1. Mass spectrometry of neutron-rich chromium isotopes into the N = 40 “island of inversion” Vladimir Manea CERN, Geneva, Switzerland D. Atanasov, K. Blaum, S. George, F. Herfurth, M. Kowalska, S. Kreim, D. Lunney, Z. Meisel, M. Mougeot, D. Neidherr, M. Rosenbusch, L. Schweikhard, A. Welker, F. Wienholtz, R. Wolf, K. Zuber Addendum to the ISOLDE and Neutron Time-of-Flight Committee IS532 experiment 1 3 February 2016

2. N = 20 “island of inversion” neutrons 20 1d 5/2 2s 1/2 1d 3/2 1d1d 2s SHO+l 2 …+l·s 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 1f1f 2p 1g 2d 5/2 2d2d 20 1d 5/2 2s 1/2 1d 3/2 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 2d 5/2 20 40 protons S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010). ENSDF database (2015). 2

3. neutrons 20 1d 5/2 2s 1/2 1d 3/2 1d1d 2s SHO+l 2 …+l·s 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 1f1f 2p 1g 2d 5/2 2d2d 20 1d 5/2 2s 1/2 1d 3/2 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 2d 5/2 20 40 protons N = 40 “island of inversion” 3 S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010). ENSDF database (2015). What does the mass surface look like?

4. Previous chromium addendum “The neutron-rich chromium isotopes in the region around N=40 are known to show an onset of collectivity based on recent data obtained, for example in Coulomb excitation experiments, providing B(E2) values and E2+ energies. Based on this experimental information it is however not evident how more accurate mass measurements will change the picture of the nuclear structure in Cr significantly. The Cr measurements are technically less challenging than that of n-rich Ca, but the masses up to 63Cr are already known even though with low precision. However, the authors have not provided reasons why to doubt the previous measurements or why the higher precision is critical. ” Minutes of 49 th INTC Meeting 11-12 February 2015 4

5. How complete is the picture of nuclear structure at N = 40? 5

6. Nuclear structure at N = 40 in the shell-model framework  E(2 + ) and B(E2) suggest an onset of collectivity at N = 40.  Large scale interaction (LNPS) devised to describe the data. 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 neutrons 28 1f 7/2 2p 3/2 1f 5/2 2p 1/2 protons … … 2d 5/2 … LNPS model space 6 S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010). ENSDF database (2015).

7.  E(2 + ) and B(E2) suggest an onset of collectivity at N = 40.  Large scale interaction (LNPS) devised to describe the data.  Authors speak of an onset of deformation. 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 neutrons 28 1f 7/2 2p 3/2 1f 5/2 2p 1/2 protons … … 2d 5/2 … LNPS model space S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010). H. L. Crawford et al., Phys. Rev. Lett. 110, 242701 (2013). ENSDF database (2015). Nuclear structure at N = 40 in the shell-model framework 7

8.  E(2 + ) and B(E2) suggest an onset of collectivity at N = 40.  Large scale interaction (LNPS) devised to describe the data.  Authors speak of an onset of deformation.  New RIKEN data published in 2015 impose a readjustment of the interaction (LNPS-m). 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 neutrons 28 1f 7/2 2p 3/2 1f 5/2 2p 1/2 protons … … 2d 5/2 … LNPS model space Nuclear structure at N = 40 in the shell-model framework 8 ENSDF database (2015). C. Santamaria et al., Phys. Rev. Lett. 115, 191501 (2015).

9.  “Islands of inversion” excellent phenomena for beyond-mean-field dynamics.  All N = 40 isotones predicted to be spherical at the mean-field level.  Excellent agreement of BMF-Gogny calculations with E(2 + ) values of N = 40 isotones for Z>28, but significant overestimation for Z<28.  Ground-state binding energies are observables more reliable to compute in mean- field-based approaches. L. Gaudefroy et al., Phys. Rev. C. 80, 064313 (2009). J.-P. Delaroche et al., Phys. Rev. C 81, 014303(2010). ENSDF database (2015). 9 Nuclear structure at N = 40 in the mean-field framework Cr Fe N = 40

10. N = 40 “island of inversion” K. Sieja, private communication. J.-P. Delaroche et al., Phys. Rev. C 81, 014303(2010). M. Wang et al., Chinese Physics C 36, 1603 (2012). 10  AME2012 trend in disagreement with all predictions.  It only confirms that LNPS model space is necessary.

11. How reliable is the knowledge of binding energies across N = 40? 11

12. Existing mass surface S. Naimi et al., Phys. Rev. C 86, 014325 (2012). M. Wang et al., Chinese Physics C 36, 1603 (2012). F. Wienholtz et al., Nature 498, 346 (2013). 12

13. 2 MeV spread Previous chromium measurements  Three measurements with the same apparatus give three different trends.  Systematic errors increase further one moves from the references. 13 X. Tu, et al., Z. Phys. A 337, 361 (1990). H. Seifert, et al., Z. Phys. A 349, 25 (1994). Y. Bai, D. J. Vieira, H. L. Seifert, J. M. Wouters, AIP Conf. Proc. 455, 90 (1998).

14.  Three measurements with the same apparatus give three different trends.  Systematic errors increase further one moves from the references.  Artefact in S 2N is expected to occur where new data set begins. 14 Previous chromium measurements X. Tu, et al., Z. Phys. A 337, 361 (1990). H. Seifert, et al., Z. Phys. A 349, 25 (1994). A. Estrade, Phys. Rev. Lett. 107, 172503 (2011) Y. Bai, D. J. Vieira, H. L. Seifert, J. M. Wouters, AIP Conf. Proc. 455, 90 (1998). M. Matos, PhD thesis, Giessen (2004)

15.  Three measurements with the same apparatus give three different trends.  Systematic errors increase further one moves from the references.  Artefact in S 2N is expected to occur where new data set begins. 15 Previous chromium measurements X. Tu, et al., Z. Phys. A 337, 361 (1990). H. Seifert, et al., Z. Phys. A 349, 25 (1994). A. Estrade, Phys. Rev. Lett. 107, 172503 (2011) Y. Bai, D. J. Vieira, H. L. Seifert, J. M. Wouters, AIP Conf. Proc. 455, 90 (1998). M. Matos, PhD thesis, Giessen (2004)

16. S. Naimi et al., Phys. Rev. C 86, 014325 (2012). M. Wang et al., Chinese Physics C 36, 1603 (2012). F. Wienholtz et al., Nature 498, 346 (2013). 16 Previous chromium measurements

17.  Three measurements with the same apparatus give three different trends.  Systematic errors increase further one moves from the references.  Artefact in S 2N is expected to occur where new data set begins.  Recent data set (NSCL2, 2015) completely off-set from old one. 17 Recent chromium measurements X. Tu, et al., Z. Phys. A 337, 361 (1990). Z. Meisel, private communication (2016). H. Seifert, et al., Z. Phys. A 349, 25 (1994). A. Estrade, Phys. Rev. Lett. 107, 172503 (2011) Y. Bai, D. J. Vieira, H. L. Seifert, J. M. Wouters, AIP Conf. Proc. 455, 90 (1998). M. Matos, PhD thesis, Giessen (2004)

18. The recent masses 18 K. Sieja, private communication (2016). J.-P. Delaroche et al., Phys. Rev. C 81, 014303(2010). M. Wang et al., Chinese Physics C 36, 1603 (2012). Z. Meisel et al., private communication (2016).  LNPS interaction modified to better describe S 2N values (LNPS’).  Precise and accurate measurements are required to compare theory to.  New Penning-trap masses would also become more reliable references for future TOF spectrometer mass measurements.

19. How feasible is the experiment? 19

20. IS532 measurements – 52,55-59 Cr  Scandium beam time, no scandium observed (even from oven).  Intense chromium beams observed: measured 52,55-59 Cr.  MR-TOF MS for beam purification or mass determination. 20

21. IS532 measurements – 52,55-59 Cr 21

22. Cr isotopes Beam-time request Isotope Half-life (ms) Target Yield † (ions/μC) MethodIon sourceShifts 60 Cr490(10) UC x 10 4 Penning trap RILIS 2 61 Cr243(9)10 3 Penning trap/ MR-TOF MS 3 62 Cr206(2)10 1 -10 2 MR-TOF MS3 63 Cr129(2)1-10MR-TOF MS5 Total shifts of radioactive beam13 22 T. D. Goodacre et al., arXiv:1512.07875 (2015) Courtesy Tania Mendonca  Factor 500 enhancement from RILIS tested with stable chromium.

23. Appendices 23

24. 24 “The largest discrepancy is found for the S 2N value of 63 Cr, which is severely overestimated. This is surprising as the present model accurately reproduces the known excitation energies of chromium isotopes, with the visible drop of the yrast 2 + excited state energies between N = 36 and N = 38, indicating that chromium isotopes undergo a shape change at N = 38. However, nothing is known about the spectroscopy of 63 Cr and the ground-state spin assignments of both 63 Cr and 61 Cr are tentative, making it difficult to evaluate whether these nuclides have the correct degree of collectivity in the present shell-model calculations. This in turn prevents us from determining why the S 2N trend from this experiment does not drop smoothly between N = 38 and N = 39, as expected in the deformation region. In spite of this discrepancy, the LNPS' shell-model trend points clearly to the development of collectivity around N = 40 and predicts continuation of the deformation onset towards higher neutron numbers.” Z. Meisel et al., private communication (2016).

25. Chromium masses 14 25

26. Chromium binding energies S. Naimi et al., Phys. Rev. C 86, 014325 (2012). M. Wang et al., Chinese Physics C 36, 1603 (2012). F. Wienholtz et al., Nature 498, 346 (2013). 26

27. Structure between 48 Ca and 78 Ni 1f 7/2 protons 1f 7/2 28 50 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 neutrons 28 1f 7/2 2p 3/2 1f 5/2 2p 1/2 protons … … G. Audi et al., Chinese Phys. C 36, 1157 (2012). ENSDF database (2015). D. Steppenbeck, Nature 502, 207 (2013). 68 Ni looks neutron-magic 64 Cr looks deformed 27 What does the mass surface look like?

28.  E(2 + ) and B(E2) suggest an onset of collectivity at N = 40.  Large scale interaction (LNPS) devised to describe the data.  Authors speak of an onset of deformation.  E(4 + )/E(2 + ) show that only the chromium chain has the expected behavior for an onset of collectivity. S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010). H. L. Crawford et al., Phys. Rev. Lett. 110, 242701 (2013). ENSDF database (2015). Nuclear structure at N = 40 in the shell-model framework 28

29.  New RIKEN data published in 2015.  LNPS interaction required readjustment for improving the description of the new data (now LNPS-m).  Interaction not fully constrained until other type of data is used for comparison. Nuclear structure at N = 40 in the shell-model framework ENSDF database (2015). C. Santamaria et al., Phys. Rev. Lett. 115, 191501 (2015). 29