Search for Isovector Valence-Shell Excitations in 140Nd and 142Sm via Coulomb excitation reactions of radioactive ion beams

Projectile Coulomb excitation experiments were performed at HIE-ISOLDE at CERN with the radioactive ion beams of 140Nd and 142Sm. Ions with an energy of 4.62 MeV/A were impinging on a 1.45 mg/cm2 thick 208Pb target. The γ-rays depopulating the Coulomb-excited states were recorded by the HPGe-array MINIBALL and scattered particles were detected by a double-sided silicon strip detector. Experimental intensities were used for the determination of electromagnetic transition matrix elements. A preliminary result of the B(M1; 23→21 ) of 140Nd and an upper limit for the case of 142Sm are revealing the main fragments of the proton-neutron mixed-symmetry 2+1,ms states.


Introduction
The proton-neutron interaction is of particular interest in respect how collectivity emerges in nuclear many-body quantum systems.The quadrupole-quadrupole part of this interaction forms the lowest-lying collective states in heavy open-shell nuclei.These states have wave functions which are completely symmetric in respect to the exchange of any proton and neutron components.In the framework of the Interacting Boson Model (IBM) [1,2] the states are dubbed fully symmetric states (FSSs).On the other hand, the distinction of protons and neutrons explicitly introduced in the IBM, the IBM-2 [1,3], results in a class of states which can be partially asymmetric in respect to the proton-neutron exchange.These are the so-called proton-neutron mixed-symmetry states (MSS).Proton-neutron MSS are collective excitations where the protons and neutrons oscillate out of phase.This type of states exhibits information about the isovector part of the proton-neutron interaction which is not accessible via the study of FSSs [1,2].* e-mail: rkern@ikp.tu-darmstadt.dei →2 + 1 transitions of even-even N=80 isotones from 132 Te (Z=52) to 138 Ce (Z=58) show the evolution of fragmentation of the 2 + 1,ms state along this isotonic chain.The question marks at 140 Nd and 142 Sm present the question which this experiment tries to answer.The graphic is taken from Ref. [4].
One-phonon MSSs are identified in many even-even vibrational nuclei in different mass regions [9].Prominent examples are found in the mass A=90 region.Several cases are reported in the mass A=130 region and recently three cases are found in the mass A=208 region [10][11][12].It is observed, that the even-even N=80 isotones form isolated proton-neutron mixed-symmetry 2 + 1,ms states from Z=52 to Z=56 [13][14][15].For 136 Ba, it was shown that the one-phonon FSSs (2 + 1 ) and MSSs (2 + 1,ms ) are formed by excitations in open orbitals -ν1h 11/2 and π1g 7/2 [16].This situation changes at 138 Ce (Z=58).In contrast to the Z<58, isotones 138 Ce shows a significant fragmentation of the 2 + 1,ms state as illustrated in Fig. 1.It was suggested that the fragmentation is caused by a fully filled π1g 7/2 orbital [17], which leads to a breaking of this filled orbital structure to form nuclear excited states.So, the configuration of the 2 + 1,ms state gets more complex and it starts mixing with near-lying 2 + states.This effect is called lack of valence-shell stabilization and leads to the suggestion of a proton sub-shell closure at 138 Ce (Z=58) [17] for the N=80 isotones.
An indirect manifestation of the Z=58 sub-shell closure is already observed in the evolution of the FSSs in the N=80 isotones.The properties of the one-phonon FSSs in N=80 isotones are measured from Z=50 to Z=62 [13,[18][19][20][21][22][23][24].The evolution of the B(E2; 2 + 1 →0 + 1 ) strength can be outlined as an almost smooth rise from the proton-shell closure Z=50 towards mid-shell, with a small decrease at Z=58 as illustrated in Fig. 2.This shallow minimum, in addition with a sudden increase of collectivity at Z=60 (cf.Fig. 2), is an indication, that the trend of the collectivity cannot be described solely by a simple proportionality to the product of the number of valence protons N π and of valence neutrons N ν [25].Apparently sub-shell effects, stemming from seniority like behavior [19,20], modulate the rise of collectivity in this isotonic chain.Applying the seniority scheme, one expects the highest contribution to the collectivity when an orbital is half filled and no contribution when it is fully filled with nucleons [19,20].A superposition of both models depicts the experimental data quite well (cf.Fig. 2).
To test directly the hypothesis of shell stabilization of MSSs in the N=80 isotones, these states have to be identified in the isotones with Z>58, i.e. in 140 Nd and 142 Sm.The main goal of the present work is to address this task by measuring the Coulomb-excitation yields of 140 Nd and 142 Sm radioactive ion beams.

Experiment
The projectile Coulomb-excitation experiments were performed at the radioactive ion beam facility HIE-ISOLDE at CERN [26].The radioactive 140 Nd and 142 Sm were produced by irradiating a thick tantalum target with 1.4 GeV protons, which were provided by the CERN PS Booster.An identical primary target has been used in previous measurements [19,20].The hot surface ion source was combined with the laser ionization system RILIS [27] to maximize the rate of the desired isotope.The mass selection is done with GPS following a post acceleration through HIE and REX cavities up to 4.62 MeV/A leading to an ion velocity of about 9% of the speed of light.The radioactive ion beam was impigning on a 1.45 mg/cm 2 thick 208 Pb target.The chosen beam energy is equivalent to about 76% of the Coulomb barrier for the 140 Nd/ 142 Sm+ 208 Pb reaction and can be considered as "safe" Coulomb excitation [28] at all relevant scattering angles.The MINIBALL spectrometer [29] consisting of 24 six-fold segmented HPGedetectors was used for the γ-ray detection.Additional a double-sided silicon strip detector (DSSD) was placed in forward direction, 21 • ÷60 • in the lab frame with respect to the beam axis.It is used for detection and identification of scattered charged particles as illustrated in Fig. 3.A total of 1.2×10 6 and 4.3×10 6 events were collected over a period of one day and five days of beam time using the    condition of a detected target-or beam-like particle with an A=140 and A=142 beam, respectively.Events with a γ-ray multiplicity of 2 or greater are sorted in the E γ −E γ matrix.

Analysis and preliminary results
The advantage of an experiment in the "safe" Coulombexcitation regime is that the population of the excited states is proportional to the Coulomb-excitation cross sections.Experimental yields of the excited states of 140 Nd and 142 Sm are determined through the observed γ-ray transition intensities, known branching ratios [30,31], and theoretical electron-conversion coefficients [32].These measured excited states' populations are used to calculate the ground-state transition matrix elements to excited states via Coulomb-excitation code CLX [33] relative to the known B(E2; 2 + 1 →0 + 1 ) [19,20].The E2 and M1 strengths of non-ground-state transitions are derived with complementary information about branching ratios and multipole mixing ratios.The focus of the experiment lies on the analysis of 2 + i →2 + 1 transitions.1,ms and its decay is highlighted with a thicker line.

140 Nd
Via Coulomb excitation of 140 Nd three 2 + states are populated.In addition to the 2 + states, three 4 + states, one 0 + state, one 3 − state and one state with uncertain spin and parity (J π =5, 6) were also populated.This results in an observation of 12 γ-ray transitions of 140 Nd.The assignment to known transitions was done by checking coincidences in the E γ −E γ matrix.The decay behaviors of the excited low-lying 2 + states were already measured via β-decay [30], especially the multipole mixing ratios δ of transitions to the 2 + 1 state.Therefore, the dominant M1 decay of the 2 + 3 state at 2140 keV to the 2 + 1 state with a multipole mixing ratio of δ= − 0.08 (8) is known.This leads to the assumption that this state is the most promising candidate for the 2 +  1,ms state.The 2 + 3 state is also the only populated quadrupole excitation in the energy region of ≈2 MeV (cf.Fig. 4).Combining the measured yield of the 2 + 3 state, determined via the γ-ray intensity of the 2 + 3 →2 + 1 transition (cf.Fig. 4) and the known branching ratio Ref. [30], with the previously known multipole mixing ratio a B(M1, 2 + 3 →2 + 1 ) strength of approximately 0.25 µ 2 N can be derived at this point of the analysis.

142 Sm
A similar level scheme is observed for the 208 Pb( 142 Sm, 142 Sm * ) 208 Pb * Coulomb-excitation reaction.In total four 2 + , one 0 + , one 4 + and one 6 + states are populated.The analysis was done analogously to 140 Nd and, as in 140 Nd, the 2 + 3 state is the only populated quadrupole excitation in the energy region of ≈2 MeV (cf.Fig. 5).The character of the 2 + 3 →2 + 1 transition of 142 Sm is unknown, but an analogy to the level scheme of 140 Nd is apparent.That leads to an assumption of a M1-dominated 2 + 3 →2 + 1 transition.Therefore, the 2 + 3 state is the most promising candidate for the 2 + 1,ms state and an upper limit for the B(M1; 2 + 3 →2 + 1 ) strength around 0.3 µ 2 N can be determined at this point of the analysis.Preliminary level schemes of 140 Nd and 142 Sm were made as presented in Fig. 6.

Summary and Outlook
In the reported experiment the states of interest of 140 Nd and 142 Sm, 2 + states in the 2 MeV energy region, were successfully populated via Coulomb excitation.A preliminary and an upper limit for the B(M1; 2 + 3 →2 + 1 ) strengths of radioactive 140 Nd and 142 Sm could be determined, respectively.The prelimary results of B(M1; 2 + 3 →2 + 1 ) strengths indicate that the one-phonon MSSs in both isotones are single isolated states.The lack of fragmentation supports the hypothesis of the isovector valence-shell re-stabilization after the proton sub-shell closure of 138 Ce.In particular the measured M1-transition strength of 140 Nd reinforces this suggestion.If the transition character of the 2 + 3 →2 + 1 transition of 142 Sm is assumed as dominantly M1, similar to the neighbouring 140 Nd, the 2 + 3 state could be identified as an isolated 2 + 1,ms state, too.

Figure 1 .
Figure 1.(Color online) The experimental M1-strength distributions of 2 +i →2 + 1 transitions of even-even N=80 isotones from 132 Te (Z=52) to 138 Ce (Z=58) show the evolution of fragmentation of the 2 + 1,ms state along this isotonic chain.The question marks at 140 Nd and 142 Sm present the question which this experiment tries to answer.The graphic is taken from Ref.[4].

Figure 3 .
Figure 3. (Color online) The spectrum of the DSSD shows the particle energy of the 208 Pb( 142 Sm, 142 Sm * ) 208 Pb * reaction in dependence of the scattering angle, ring #1 corresponds to 21 • and ring #16 to 60 • .The used gates for the scattered projectile (black) and the recoiling target (red) particles are marked.

Figure 4 .
Figure 4. (Color online) The time-background subtracted, particle-gated and Doppler-corrected spectrum of 140 Nd is shown and the most prominent transitions of Coulomb-excited 140 Nd are marked.Transitions of the main beam contaminant 140 Sm are also prominent in the spectrum.The energy region of the 2 + 3 →2 + 1 transition is zoomed in and gaussians are fitted to the 2 + 3 →2 + 1 transition of 140 Nd (black) and on a ground-state transition of 140 Sm at 1420 keV (blue).

Figure 5 .
Figure 5. (Color online) The time-background subtracted, particle-gated and Doppler-corrected spectrum of 142 Sm is shown and the most prominent transitions of Coulomb-excited 142 Sm are marked.The energy region of the 2 + 3 →2 + 1 transition is zoomed in and gaussians are fitted to the 2 + 3 →2 + 1 (black) and 0 + 3 →2 + 1 (green) transitions of 142 Sm.