Quadrupole Collectivity beyond N=28: Intermediate-Energy Coulomb Excitation of Ar47,48

Phys. Rev. Lett. 108, 182501
Particle-identification spectrum for the neutron-rich projectile beam passing through the Au target. The energy loss measured in the S800 ionization chamber is plotted versus the ion’s flight time. Ar47 and Ar48 can be unambiguously identified among the other species in the cocktail beam.Particle-identification spectrum for the neutron-rich projectile beam passing through the Au target. The energy loss measured in the S800 ionization chamber is plotted versus the ion’s flight time. Ar47 and Ar48 can be unambiguously identified among ... Show more

Developing predictive power for the fundamental properties of atomic nuclei is driving experimental and theoretical research worldwide. Single-particle motion in a defined nuclear potential is one of the crucial building blocks for a comprehensive picture of these strongly interacting fermionic quantum many-body systems. Large stabilizing energy gaps occur between groups of single-particle states at certain “magic” fillings with protons or neutrons. The nuclear potential and resulting shell structure have been established in the valley of stability; however, dramatic modifications to the familiar ordering of single-particle orbits in “exotic” nuclei with a large imbalance of proton and neutron numbers have been found: New shell gaps develop and conventional magic numbers break down. Current efforts in nuclear physics are aimed at unraveling the driving forces behind those structural modifications, which are most pronounced in neutron-rich species [1–3].

The neutron magic number N=28 has attracted much attention in recent years. On the neutron-rich side of the nuclear chart, below doubly magic Ca2848, the N=28 shell closure was shown to disappear progressively below Z=20 in S2844 [4] and Si2842 [5], however, with conflicting experimental data on Ar2846 [6–8]. Much of the initial spectroscopic information referenced above stems from measurements of the energy of the first 2+ state, E(21+), and the absolute B(E2;01+21+)B(E2) quadrupole excitation strength. These observables can signal the breakdown or persistence of a magic number, with high E(21+) and low B(E2) values at a shell gap (reduced collectivity) and the reverse in the middle of a shell (collective character or deformation).

The role of the Ar isotopes around N=28 is of great interest. They are, with Z=18, between doubly magic Ca48 and the already collective S isotopes ( Z=16) on the path to Si42, which has the lowest-energy 21+ state along the N=28 isotonic chain to date. Early intermediate-energy Coulomb excitation measurements [4,6] showed that S40,42,44 are collective with high B(E2) values, while, in two independent measurements, the B(E2) value for Ar46 was found low as one would expect for a persisting N=28 shell gap [6,7]. Shell-model calculations were unable to explain the reduced collectivity in Ar46 [9,10] and rather predict the breakdown of N=28 as a magic number and an onset of collectivity already in Ar. A recent, marginal-statistics excited-state lifetime measurement extracted a much higher B(E2) value in agreement with the shell-model description [8].

Event-by-even Doppler-reconstructed γ-ray spectra detected in coincidence with scattered Ar48 (left) and scattered Ar47 (right). Gamma-ray transitions at 1040 and 1227 keV can be clearly identified and are attributed to the deexcitation γ rays from the first excited 2+ state in Ar48 and the first excited 5/2 state in Ar47, respectively.Event-by-even Doppler-reconstructed γ-ray spectra detected in coincidence with scattered Ar48 (left) and scattered Ar47 (right). Gamma-ray transitions at 1040 and 1227 keV can be clearly identified and are attributed to the deexcitation γ rays from t... Show more

Here, we present the first study of quadrupole collectivity in the N=30,29 Ar isotopes Ar48,47 with intermediate-energy Coulomb excitation. Measured B(E2;01+21+) and B(E2;3/21-J) values are compared to state-of-the-art shell-model calculations, taking into account possible effects of large neutron excess.

Little is known about the N=30 isotones in even- Z nuclei below Ca50. In 2007, Si44 was proven to be bound [11], and in 2009 excited states in S46 were first observed by using in-beam γ-ray spectroscopy following nucleon-exchange reactions [12]. Excited states in Ar48 were studied in 2008 with deep-inelastic reactions [13] and in 2009 with nucleon-exchange reactions [12]. Rare-isotope beams in this region of the nuclear chart are typically produced by the fragmentation of a primary Ca48 beam on a light target. In this scheme, the production of exotic projectiles with N=30,29 necessarily involves neutron pickup and/or nucleon-exchange processes which proceed with small cross sections compared to reactions that involve only proton or neutron removals. Here we show that, in spite of the small production cross sections, Ar47,48 projectile beams can be produced from a Ca48 primary beam at intensities sufficient for γ-ray-tagged, thick target intermediate-energy Coulomb excitation measurements, allowing for the study of quadrupole collectivity in these very neutron-rich systems.

The measurements were performed at the Coupled Cyclotron Facility at National Superconducting Cyclotron Laboratory (NSCL) on the campus of Michigan State University. The secondary projectile beam containing Ar47,48 was produced from a 140MeV/u Ca48 stable primary beam impinging on a 681mg/cm2 Be9 production target and separated by using a 195mg/cm2 Al wedge degrader in the A1900 fragment separator [14]. The total momentum acceptance of the separator was restricted to 2%. The resulting rare-isotope beam was composed of 6.5% Ar48 and 57% Ar47. Typical rates of 150 Ar48/sec and 1300 Ar47/sec were delivered to the experimental end station.

(Upper panel) Measured B(E2) for the chain of Ar isotopes [6, 7, 8, 22] compared to shell-model calculations using two different effective interactions with the standard effective charges ep=1.5e and en=0.5e (solid lines) and N- and Z-dependent effective charges following Bohr and Mottelson (dashed lines). (Lower panel) Measured and calculated E(21+) energies for the Ar isotopic chain.(Upper panel) Measured B(E2) for the chain of Ar isotopes [6, 7, 8, 22] compared to shell-model calculations using two different effective interactions with the standard effective charges ep=1.5e and en=0.5e (solid lines) and N- and Z-dependent effe... Show more

At the pivot point of NSCL’s S800 spectrograph [15], a gold target of 518mg/cm2 thickness was surrounded by the Segmented Germanium Array (SeGA) consisting of 32-fold segmented high-purity germanium detectors for high-resolution γ-ray spectroscopy [16]. The segmentation allows for event-by-event Doppler reconstruction of γ rays emitted in flight by the scattered projectiles. For this, the γ-ray emission angle entering the Doppler reconstruction is determined from the location of the detector segment with the largest energy deposited. Sixteen detectors were arranged in two rings with central angles of 90° and 37° with respect to the beam axis. The 37° ring was equipped with seven detectors, while nine detectors occupied 90° positions. The photopeak efficiency of the array was measured with a Eu152 standard calibration source and corrected for target absorption and the Lorentz boost of the γ-ray angular distribution emitted by nuclei moving at velocities of more than v/c=0.4.

Scattered projectiles were identified on an event-by-event basis with the focal-plane detection system of the large-acceptance S800 spectrograph [15]. The ion’s energy loss measured in the S800 ionization chamber and flight-time information measured with two plastic scintillators—corrected for the angle and momentum of each ion—were used to unambiguously identify the scattered projectiles emerging from the target. The identification spectrum is shown in Fig. 1.

In intermediate-energy Coulomb excitation [3,17,18], projectiles are scattered off stable high- Z targets and are detected in coincidence with the deexcitation γ rays, tagging the inelastic process. Very peripheral collisions are selected in the regime of intermediate beam energies to exclude nuclear contributions to the electromagnetic excitation process. This is typically accomplished by restricting the data analysis to events at very forward scattering angles, corresponding to large impact parameters b in the interaction between projectile and target nuclei—here, we chose b>1.2Ap1/3+1.2At1/3. Position measurements from the cathode readout drift chambers in the S800 focal plane were combined with ion optics information to reconstruct the projectile’s scattering angle on an event-by-event basis. The angle-integrated Coulomb excitation cross section σ(θlabθlabmax)σ was determined from the efficiency-corrected γ-ray intensity relative to the number of projectiles per number density of the target and translated into absolute B(σλ) excitation strengths by using the Winther-Alder description of intermediate-energy Coulomb excitation [19].

B(E2;3/2J) strength distribution for the lowest-lying excited 1/27/2 states. The experimental values for J=7/2 and 3/2 are upper limits as described in the text. Standard effective charges were used in both shell-model calculations. B(E2;3/2J) strength distribution for the lowest-lying excited 1/27/2 states. The experimental values for J=7/2 and 3/2 are upper limits as described in the text. Standard effective charges were used in both shell-model calculations. Show more

For the present analysis we use maximum scattering angles of θlabmax=1.94(5)° and 1.97(5)° for Ar47 ( 100MeV/u midtarget energy) and Ar48 ( 96MeV/u midtarget energy), respectively, corresponding to minimum impact parameters just above bmin=13.3fm for both projectile-target systems. The event-by-event Doppler-reconstructed γ-ray spectra taken in coincidence with Ar48,47—with the scattering-angle restrictions applied—are shown in Fig. 2. The γ-ray transition at 1040 keV observed in Ar48 is attributed to the decay of the first 2+ state, in agreement with Refs. [12,13]. The γ-ray transition apparent at 1227 keV in the spectrum of Ar47 is assigned to the decay of the first excited 5/2- state to the 3/2- ground state, following Refs. [13,20]. The peaklike structure at about 820 keV in the Ar48 spectrum is an artifact from Doppler reconstruction applied to background lines, only seen in the 37° ring of SeGA. Similar structures at the same energy are visible in the spectrum of Ar47.

An angle-integrated Coulomb excitation cross section of σ(Ar48)=74(11)mb was derived for the excitation of the first 2+ state of Ar48, translating into B(E2;01+21+)=346(55)e2fm4 for this most neutron-rich Ar isotope studied with this technique. The cross section includes statistical uncertainties and a 5% uncertainty on the in-beam γ-ray detection efficiency. For the extracted B(E2) values, an additional 5% systematic uncertainty originating from the projectile’s scattering-angle reconstruction was added in quadrature.

The Coulomb excitation of the odd- N Ar47 is more complicated. A mixed E2-M1 multipolarity is expected for the 5/2-3/2- γ-ray transition. The multipole character of the radiation affects the γ-ray angular distribution and thus the detection efficiency. Large-scale shell-model calculations with different interactions, SDPF-U [10] and EPQQM [21], compute an identical multipole mixing ratio of δ(E2/M1)=1.01, corresponding to 50% M1 character. This δ(E2/M1) was used in the determination of the in-beam detection efficiency of SeGA. To put this into perspective, assuming 100% E2 character would introduce a relative change of only 1.5% in the detection efficiency. However, in the excitation process, E2 multipolarity dominates over M1 by orders of magnitude, with 20.9mb/100e2fm4 and 0.18mb/0.1μN2 for Coulomb excitation via E2 and M1, respectively. Shell-model calculations predict B(M1;3/2-5/2-)=0.0236μN2 (SDPF-U) [10] or less (EPQQM) [21], and we thus assume that the excitation proceeds solely via E2 character. B(E2;3/2-5/2-)=135(17)e2fm4 is deduced from the measured cross section of σ(Ar47)=28(3)mb, with an error budget as detailed for Ar48.

The consistent description of the onset of collectivity at N=28 in the isotopic chains of sulfur ( Z=16) and silicon ( Z=14) has been a challenge for large-scale shell-model calculations and was accomplished by Nowacki and Poves by devising two effective interactions (SDPF-U) for the sdpf model space, one valid for Z14 and one to be applied for Z>14 [10]. In a recent shell-model work by Kaneko et al., the extended pairing plus quadrupole-quadrupole force with inclusion of a monopole interaction (EPQQM) was proposed to provide a consistent description of the breakdown of N=28 across the Z=20 to Z=14 isotopic chains [21]. Both shell-model interactions use ep=1.5e and en=0.5e for the effective charges that enter the computation of B(E2) transition strengths from the proton and neutron shell-model transition amplitudes Ap and An via B(E2;JiJf)=(enAn+epAp)2/(2Ji+1). In Fig. 3 (upper panel), the shell-model B(E2;01+21+) values calculated with the two different effective interactions—using the standard effective charges quoted above—are compared to the available measured values in the chain of Ar isotopes, starting from semimagic Ar2038 [6–8,22]. The two calculations describe the trend of the data on the even-even isotopes well only if one neglects the two consistent, low B(E2) values at N=28 [6,7] and assumes that the marginal-statistics excited-state lifetime measurement for Ar46 is correct—with small differences in the detailed trends of the two calculations. For Ar48 the calculation is within 2σ of the experimental value for the SDPF-U effective interaction. The EPQQM effective interaction differs somewhat in the trend approaching N=28, with a marked drop in the B(E2) strength at N=26 that is not present in the SDPF-U results but consistent with the data. For Ar48, the EPQQM calculation is within 1.5σ of the measured value. The trend beyond N=30 is predicted very differently by the two interactions, with rather constant B(E2) values out to N=34 for the SDPF-U interaction and a rise in collectivity for EPQQM, with Ar3452 being the most collective in the chain. The calculated E(21+) energies reproduce the measured energies well where available, with the SDPF-U and EPQQM predictions diverging at N=34. At N=28, both calculations predict high B(E2) and E(21+) values, deviating from established systematics [22] that rather suggests their anticorrelation as observed for Ar2038, for example.

The question arises as to the effects of neutron excess on the transition strength. The effective charges, which generally compensate for missing excitations beyond the (necessarily) limited model space, can be formulated following Bohr and Mottelson [23] to explicitly include neutron excess via enBM=epol and epBM=1+epol, where epol=e{Z/A-0.32(N-Z)/A+[0.32-0.3(N-Z)/A]τz} is the polarization charge with τz=1 and -1 for neutrons and protons, respectively. This approach approximates the coupling of the particle motion to higher frequency quadrupole modes that are beyond the model spaces of the effective shell-model interactions [23]. Figure 3 confronts the experimental data with the shell-model B(E2) values calculated with ep,n=1.14ep,nBM (dashed line). A slight renormalization of the effective charges by 1.14 was introduced to have the results with both interactions reproduce the B(E2) value of semimagic Ar38. With the calculations anchored in this way and the effective charges evolving with neutron excess, subtle changes in the theory trends are visible. The description of the available data by the EPQQM effective interaction improved, in particular, below N=28, and the quality of the SDPF-U calculation remains roughly the same. The differing trend beyond N=30 is amplified, with a larger discrepancy in the prediction of the B(E2) value at N=34. If the low B(E2) value for Ar46 should be proven correct, certainly the modified effective charges would not reverse the trend at N=28 and leave a striking disagreement between experiment and shell model as to the evolution of collectivity below Ca48 towards Si42.

With conflicting experimental results at Ar46 and rather robust shell-model calculations at N=28, it is interesting to turn to the odd- N neighbor Ar47. In odd- A nuclei, core-coupled states are expected to carry the E2 strength. These states can be qualitatively described as originating from a particle or hole weakly coupled to the neighboring even-even core [24]. For Ar47, the coupling of the odd p3/2 proton to the Ar46 21+ state would give rise to a quartet of states with spin values of 1/2-, 3/2-, 5/2-, and 7/2- at about E(21+(Ar46))=1555keV [7] and with a total E2 excitation strength of ΣJB(E2;3/2-J)=B(E2)Ar46. Indeed, in both shell-model calculations, the lowest-lying 1/2--7/2- excited states are found between 1139–2125 and 950–2343 keV in the SDPF-U and EPQQM calculations, respectively. As one would expect in this extreme weak-coupling scheme, 85.0% and 99.7% of the shell-model B(E2)Ar46 are exhausted by this multiplet in the respective interactions.

In the present measurement, there is only clear evidence for one strongly excited state, at 1227 keV with alleged 5/2- spin assignment [13,20]. Using the Ar47 level scheme presented in Refs. [13,20], and assuming that the observed 1747 and 2190 keV states are the 7/2- and 3/2- members of the multiplet, we can establish upper limits for the B(E2) excitation strengths in the present work (we neglect the 1/2- member of the multiplet, as this state is expected to be only weakly excited). From the γ-ray spectrum of Ref. [13], we roughly estimated 60% and 40% branches to the ground state and the alleged 5/2- first excited state, respectively, for both states. We estimated a possible maximum number of γ-ray counts in the expected transitions to the ground state and—taking into account the assumed branching ratios—extract upper limits of σ(7/2-)16(8)mb and σ(3/2-)4(2)mb with conservative 50% uncertainties, translating into generous upper limits of B(E2;3/2-7/2-)<74(37)e2fm4 and B(E2;3/2-3/2-)<20(10)e2fm4 for the E2 excitation strength. In Fig. 4, the measured B(E2) values and limits are compared to the two shell-model calculations (with standard effective charges). First, this comparison supports the assignment of the level at 1227 keV as the 5/2- state, which—in both calculations—is predicted to carry the largest fraction of the E2 excitation strength. We note that the EPQQM interaction predicts the centroid of the E2 strength to lie about 500 keV higher than in the SDPF-U calculation.

The total ΣJB(E2;3/2-J-) strength concentrated in these states is included in the B(E2) systematics of Fig. 3 at N=29 for experiment as well as theory. The comparison shows that both shell-model effective interactions significantly overpredict the B(E2) strength concentrated in the low-lying states of Ar47. The experimental B(E2) range given in the figure marks the possible span of the total B(E2) strength ranging from the sole excitation of the 5/2- states to the maximum strength observed in case the upper limits for the excitation of the 7/2- and 3/2- members of the quartet should be realized. This discrepancy is consistent with the situation at N=28 if the measured low B(E2) value for Ar46 should be proven correct. This result for Ar47 indicates that challenges remain for the most modern shell-model effective interactions in this area of rapid structural change, and it also demonstrates the seldom exploited, sensitive benchmark posed by measures of collectivity in odd- A nuclei.

In summary, we studied the quadrupole collectivity in the very neutron-rich nuclei Ar47,48 via intermediate-energy Coulomb excitation. While the two most recent effective shell-model effective interactions predict B(E2) values for Ar48 close to the experimental result, the low-lying quadrupole collectivity in Ar47 is significantly overpredicted by theory, reminiscent of the situation in Ar46 if the lower of the conflicting B(E2) values in the literature should be proven correct. We show that modified effective charges that approximate effects of neutron excess do not resolve the discrepancy at N=28,29 in the Ar isotopes and demonstrate the potential of studies of quadrupole collectivity in odd- A nuclei to sensitively probe nuclear structure calculations.


  1. B. A. Brown, Prog. Part. Nucl. Phys. 47, 517 (2001).
  2. O. Sorlin and M.-G. Porquet, Prog. Part. Nucl. Phys. 61, 602 (2008).
  3. A. Gade and T. Glasmacher, Prog. Part. Nucl. Phys. 60, 161 (2008).
  4. T. Glasmacher et al., Phys. Lett. 395, 163 (1997).
  5. B. Bastin et al., Phys. Rev. Lett. 99, 022503 (2007).
  6. H. Scheit et al., Phys. Rev. Lett. 77, 3967 (1996).
  7. A. Gade et al., Phys. Rev. C 68, 014302 (2003).
  8. D. Mengoni et al., Phys. Rev. C 82, 024308 (2010).
  9. S. Nummela et al., Phys. Rev. C 63, 044316 (2001).
  10. F. Nowacki and A. Poves, Phys. Rev. C 79, 014310 (2009).
  11. O. B. Tarasov et al., Phys. Rev. C 75, 064613 (2007).
  12. A. Gade et al., Phys. Rev. Lett. 102, 182502 (2009).
  13. S. Bhattacharyya et al., Phys. Rev. Lett. 101, 032501 (2008).
  14. D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever, Nucl. Instrum. Methods Phys. Res., Sect. B 204, 90 (2003).
  15. D. Bazin, J. A. Caggiano, B. M. Sherrill, J. Yurkon, and A. Zeller, Nucl. Instrum. Methods Phys. Res., Sect. B 204, 629 (2003).
  16. W. F. Mueller, J. A. Church, T. Glasmacher, D. Gutknecht, G. Hackman, P. G. Hansen, Z. Hu, K. L. Miller, and P. Quirin, Nucl. Instrum. Methods Phys. Res., Sect. A 466, 492 (2001).
  17. T. Motobayashi et al., Phys. Lett. B 346, 9 (1995).
  18. T. Glasmacher, Annu. Rev. Nucl. Part. Sci. 48, 1 (1998).
  19. A. Winther and K. Alder, Nucl. Phys. A319, 518 (1979).
  20. L. Gaudefroy et al., Phys. Rev. Lett. 97, 092501 (2006).
  21. K. Kaneko, Y. Sun, T. Mizusaki, and M. Hasegawa, Phys. Rev. C 83, 014320 (2011).
  22. S. Raman, C. W. Nestor, and P. Tikkanen, At. Data Nucl. Data Tables 78, 1 (2001).
  23. A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, New York, 1975), Vol. 2, p. 515.
  24. A. Arima and I. Hamamoto, Annu. Rev. Nucl. Sci. 21, 55 (1971).

About the Authors

Image of R. Winkler
Image of A. Gade
Image of T. Baugher
Image of D. Bazin
Image of B. A. Brown
Image of T. Glasmacher
Image of G. F. Grinyer
Image of R. Meharchand
Image of S. McDaniel
Image of A. Ratkiewicz
Image of D. Weisshaar

Related Articles

Synopsis: Flocks Without Memory
Biological Physics

Synopsis: Flocks Without Memory

Moving particles with no memory can group together in complex flock configurations using only instantaneous cues.   Read More »

Viewpoint: Superfluids Hit the Street
Atomic and Molecular Physics

Viewpoint: Superfluids Hit the Street

A flow pattern dubbed the von Kármán vortex street, which is renowned for its aesthetic beauty and extreme power, has been created in a superfluid. Read More »

Synopsis: Wetting Matters When Emptying a Tank
Fluid Dynamics

Synopsis: Wetting Matters When Emptying a Tank

The speed at which water drains out of a tank depends on the affinity of water with the outside surface of the orifice through which it drains.   Read More »

More Articles