = 50 and N = 82 makes the neutron-rich Cd isotopes a perfect test case for nuclear theories. The energy of the first excited 2+-state in the even 122-128 shows an irregular behaviour as the Cd isotopes exhibit only a slight increase for 122Cd to 126Cd and even a decrease from 126Cd to 128Cd. This anomaly can so far not be reproduced by shell model calculations. Only beyond mean field calculations with a resultant prolate deformation are capable to describe this anomalous behaviour. In order to gain more information about the neutron-rich Cd isotopes a Coulomb excitation experiment was performed with MINIBALL at REX-ISOLDE, CERN. The extracted transition strengths B (E2,0+gs → 2+1) for 122,124,126,128Cd agree with beyond mean field calculations. The spectroscopic quadrupole moments Qs (2+1) are compared with measurements on odd neutron-rich Cd isotopes.

1 are compared with measurements on odd neutron-rich Cd isotopes. 1

. Motivation
The neutron-rich Cd isotopes provide a perfect test for nuclear theory, as they are only two protons away from the shell closure at Z = 50 and close to the N = 82 magic number. Already twenty years ago a quenching of the shell gap at N = 82 has been proposed by Dobaczewski et al. [1]. However, the astrophysical r-process path is expected to pass this region with the waitingpoint nucleus 130 Cd. Experimental investigations of this semi-magic nucleus found a high Q β value of 130 Cd which supports the idea of a shell gap reduction [2], whereas information on the isomeric decay found no evidence of a total shell quenching [3]. However, the solar abundance peak at A ≈ 130 is better described including a quenching of the shell gap at N = 82 [4]. Such an eect should be reected in lowered excitation energies and an enhanced transition strength.
The excitation energy of the rst excited 2 + -state in the neutron-rich Cd isotopes show an irregular behaviour.
The rise towards the N = 82 shell closure is not as steep as expected from comparison to the isotones Ba, Te, Xe and Pd, and even decreases from 126 Cd (E(2 + 1 ) = 652 keV [5]) to 128 Cd (E(2 + 1 ) = 645 keV [5,6]  γ-ray spectrum obtained in the period when the RILIS laser was turned o can be subtracted from the γ-ray spectrum when the laser was turned on. During the laser o period no transitions in Cd are visible in the γ-ray spectra. Therefore the surface ionised Cs as well as the isobaric contaminant In are eliminated [11]. In the 128 Cd experiment the Cs contamination was not constant over the time of the measurement and could only be subtracted from the spectra by applying time gates. A gate on late times T (1300 ms ≤ T ≤ 2300 ms) after proton pulse impact reveals only contributions to the γ-ray spectra from the Cs contamination. Subtracting this from the γ-ray spectrum with a gate set on early times T (200 ms ≤ T ≤ 1200 ms) after proton pulse impact cancels the Cs contaminant. The isobaric In contamination from the decay of Cd and directly from ISOLDE can be deduced also from the γ-ray spectrum after β-decay. Therefore the beams of 124,126,128 Cd were stopped in a thick target and the γ-rays detected. The relative amount of each isotope is extracted by simultaneously tting it and the eciency to the γ-ray yields after β-decay. In the case of 128 Cd the relative intensities for the γ-ray transitions in 128 In and 128 Sn were determined. A deviation from literature for transitions in 128 Sn was found [12].
In all the experiments a contamination of the 8 − isomeric state of In was present in the beam, which had to be taken into account. The relative amount of Cd for the dierent experiments are displayed in table 1.
The prompt Doppler-corrected γ-ray spectra show the expected deexcitation of the 2 + 1 state of the used target and the investigated Cd nucleus. Note, that in the case of 128 Cd the deexcitation peak at 645 keV proofs the 2 + 1 state of 128 Cd being at this energy, which was not clear before.
The Coulomb excitation cross section of the projectile nucleus σ proj can be determined with the information from the obtained γ-ray spectrum with M(E2) being the electric quadrupole operator. Varying these matrix elements in the input for the programs CLX/DCY until the cross section reproduces the experimentally found one gives sets for possible combinations of (M 02 , M 22 ). Because the cross section exhibits a dierent sensitivity to the matrix elements at dierent angles, a division of the scattered particles into distinct center of mass angular ranges restricts the possible combinations of the matrix elements.
By performing a maximum likelihood analysis the transition strength and the spectroscopic quadrupole moment eQ s (I) = 16π 5 (2I + 1) < II20|II > I M(E2) I can be extracted.